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EMERGE. 多属性分析. Hampson-Russell Software Services Ltd. EMERGE WORKSHOP. 理论和练习. 2002 年3月21日. EMERGE 课程目录. EMERGE 简介 3 练习 1: 建立 EMERGE 工区 7 地震属性 32 交绘图 54 练习2 : 单属性列表 59 多属性分析 69 地震属性的有效性 76 练习 3: 多属性列表 82 褶积因子的运用 89 练习 4: 褶积因子 94

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slide1

EMERGE

多属性分析

slide2

Hampson-Russell Software Services Ltd.

EMERGE

WORKSHOP

理论和练习

2002年3月21日

emerge
EMERGE 课程目录
  • EMERGE简介 3
  • 练习 1: 建立EMERGE工区 7
  • 地震属性 32
  • 交绘图 54
  • 练习2: 单属性列表 59
  • 多属性分析 69
  • 地震属性的有效性 76
  • 练习3: 多属性列表 82
  • 褶积因子的运用 89
  • 练习 4: 褶积因子 94
  • 练习 5: 三维数据体的处理99
  • 神经网络在EMERGE中的应用 110
  • 练习 6: 预测孔隙度井 140
  • 神经网络的学习 162
  • 练习7: 使用神经网络 177
  • 练习8: 从井预测井 200
  • 总结 222
slide4

EMERGE简介

EMERGE程序的目标:

  • EMERGE 是一个分析测井曲线和地震资料的程序.
  • EMERGE is a program that analyzes well log and seismic data.
  • 它能建立在井位处井与地震数据之间的关系.
  • It finds a relationship between the log and seismic data at the well locations.
  • 它运用这种关系去预测或者去估算整个地震体范围内的井的各种性质.
  • It uses this relationship to “predict” or estimate a volume of the log property at all locations of the seismic volume.

EMERGE所用的数据:

  • 地震体(通常是 3D).
  • 与地震体相约束的一系列井资料.
  • 每口井包含一个即将被预测的目标曲线, 例如孔隙度曲线.
  • 每口井包含深时转换的信息, 通常都是经过check-shot 校正后的声波测井曲线.
  • Each well also contains the information for converting from depth to time, usually in the form of a check-shot corrected sonic log.
  • (可选项): 3维地震体的一个或多个外在属性.
  • One or more “external” attributes in the form of seismic 3D volumes.
slide5

EMERGE简介

首先将井资料加载到GEOVIEW数据库中:

The log data must be inserted into the GEOVIEW database:

下图显示出单井的测井曲线:

This display shows the data for a single well:

slide6

EMERGE简介

从理论上讲, 任意类的井的性质都可以是ENERGE预测的目标. Theoretically, any type of log property may be used as a target for EMERGE.

实际上, 以下类型的测井曲线都已被成功地预测:

Practically, the following types have been successfully predicted:

  • P波速度 (P-wave velocity)
  • 孔隙度 (Porosity)
  • 密度 (Density
  • 伽玛测井(Gamma-ray)
  • 水饱和度*Water saturation)
  • 岩性井(Lithology logs)

唯一的条件就是每口井都必须存在将要进行预测的测井曲线.

The only requirement is that an example of the target log must exist within each of the wells.

因为ENERGE假设目标曲线是无噪的, 所以在用ENERGE之前,编辑目标井是非常重要的.

Since EMERGE assumes that the target log is noise-free, it is usually important to edit the target logs before applying EMERGE.

因为ENERGE要将目标曲线与地震资料相关, 所以正确的深时转换关系是很关键的. 基于此, check-shot校正和手动校正是必须的. Since EMERGE will be correlating the target logs with seismic data, the proper depth-to-time conversion is critical. For this reason, check-shot corrections and manual correlation are usually necessary.

slide7

EMERGE简介

EMERGE可以当作常规迭后反演的延伸.EMERGE can be thought of as an extension of conventional post-stack inversion:

1 emerge
练习 1: 建立EMERGE工区

从地震属性中估计P波速度

Estimating P-Wave Velocity from Seismic Attributes

现在来做EMERGE的例子. 本例中, 我们将从地震属性来估算P波速度.

We are now ready to do the first EMERGE example. In this example, we will estimate p-wave or sonic log velocity from seismic attributes.

数据体包括以下各项:The data set consists of the following:

  • SEGY文件seismic.sgy为三维迭后数据体文件.
  • A SEGY file, seismic.sgy, which is a 3D post-stack data set.
  • SEGY文件 inversion.sgy , 它是对输入的地震资料进行反演后的结果文件.
  • A SEGY file, inversion.sgy, which is the 3D result of performing inversion on the input seismic data.
  • 12口井用于约束以上两个SEGY文件. 每口井都包括声波测井曲线和check-shot文件.
  • 12wells that tie the two SEGY files. Each of these wells contains a sonic log and a check-shot file.

该练习的目的是通过地震资料和反演结果来预测三维地震体的新的声波测井曲线.

The objective of this analysis is to predict new sonic logs for the entire 3D survey, using the seismic data and the inversion result.

slide9

数据加载

如果GEOVIEW程序没有启动, 则键入geoview启动该程序. 主窗口如下:

If the GEOVIEW program has not been started, start it now by typing geoview in the command window. The GEOVIEW main window now appears:

点击Database/Open加载本次练习所用的井的数据库. 菜单如下:

To load the complete well log database for this exercise, click on Database/Open. The menu will look like this:

slide10

数据加载

数据库的扩展名为wdb. 选择名为guide.wbd的数据库, 点击OK. GEOVIEW界面如下:

A database is identified by the extension wdb. Select the database guide.wdb as shown above and click on OK. Your GEOVIEW window will now look like this:

如你所见, 12口井都被加载到GEOVIEW中.

As you can see, all 12 wells have now been loaded.

slide11

启动GEOVIEW

井的数据库已经加载到GEOVIEW中了, 点击EMERGE按钮, 启动EMERGE程序. 下面的菜单出现了.

Now that the logs have been loaded into GEOVIEW, we are ready to start the EMERGE program. To do this, click on the EMERGE button on the GEOVIEW main window. The following menu will appear:

点击OK开始一个新的工区. 如下所示, 填入文件名称后, 点击OK(注意该工区命名为velocity).

Click on OK to Start a New Project. The File Selection window now appears. Fill it in as shown below and click on OK (note that we are calling the new project velocity):

slide12

启动EMERGE

EMERGE主窗口显示出来(如下):

The main window now appears:

现在来回顾一下EMERGE程序的分析过程. 我们希望用地震数据来预测三维地震体任一处的新的声波测井曲线.

Let us now review the EMERGE process. We wish to use the seismic data to “predict” new sonic logs at every location in the 3D seismic volume.

我们搜集一些井位附近的样品数据, 极力寻找出井位附近的地震数据与测井资料之间的一种关系, 这一步叫“学习” (“training”). “training”完成后, 假设这样推导出的关系对整个地震体来说都是成立的, 然后将该关系应用到整个3维数据体.

To do this, we will collect some sample data around the well locations and find a relationship between the seismic at those locations and the measured logs. This step is called “training”. After the training is completed, we will assume that the derived relationship is valid for the entire 3D volume, and apply that relationship to the entire 3D data set.

slide13

启动EMERGE

点击Wells/Read From Database从GEOVIEW中将声波测井曲线读入EMERGE, 开始“training”. 菜单如下:

To start the training process, we need to read the sonic logs from GEOVIEW into the EMERGE main window. To do this, click on Wells/Read From Database. The following menu appears:

该项菜单有多页, 可以点击Next或Back来看这些, 只有将要求的各项填好后才可以点击OK.

Notice that this menu has a series of pages, which can be viewed by using the Next >> and << Back buttons. You will not be able to click on OK until the required pages have been filled in.

首页是关于井位的菜单, 在该页上选择那口井要用于EMERGE分析. 在上面看到的菜单中, guide数据库的所有井都列在左列. 我们希望用全部的井资料, 所以点击Add all.

The first page is the Wells page, which allows us to select which wells to include in the EMERGE analysis. As you can see above, the left column contains all the wells in the guide database. We wish to use all of them in the training, so click on Add all >>.

slide14

启动EMERGE

菜单如下: The menu now looks like this:

点击Next, 下一页显示如下: Now click on the Next >> button at the bottom of the menu. The new page will now appear:

slide15

启动EMERGE

该页上, 我们要明确数据库中的那条测井曲线是将要预测的, 即“目标体”. 本例中, 如上所示, 我们将要预测P波即声波测井曲线. 需要强调的是, 尽管井曲线是深度域, 处理却要在时间域内进行. 这是因为地震资料来自于时间域.

This page is used to tell EMERGE which of the logs in the database is the one that we are trying to predict, i.e., which one is the “Target”. For this guide example, we wish to predict the P-wave or sonic log, as shown above. Also, we are specifying that, although the log is measured in depth, the analysis (Processing Domain) will be done in time. This is because the seismic data is measured in time.

所以我们需要指定适当的采样率, 而EMERGE恰好能够进行正确的深时转换. 注意: 该反演要用到声波测井的check-shot 校正.

We need to specify the sample rate correctly (Processing Sample Rate), so that EMERGE can do the depth-to-time conversion properly. Note that the check-shot corrected sonic log will be used for this conversion.点击Next, 显示下一页: Click on the Next >> button at the bottom of the menu. The new page will now appear:

slide16

启动EMERGE

通过学习(training)那些已经加载到GEOVIEW中的井曲线的顶部, Tops 菜单确定分析窗口内的各项参数.

The Tops page allows you to specify the analysis window for training in terms of the tops that have already been entered into the GEOVIEW database.

本工区中, 有四个层位: viking, mann, ch_top, and miss . 如上所示, 分析窗口以viking 开始, 以miss结束. 当然了, 分析窗口可以改变.

In this project, we have entered four tops: viking, mann, ch_top, and miss. As shown above, select the viking as the start of the analysis window and the miss as the end of the analysis window. Note that the analysis window can be changed later if desired.

之后, OK键被激活, 表明EMERGE已有足够的井来进行处理. 点击OK, 又一个菜单显示出来:

At this point, the OK button is enabled, indicating that EMERGE has enough data from the GEOVIEW database to proceed.

Now that the entire menu has been filled in, click on OK. One more confirmation menu appears:

slide17

Starting EMERGE

对每个所选择的井位而言, 它们都有两条P波测井曲线, 其一是原始曲线, 其二是经过check-shot后的井曲线。 系统默认最近创建的井曲线都要用于处理. 表中显示的是经过check-shot校正后的井. 点击任一口井的“P-wave CheckShotCorrected” 这一项, 会产生一个下拉菜单, 我们可以选择所需要的井曲线. 此处, 接受默认选项, 点击OK。 EMERGE主窗口如下所示:

This menu appears because for each of the selected wells, there are actually two P-wave logs. One is the original log and the second is the check shot corrected log. By default, the most recently created log will be used. This is the check shot corrected log, which is shown in the table. If you wished to use the other log, clicking on the words P-wave CheckShotCorrected for any of the wells will produce a pullDown menu allowing you to select the desired log. For our case, accept the defaults by clicking on Ok on this menu.The EMERGE main window now looks like this:

EMERGE窗口显示出各个井的目标井曲线. 棕色的横线表示以前选择的时窗. 后面我们会说明如何改变这个时窗. 移动滚动条, 可以看到所有的井曲线.

The EMERGE window now shows the target log for each of the wells. The brown horizontal lines indicate the analysis window selected in the previous menu. We will examine how to change that later. By moving the horizontal scroll bar, you can see all the remaining wells.

slide18

启动 EMERGE

现在我们读入井位附近的地震数据. 如前面概论中所讲, 地震数据包括两个SEGY文件: seismic.sgy and inversion.sgy.

Now we wish to read in the seismic data near the well locations. As mentioned at the beginning of the guide, the seismic data actually consists of two SEGY files, seismic.sgy and inversion.sgy.

点击Seismic/Add Seismic Input / From File 读入地震数据,界面如下:Now we will read in the seismic training data. To do this click on Seismic/Add Seismic Input / From File. The following menu appears:

slide19

启动EMERGE

在文件列表中选择文件seismic.sgy, 然后点击Add>>, 使之添加到右列(如下):

On the file selection menu, select the file seismic.sgy and click Add >> to make it appear on the right column as shown:

点击Next>>. 下页是指定SEGY文件的格式和几何结构的。

Click on Next >> on this menu. The next menus are used to specify the format and geometry of the SEGY file.

slide20

启动EMERGE

界面如此:The next menu that appears is this one:

我们必须说明加载的三维体的道头是否有Inline/Xline数或者是否有 X & Y坐标。 这意味着设置地震道的关键是设为“CDP(矩形)”, 即, 地震数据是否要设置成均匀的inlines和crosslines.

On this page, we must tell the program that we are loading a 3D volume that does not have either Inline/Xline numbers or X & Y coordinates in the trace headers. This means that the primary key for assigning traces will be set to “CDP(Rectangular)”, i.e., the seismic has a uniform series of inlines and crosslines.

slide21

Starting EMERGE

点击Next >> , 有以下界面:

Click on Next >> to get this menu:

在Type of Data选项中, 选择属性类型. 点击Type of Data, 选择“Raw Seismic”, 该属性的名字也将自动设置为Raw Seismic.

In the box that defines the Type of Data, we must select the attribute type. When the menu first appears, it shows “<Unknown>”. Click in this box, and choose “Raw Seismic”, as shown. The attribute name will also be set to Raw Seismic automatically.

slide22

启动EMERGE

点击Next >>, 显示如下:

该菜单用来设置SEGY格式的属性. 因为地震数据文件不包含inline/crossline 数和X & Y坐标, 菜单上的许多参数都不被激活.

This menu allows you to set attributes of the SEGY format. Since we have told the program that the seismic file does not contain inline/crossline numbers or X & Y coordinates, many of the parameters on this page are not active.

点击最后一个Next后, 会看到对话框, 指明需要浏览的数据文件, 此时点击Yes, 进行文件浏览。

Click on Next >> one last time. You will see a dialog that indicates that the data file needs to be scanned. Click on Yes on this dialog to proceed with the scanning.

slide23

启动EMERGE

本页菜单中,我们来指定三维地震体的几何结构。 在此, 我们仅仅改变其Cross-line数。 按照上示的菜单填好, 点击Ok. 显示出两个窗口。 其一为表格, 显示出井的位置及其与地震道的相关程度。

On this menu, we specify the geometry of the 3D volume. Note that the only change we have made is to set the Number of Cross-lines.

Fill in the menu as shown above and click on Ok.

Two new windows will now appear. One window shows a table, indicating how the wells are correlated with the seismic data:

slide24

启动EMERGE

其二, 为地震道:

The second window shows the seismic data:

因为GEOVIEW数据库中的X-Y 坐标处理得当, 井与地震道的相关正确无误。 对于其它的数据体,则需要改变列表中的Inline 和 Xline。 点击Ok。

For this data set, the correlation is correct because the X-Y locations were entered appropriately in the GEOVIEW database. For other data sets, you may need to modify the Inline and Xline columns of the table. Now click on Ok to get the next menu.

slide25

启动EMERGE

该菜单用来抽取井位(该井位用于验证)附近的地震道。半径取为1。即, 组合地震道是井位附近一个Inline和 Xline的平均道。 此处取第9道为例. “Distance”是该点到各井位的地震道的平均, 我们可以改变该值。 按上示菜单填写, 点击Ok.

This menu tells the EMERGE program how to extract the trace at each well location that is used in the training process. We will use a Neighborhood radius of 1, as shown. This means that the composite trace will be the average of those traces within 1 Inline or Xline of the well location. This is an average of 9 traces. Alternatively, you could modify the Capture option to “Distance”, which will average all traces within a specified distance from each well. Make sure that the parameters on the menu are set as shown above, then click on Ok.

slide26

启动EMERGE

从SEGY文件中抽取每口井的综合记录。 EMERGE主窗口显示出已加载的数据:

The composite trace at each well location will be extracted from the SEGY volume and the EMERGE main window will be modified to show the added data:

slide27

启动 EMERGE

点击 Seismic / Add Seismic Input / From File,加载来自SEGY文件inversion.sgy的外部属性。

The final piece of data to add is an external attribute from the SEGY file inversion.sgy. To do this, click on Seismic / Add Seismic Input / From File. Fill out the next menu as follows:

以下几个菜单等同于加载Raw Seismic文件时的操作.

The next series of menus is identical to those used in adding the Raw Seismic.

slide28

启动EMERGE

指定一般格式:

该属性命名为Inversion Result,类型为外部属性。

We must tell EMERGE that this is an External Attribute with the name Inversion Result.

点击Next. 直到最后点击Yes.

Click on Next >> on this menu and the one that follows. When you see the dialog that says that the file must be scanned, click on Yes.

slide29

启动EMERGE

几何结构如下: Describe the geometry:

点击Ok后,窗口会显示出彩色的地震反演数据。

When you click Ok on this menu, two things will happen. First, the seismic display window will be updated to show the inversion data in color:

slide30

Starting EMERGE

同时, 地震道提取菜单重新显示出来, 允许指定用于提取外部属性的参数:

The second thing that will happen is that the Trace Extraction menu will appear again to allow you to specify parameters for extracting the External Attribute trace:

点击Ok,提取单道, 该道为井位附近一个 Inline 或 Xline距离内的地震道的平均。EMERGE主菜单会包括该道数据。

Once again, click on Ok on this menu to extract a single trace, which is the average of those traces within one Inline or Xline of the well location. The EMERGE main window will be updated to include this new data.

slide31

启动EMERGE

EMERGE 主窗口显示出对每口井的分析;红色代表目标井曲线; 黑色代表单地震道; 蓝色代表外部属性. 分析时窗用棕色的横线表示. 注意: 每口井的时窗可能都不相同。

The EMERGE main window shows the analysis data for each well: the target log in red, the single seismic trace in black, and the external attribute in blue. The analysis window is also shown by brown horizontal bars on each log. Note that this window may be different for each well.

slide32

启动EMERGE

点击Wells / Set Analysis Windows , 通过下表来验证(可能会改变)分析时窗:

To examine (and possibly change) the analysis window, click on to get the following table:

如果我们对分析时窗感到满意的话, 点击Cancel .(练习1毕)

Since we are happy with the analysis windows as shown, click on Cancel to remove this menu.

(End of Exercise 1)

slide33
地震属性

地震属性通常时地震道的线性转化。

are transforms, generally non-linear, of a seismic trace.

地震属性的两种类型: Two types of attributes:

基于采样的:Sample-based: calculated from the trace on a sample-by sample basis.

举例: 振幅包络 Example: amplitude envelope.

基于层位: 由两个层位的平均值计算出来

Horizon-based: calculated as averages between two horizons.

举例: 两层位置之间的空隙率

Example: average porosity between two horizons.

对EMERGE而言, 所有的属性都是基于采样的。

For EMERGE, all attributes must be sample-based.

地震属性如下: Examples of seismic attributes :

slide34

地震属性

EMERGE 能够计算下列的内部属性:

EMERGE can calculate the following attributes internally:

振幅包络 Amplitude Envelope

振幅加权cosine振相 Amplitude Weighted Cosine Phase

振幅加权频率 Amplitude Weighted Frequency

振幅加权相位 Amplitude Weighted Phase

平均频率 Average Frequency

视极性 Apparent Polarity

瞬时Cosine相位 Cosine Instantaneous Phase

导数 Derivative

瞬时振幅的导数 Derivative Instantaneous Amplitude

主频 Dominant Frequency

滤波切片 Filter Slices

瞬时频率 Instantaneous Frequency

瞬时相位 Instantaneous Phase

积分 Integrate

绝对振幅积分 Integrated Absolute Amplitude

二阶导数 Second Derivative

瞬时振幅的二阶导数 Second Derivative Instantaneous Amplitude

时间 Time

slide35

地震属性

EMERGE可以输入外部属性。 它们不能通过内部属性计算出来, 因为:

EMERGE can also import external attributes. These are seismic attributes that cannot be calculated internally because:

比如: 相关性。They are proprietary – e.g. : coherency

太复杂, 如地震反演, AVO属性, 等等。

They are too complicated – e.g. : seismic inversion, AVO attributes, etc.

内部属性可以归为以下几类:The internal attributes can be grouped into the following categories:

瞬时属性 Instantaneous attributes

时频属性 Windowed frequency attributes

滤波切片 Filter slices

导数属性 Derivative attributes

积分属性 Integrated attributes

时间(线性渐变)Time (a linear ramp)

以地震数据为例,现在来关注一下关于群属性的理论。

We will now look at the theory of each group of attributes with seismic examples.

slide36

h(t)

A(t)

Hilbert

Transform

f(t)

Seismic

s(t)

Time

瞬时属性

Taner, et al首先提出瞬时属性(Geophysics, June, 1979). 他们从复地震道C(t)算起。 C(t) 由地震道s(t)和其希尔伯特变换 h(t)(希尔伯特变换即对地震道作90° 相 移 ). 如下所示, 将复数地震道写成极坐标形式, 图中标示出了两个基本属性: 振幅包络A(t) (也称为瞬时振幅)和瞬时相位f(t).

Instantaneous attributes were first described in the classic s(t), paper by (Geophysics, June, 1979). They are computed from the complex trace, C(t), which is composed of the seismic trace, s(t), and its Hilbert transform, h(t), which is like a 90° phase shifted trace. Writing the complex trace in polar form, as shown below, gives us the two basic attributes: the amplitude envelope, A(t), and instantaneous phase, f(t). (Note that the term instantaneous amplitude is used synonymously with amplitude envelope.)

slide37

瞬时属性

Instantaneous Attributes

第三个属性, 瞬时频率是瞬时相位对时间的导数. 方程式如下:

A third basic attribute is the instantaneous frequency, which is the time derivative of the instantaneous phase. In equation form, we can write:

另一个瞬时属性则是前面三个基本属性的结合.

The other instantaneous attributes in EMERGE are combinations of the three basic attributes, as shown below:

视极性属性便是由振幅包络乘以该地震道的波峰的极性符号而得. 用于该波峰相邻的波谷之间的一段地震道.

Finally, the apparent polarity attribute is the amplitude envelope multiplied by the sign of the seismic sample at its peak value, applied in a segment between the troughs on either side of this peak.

slide38

瞬时属性

我们来看某三维体inline95处各个瞬时属性的图像. 08-08井也标在其上.

Now, let’s look at examples of each of the instantaneous attributes applied to inline 95 from the input 3D volume. The line is shown below in colour amplitude form with wiggle trace overlay. The sonic log from well 08-08 has also been overlain.

slide39

瞬时属性

inline 95处的瞬时相位Instantaneous phase of inline 95.

inline 95处的振幅包络

Amplitude envelope of inline 95.

slide40

瞬时属性

inline 95 处的Cosine瞬时相位

Cosine of instantaneous phase of inline 95.

inline 95 处振幅的加权cosine相位

Amplitude weighted cosine phase of inline 95.

slide41

瞬时属性

inline 95处振幅的加权相位

Amplitude weighted phase of inline 95

inline 95处视极性

Apparent polarity of inline 95.

slide42

瞬时属性

inline 95处的瞬时相位

Instantaneous frequency of inline 95.

inline 95处振幅的加权频率

Amplitude weighted frequency of inline 95.

slide43
时窗频率属性

EMERGE的另一类属是基于地震道的时窗频率分析. 在此过程中, 系统默认在64倍采样时窗中对每个地震道进行傅里叶变换.

A second set of attributes in EMERGE is based on a windowed frequency analysis of the seismic trace. In this process, the Fourier transform of each seismic trace is taken over a 64 sample window ( the default).

在本窗口中, 选择好平均频率振幅或主导频率振幅, 并将该值赋予时窗中心点.

From this window, either the average frequency amplitude or the dominant frequency amplitude is chosen, and this value is placed at the center of the window.

随后, 设置32倍采样时窗, 计算此时的频率振幅. 注意: 在属性参数菜单中可以修改采样时窗的默认值, 如下所示:

A new window is then chosen 32 samples later (the default), and the new frequency attribute is calculated, and so on. Note that the defaults can be changed in the Attribute/Attribute Parameters menu, shown below.

slide44

时窗频率属性

inline 95 处的主导频率

Dominant frequency of inline 95.

inline 95 处的平均频率

Average frequency of inline 95.

filter slice attributes
滤波切片属性Filter Slice Attributes

第三类属性为地震道的窄频滤波切片. 以下六种为通常所用:

A third set of attributes in EMERGE is comprised of narrow band filter slices of the seismic traces. The following 6 slices are used:

5/10 – 15 20 Hz

15/20 – 25/30 Hz

25/30 – 35/40 Hz

35/40 – 45/50 Hz

45/50 – 55/60 Hz

55/60 – 65/70 Hz

下面分别显示最低频和最高频切片.

The figures on the next slide show the lowest and highest frequency slices.

slide46

Filter Slice Attributes

inline 95处5/10 – 15/20 Hz滤波切片

5/10 – 15/20 Hz filter slice of inline 95.

inline 95处55/60 – 65/70Hz滤波切片

55/60 – 65/70 Hz filter slice of inline 95.

derivative attributes
导数属性Derivative Attributes

EMERGE中第四类属性是基于地震道或相应的振幅包络(亦称瞬时振幅)的一阶或二阶导数.

A fourth set of attributes in EMERGE is based on the first or second derivative of the seismic trace or its amplitude envelope (or instantaneous amplitude, which you recall is synonymous with amplitude envelope). 通过以下的公式来计算导数:

The derivatives are calculated in the following way, where si = the ith seismic or amplitude envelope sample, d1i = the ith first derivative, d2i = the ith second derivative, and Dt = the sample rate:

其中, si是第i个地震道或振幅包络; d1i为第i个一阶导数; d2i为第i个二阶导数; Dt为采样间隔.

以inline95处的地震道和振幅包络为例:

The derivative examples on the next two slides are from inline 95.

slide48

导数属性

inline 95 处的地震道的导数Derivative of inline 95

inline 95 处的振幅包络的导数

Derivative of amplitude envelope of inline 95.

slide49

导数属性

Inline95处地震道的二阶导数

Second derivative of inline 95.

Inline95处的振幅包络的二阶导数

Second derivative of amplitude envelope of inline 95.

slide50
积分属性

第五类属性基于地震道积分或相应的振幅包络(瞬时振幅)积分. 通过以下方程计算:

A fifth set of attributes in EMERGE is based on the integrated seismic trace or its amplitude envelope (or instantaneous amplitude, which you recall is synonymous with amplitude envelope). The integrated values are calculated in the following way, where si = the ith seismic or amplitude envelope sample, Ii = the integrated value. Note that this is a running sum.

其中, si 代表第i个地震道或振幅包络,Ii代表 相应的积分值.

最后, 地震道积分要对默认的50个点进行平滑滤波以便去除反演结果的低频趋势.

At the end of the running sum the integrated seismic trace is filtered by running a default 50 point smoother along it, and removing the resulting low frequency trend.

将振幅包络除以最大最小采样数之差, 使之归一化. 同样, 默认选项均可在属性参数菜单中修改.

The integrated amplitude envelope is normalized by dividing by the difference between the minimum and maximum samples over the total number of samples. Note that the defaults can be changed in the Attribute / Attribute Parameters menu, shown earlier.

以inline 95处的积分为例:

The integrated examples on the next slide are from inline 95.

slide51

积分属性

inline 95 处的地震道积分Integrated traces of inline 95.

inline 95处的振幅包络积分

Integrat ed amplitude envelope of inline 95.

slide52
时间属性

最后谈谈时间属性. 它只是将地震道的时间做渐变, 以延续所计算的储层参数的变化趋势.

The last attribute is the time attribute. This is simply the time value of the seismic trace, and thus forms a “ramp” function that can add a trend to the computed reservoir parameter.

时间属性的图片如下:

Here is a plot of the time attribute.

Inline95处的时间属性(对于该地震体的任一测线时间属性看起来似乎都是相同的).

Time attribute of inline 95 (Note: it would look the same for any line in the volume!).

slide53

地震属性

EMERGE 力求找到目标曲线与地震道的各个属性之间的关系. EMERGE actually tries to find a relationship between the target log and a combination of attributes of the seismic trace.

单井的所有属性如下: All attributes for a single well:

slide54
交汇图

目标曲线与任一地震属性的交汇图能够标识二者的相关性.

One way of measuring the correlation between the target data and an attribute is to cross plot the two.

下图给出了目标曲线, 地震道以及一个外部属性:

This Display shows the target log, a seismic trace, and an external attribute:

slide55

交汇图

下面是纵轴的目标曲线(P波波速)与横轴的外部属性(反演结果)的交汇图.

This is a cross plot, showing the target, P-wave, on the vertical axis against a particular attribute.

slide56

交汇图

回归分析方程如下:

The regression line has the form:

y = a + b*x

该方程使得预测目标的误差达到最小:

This line minimizes the total prediction error:

协方差定义如下:The covariance is defined as:

其中, 平均值 where the mean is:

slide57

交汇图

归一化的协方差定义如下:

The normalized covariance is defined as:

通过应用回归方程来预测目标属性:

Applying the regression line gives a prediction of the target attribute:

预测误差为目标测井曲线的真实值与预测值之间的均方根差.

The prediction error is the RMS difference between the actual target log and the predicted target log.

slide58

交汇图

对目标变量或地震属性变量(同时或只对其一)进行非线性的变换运算, 有时可以提高其相关性.

The correlation can sometimes be improved by applying a non-linear transform to either the target variable or the attribute variable or both:

2 the single attribute list
练习2: 单属性 The Single-Attribute List

本练习中, 我们将要针对练习1中加载的数据做交汇图, 生成单属性列表.

In this exercise, we will perform cross plotting on the data loaded in Exercise 1, and generate the Single-Attribute List.

交汇图绘制:

首先, 点击Display/Well来看01-08井的内部属性.

First let’s look at some of the internal attributes for a particular well. Click on Display/Well to get the following menu:

如上图所示选择属性类别. 我们可以看到可利用的内部属性全部显示在左列, 而我们所选择的属性显示在右边列表.

Fill in the menu as shown above. Note that the list of all available internal attributes is shown on the left, while we have chosen to display one particular attribute on the right.

slide60

点击Ok得到下图:Click on Ok to get this plot:

练习2: 单属性表

点击Display / Crossplot 查看该属性与目标曲线的相关程度.

To see how well any attribute correlates with the target logs, click on Display / Crossplot to get this menu:

exercise 2 the single attribute list
Exercise 2: The Single-Attribute List

这个菜单能够创建目标曲线与任一个其他的内部或外部属性的交汇图. 我们可以用单井或所有的井. 另外, 还可以对目标曲线和所用的属性进行一系列非线性变换.

Note that this menu will create a cross plot between the target log and any other internal or external attribute. We may use a single well or all the wells (by clicking on Use all the wells). In addition, we may apply one of a series of non-linear transforms to the target and/or to the attribute.

填好上示菜单, 点击Ok, 下面的交汇图显示出来.

Fill in the menu as shown above and click Ok. The cross plot appears:

该交汇图用了分析时窗内所有井的全部点. 纵坐标为目标声波测井曲线, 横坐标为一外部地震属性, 即反演结果. 该图的上部分显示了回归方程的斜率和截距以及归一化的相关系数. 该相关系数是衡量用该地震属性去预测目标曲线的合适程度.

The cross plot has used all points for all wells within the analysis windows. The vertical axis is the target sonic log value, and the horizontal axis is the selected attribute, Inversion Result. A regression curve has been fit through the points and the normalized correlation value of 0.47 has been printed at the top of the display. The normalized correlation is a measure of how useful this attribute is in predicting the target log.

slide62

单属性分析

点击Attribute / Create Single Attribute List , 计算所有地震属性的相关系数, 并进行排序.

Now let’s calculate the correlation coefficients for all the attributes and rank their values. Click on Attribute / Create Single Attribute List to get this menu:

左上角显示出工区中的所有井位. 右上角显示出分析中将要用的井. 系统默认使用所有的井.

The upper left box shows all the wells in the EMERGE project. The upper right box shows the wells to be used in performing this analysis. The default is to use all the wells.

slide63

单属性分析

中间左边显示出所有的地震属性, 包括该工区内的内部属性和外部属性. 中间右边显示出属性分析中欲用的属性. 如要用全部属性, 则点击Add all>>. 当然, 我们也可以选择是否要对目标曲线和地震属性做非线性变换以提高其相关程度.

The center left box shows all the attributes (internal and external) in the project. The center right box shows the attributes to be used in this analysis. To use all the attributes, click on Add all >> as shown above. Note that we have also selected to test whether non-linear transforms applied to either the target log or to the external attributes will enhance the correlation.之后, 点击Ok, 结果显示如下:

When the menu has been filled in as shown above, click on Ok and the resulting table will be displayed:

从上表中我们看到使用外部属性“反演结果”的误差最小, 可达298.76. 有时, 应用目标曲线和地震道之间的剩余时移以及check-shot校正都能够提高反演的相关程度, 尽可能减小误差.

We note that the minimum error of 298.76 results from taking the inverse of the external attribute Inversion Result. Sometimes this can be improved by applying residual time-shifts between the target logs and the seismic data, in addition to the check shot corrections.

slide64

单属性分析

这一点可以点击Wells / Shift Target Logs来验证一下:

One way to check this is to click on Wells / Shift Target Logs to get this menu:

该菜单允许输入每条目标曲线的时移. 点击Optimize按钮, 我们可以得到时移.

This menu allows you to enter time-shifts to be applied to each of the target logs. Of course, we don’t know what numbers to enter. To estimate these shifts, click on Optimize to get this menu:

slide65

单属性分析

你可以在优化时移菜单中选择变化的类型, 此处, 我们选择单属性变换, 1/inversion result.

The Optimize Shifts menu allows you to select any one transform – in this case, the single attribute transform: 1/Inversion Result.

系统会对每口井施行一系列时移来找出最优化的时移, 使得相关系数尽可能达到最大. 此处选择的时移为10s.

The program then tries a series of time shifts for each well to find the set of shifts that will maximize the correlation, subject to a Maximum Shift of 10 milliseconds.

选好之后,点击Ok. 则下面的时移菜单就会显示出最佳的时移.

With the menu set as shown above, click on Ok. The Shift Logs menu now shows the suggested shifts:

默认这些结果, 点击Ok. EMERGE主窗口会更新这些经过时移的井位.

To accept these shifts, click on Ok. The EMERGE main window will be updated to show the shifted logs.

点击Attribute / Create Single Attribute List重新计算单属性变换.

Now recalculate the single attribute transforms by clicking on Attribute / Create Single Attribute List.

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单属性分析

采用系统默认的值, 结果如下:

Using the default values on this menu, the new list will look like this:

现在我们可以看到目标曲线的平方根与1/(Inversion Result)之间的误差最小, 为289.75.

Note that the minimum error has now decreased to 289.75, corresponding to predicting the square root of the target log with the attribute 1/(Inversion Result).

单属性列表显示出每个属性的交汇图结果, 并且按照误差从小到大排序.

The Single Attribute List shows the result of cross-plotting each attribute and ranking the result by increasing error.

如果你选中某个属性比如(P-wave)的平方根 & 1/Inversion Result)然后点击Cross Plot按钮,就会显示出相应的交汇图.

If you select any particular attribute name by clicking on it (say,Sqrt(P-wave) & 1/Inversion Result) and pressing the Cross Plot button at the bottom of the table, the cross plot will be displayed.

slide67

单属性分析

当你选中某个属性如1/Inversion Result, 然后点击Apply按钮, 就会看到以下所示的界面:

If you select any particular attribute name by clicking on it (1/Inversion Result, for example) and pressing the Apply button at the bottom of the table, the following display will appear:

上图显示出用指定的属性(1/inversion result)来预测得到的目标曲线和真实的目标曲线, 还有回归方程的截距和斜率. 点击窗口顶部的View / Zoom, 用鼠标分别对三口井选取时窗附近一个区域, 则会看到更清楚的曲线.

This display shows the target log for each well along with the “predicted” log using the selected attribute and the derived regression curve. To get a closer look at the result, click on View / Zoom at the top of this window, and use the mouse to select a rectangle around the analysis window for the first three wells.

slide68

单属性分析

结果如下: The resulting plot will look like this:

图形显示出真实的目标曲线(黑色表示)与由属性预测得到的目标曲线(红色表示). 上部的Average Error(平均误差)是真实的测井曲线值与所预测的值的均方根差.

The plot shows the target logs in black with the “predicted” logs in red. The Average Error reported at the top of the plot is the root mean-square difference between the target log values and the predicted values.

注意到对Inversion Result应用回归方程会产生与真实的目标曲线相一致的变化趋势, 但是不能够准确地预测它的细微的特征.

Notice that applying a regression curve to the Inversion Result produces a result which tracks the general trend of the target logs, but does not adequately predict the subtle features.

这是由于 Inversion Result的分块太粗略. 而EMERGE的目的便是通过别的一些地震属性来提高对细微特征的分辨能力.

This is because the Inversion Result has been blocked with a relatively coarse block size. One of the objectives of EMERGE is to improve on this prediction using other attributes of the seismic data.

(练习2毕) (End of Exercise 2)

slide69
多属性

常规交汇图延伸出来即是利用多属性.

An extension of the conventional cross plot is to use multiple attributes.

一个属性的交汇图

Cross plotting against 1 attribute:

两个属性的交汇图

Cross plotting against 2 attributes:

slide70

多属性

多属性的线性回归:

对每个时窗而言, 目标曲线都被模拟成多个属性的线性组合. At each time sample, the target log is modeled as a linear combination of several attributes.

slide71

多属性

用三个属性来预测孔隙度

Predicting porosity with three attributes:

(t) = w0 + w1I(t) + w2E(t) + w3F(t)

其中 (t) =孔隙度 porosity

I(t) = 声波阻抗 acoustic impedance

E(t) = 振幅包络amplitude envelope

F(t) = 瞬时频率 instantaneous frequency

上是可以分解为一系列线性方程:

This can be written as a series of linear equations:

1 = w0 + w1I1 + w2E1 + w3F1

2 = w0 + w1I2 + w2E2 + w3FN

. . . . .

N = w0 + w1IN + w2EN + w3FN

用矩形表示如下: In matrix form:

  • 或者P = AW
slide72

Multiple Attributes

通过最小二乘平方法来解上式, 我们可以得到:

This can be solved by least-squares minimization to give

W = [ATA]-1ATP

详细计算如下: As a detailed computation, note that:

或:

这些系数满足预测误差最小化这个条件.

These coefficients minimize the total prediction error:

slide73

多属性预测

减小预测误差 Decreasing Prediction Error:

并不是说用的属性个数越多误差越小. 为什么呢?

The prediction error for N+1 attributes can never be larger than the prediction error for N attributes.

How can we be so sure?

我们可以将最后一个系数改为0来试验.

If it were not true, we could always make it so by setting the last coefficient to zero.

slide74

多属性

属性组合的选择 Choosing combinations of attributes:

给定所有的内部属性和外部属性, 我们怎样能够发现那些属性组合在一起能够得到最好的预测效果呢?

Given the set of all internal and external attributes, how can we find combinations of attributes which are useful for predicting the target log?

EMERGE 用step-wise regression 来达到最好的属性组合.

EMERGE uses a process called step-wise regression:

(1) 第一步: 用试错法找到最好的属性. Step 1: Find the single best attribute by trial and error. For each attribute in the list,

 Amplitude Weighted Phase

 Average Frequency

 Apparent Polarity etc,

calculate the prediction error. The best attribute is the one with the lowest prediction error. Call this attribute1.

  • 对列表中的每个属性(振幅权重相位, 平均频率, 和视极性等), 计算预测误差. 误差最小的那个属性便是最好的属性, 命名为属性1.
  • (2) Step 2: Find the best pair of attributes, assuming that the first member is attribute1. For each other attribute in the list, form all pairs,

第二步: 找到最好属性对. 假设第一个属性为属性1, 用它与列表中的别的属性形成属性对,如下:

(attribute1, Amplitude Weighted Phase)

(attribute1, Average Frequency), etc.

最好的属性对便是预测误差最小的对. 这样, 第二个属性就选出来了,命名为属性2.

The best pair is the one with the lowest prediction error. Call this second attribute attribute2.

slide75

多地震属性

(3) 第三步: 找到最好的第三个属性. 假设前两个最好的属性分别为属性1 和属性2. 用它们和属性列表中的成员分别组成三个属性的组, 如下:

Step 3: Find the best triplet of attributes, assuming that the first two members are attribute1 and attribute. For each other attribute in the list, form all triplets,

(attribute1, attribute2, Amplitude Weighted Phase),

(attribute1, attribute2, Average Frequency), etc.

最小误差的便是第三个最好的属性, 称为属性3.

The best triplet is the one with the lowest prediction error. Call this third attribute attribute3.

不断地这样优选出你需要的属性.

Carry on this process as long as desired.

减小预测误差: Decreasing Prediction Error:

N个属性的预测误差EN总是 小于或等于N-1个属性的预测误差.

The prediction error, EN, for N attributes is always less than or equal to the prediction error, EN-1 , for N-1 attributes, no matter which attributes are used.

validation of attributes
属性的有效性Validation of Attributes

我们如何知道选取多少个属性为最佳呢?

How can we know when to stop adding attributes?

增加属性就相当于用高次的多项式来拟合曲线.

Adding attributes is similar to fitting a curve through a set of points, using a polynomial of increasing order:

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属性的有效性

我们能够计算出每个多项式的预测误差, 它等于真实的y值与预测得到的y值之间的均方根差.

For each polynomial, we can calculate the Prediction Error, which is the RMS difference between the actual y-value and the predicted y-value.

  • 随着多项式的阶数增加, 预测误差趋于减小.
  • As the order of the polynomial is increased, the prediction error will always decrease.
  • 问题在于, 当高阶多项式拟和得越好时, 数据的内插或外推情况就更为糟糕, 如下所示, 这就是“过于约束”的问题.
  • The problem is that, while the higher order polynomial predicts the training data better, it is worse at interpolating or extrapolating beyond the limits of the data as shown below. It is said to over-trained:
slide78

属性的有效性

EMERGE用以下的步骤来验证地震属性的有效性:

To determine the validity of attributes, EMERGE uses the following Validation procedure:

(1) 将数据体分为两个集合: Divide the entire data set into two groups:

 学习数据集合 Training data set

 验证数据集合Validation data set

(2) 用学习数据集合确定回归系数.

When determining coefficients by regression, use the Training data set.

(3) 用验证数据集合来计算预测误差.

When measuring the prediction error, use the Validation data set.

如上图所示, 用高阶的多项式对学习数据集合拟和,效果较好, 但对验证数据集合拟合的较差. 这表明多项式的阶数太高了.

As the figure above shows, a high order polynomial which fits the Training data well may still fit the Validation data poorly. This indicates that the order of the polynomial is too high.

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属性的有效性

EMERGE 可以系统地删除一些井以改善地震属性的有效性.

EMERGE performs Validation by systematically leaving out wells.

假设有5口井和3个属性: Assume we have 5 wells :

{Well1, Well2, Well3, Well4, Well5}

Assume we have 3 attributes:

{Impedance, Envelope, Frequency}

通过以下的步骤来验证属性的有效性:

Perform the Validation this way:

(1) 去除井1. 用来自{井2, 井3, 井4, 井5 }的数据体来解回归系数. 即, 解下面的方程组, 井1的系数为0.

(1) Leave out Well1. Solve for the regression coefficients using only data from {Well2, Well3,Well4, Well5}. This means solving this system of equations, where the rows contain no data from Well1:

1 = w0 + w1I1 + w2E1 + w3F1

2 = w0 + w1I2 + w2E2 + w3FN

. . . . .

. . . . .

N = w0 + w1IN + w2EN + w3FN

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属性的有效性

(2) 用导出的系数来计算井1的预测误差. 用下式来计算: With the derived coefficients, calculate the prediction error for Well1. This means calculate the following:

  • 只用井1的数据来算, 这样得到井1的校验误差E1.
  • where now only data points for Well1 are used. This gives us the Validation Error for Well1, E1.
  • (3) 分别去掉井2, 井3, 井4, 井5, 依上述分别计算回归系数和验证误差.
  • Repeat this process for Well2, Well3, etc., each time leaving the selected well out in the calculation of regression coefficients, but using only that well for the error calculation.
  • (4) 计算所有井的平均验证误差:
  • Calculate the Average Validation Error for all wells:
  • EA = (E1+E2+E3+E4+E5) / 5
slide81

属性的验证

下面是某个属性的验证图:

This is a validation plot for an EMERGE analysis:

横坐标表示用于预测的属性的个数, 纵坐标表示相应个数的属性的均方根误差.

The horizontal axis shows Number of Attributes used in the prediction. The vertical axis shows the Root-Mean-Square Prediction Error for that number of attributes.

黑色曲线表示用学习数据计算的误差, 红色曲线表示用验证数据计算的误差.

The black (lower) curve shows the error calculated using the Training Data.

The red (upper) curve shows the error calculated using the Validation Data.

从上图我们得知, 当属性个数多于5时, 验证误差增加, 说明属性太多了, 过于拟合. The figure above shows that when 5 or more attributes are used, the Validation error increases, meaning that these additional attributes are over-fitting the data.

slide82
练习3: 多属性列表

本练习中, 我们要对前两个练习中的数据体进行多属性分析.

In this exercise, we apply Multi-Attribute analysis to the data set from the first two exercises.

多属性分析: Performing Multi-Attribute Analysis

点击Attribute / Create Multi Attribute List进行多属性分析, 以下菜单显示出来.

To initiate the multi-attribute transform process, click on Attribute / Create Multi Attribute List to get this menu:

该菜单包括两页. 第一页选择用于多属性分析的井位. 此处采用默认选项, 点击Next>>.

This menu contains two pages of parameters. The first page is used to select which wells will be used in the training. To accept the default, which is all the wells, click on Next >>.

slide83
练习3: 多属性列表

第二页如下所示, 用来创建多属性列表:

The second page of the Create Multi-Attribute List menu looks like this:

第一项确定创建一系列变换还是单个变换. 通常, 我们创建一系列变换, 用step-wise regression来验证各个属性. 有时也需要指定单个变换的特性.

The first item on the menu determines whether we will be creating a list of transforms or a single transform. Usually, we want to create a list by examining all the available attributes using the process of step-wise regression. Alternatively, you may sometimes wish to specify in detail the specific properties of a single transform. In that case, you would select one of the other two options from the first item.

slide84
练习3: 多属性列表

最大属性个数是个很重要的参数. 在此分析中, EMERGE 通过step-wise regression搜索到预测目标体的属性集合.

An important parameter is Maximum number of attributes to use. In this part of the analysis, EMERGE searches for groups of attributes that can be combined to predict the target. It does this by the process of step-wise regression.

最大属性个数控制着何时停止搜索. 这个搜索过程影响着运行时间.

The parameter “Maximum number of attributes to use” tells EMERGE when to stop looking. This of course affects the run-time for the analysis.

因子长度是另一个很关键的参数, 后面详细介绍. 现在, 默认选择1ms的采样率.

Operator Length A second important new parameter is the Operator Length. This parameter will be explained in a later exercise. For now, leave the default of 1 sample.

与单属性分析一样, 我们将对目标体和外部属性进行非线性变换的检验.

Also, as we did with the Single-Attribute Analysis, we will be testing non-linear transforms on both the target and the external attributes.

不断地点击Next>>, 直到该菜单的最后一页, 验证所选的选项.

To verify that these options have been selected, click on Next >> to display the final page of this menu.

之后, 点击Ok. 几分钟后, 你会看到以下列表:

When the menu has been filled in as shown, click on OK. This analysis will take several minutes. When it completes, you will see the following table:

slide85
练习3: 多属性列表

多属性相关结果给出了计算结果. 每一行对应于一个多属性变换, 包括实行变换的属性对.

The Multi Attribute Correlation Results table shows the results of the calculation. Each row corresponds to a particular multi-attribute transform and includes all the attributes above it.

比如: 第一行, 1/Inversion Result 表示单独使用时的最好属性为Inversion Result .

For example, the first row, labeled 1/Inversion Result, tells us that the single best attribute to use alone is the inverse of Inversion Result.

第二行, Time, 指的是用1/Inversion Result 和Time同时进行变换时, 这是最好的属性对.

The second row, Time, actually refers to a transform using both 1/Inversion Result and Time simultaneously, and this is the best pair.

依此, 我们得到了最好的三个属性组合和四个属性组合, 等等. 训练误差的减小说明随着属性个数的增加, 预测误差降低.

As we proceed down the list, we get the best triplet, the best four, etc. The decreasing Training Error shows that the prediction error decreases with increasing number of attributes, as expected.

也可看到预测误差的显示: You will also see a display of the prediction errors:

slide86
练习3: 多属性列表

下面的曲线(黑色)表示纵轴上的学习误差和横轴上属性个数之间的关系.

The lower (black) curve shows the training error on the vertical axis and the number of attributes on the horizontal axis.

上面的曲线(红色)是验证误差, 显示出7个属性效果最好.

The upper (red) curve is the Validation Error, which tells us that we should not use more than 7 attributes.

用多属性因子, 主频, 即第7个属性来绘制交汇图, 如下:

To see a cross-plot of one of the multi-attribute operators, highlight the words Dominant Frequency, which selects the seventh attribute and click on the Cross Plot button. The following plot appears:

slide87
练习3: 多属性列表

这个交汇图不同于前面所述. 它显示了预测的目标体和真实的目标体之间的关系. 红色曲线不是回归曲线, 而是斜率为1截距为0的直线, 这是最好的相关. 实际的相关系数和误差显示在图的上部分. 我们可以看到用7个属性得到的相关系数几乎达到62%.

This cross plot differs from the previous in that it shows the predicted target value against the actual target value. The red line is not a regression line but a line with zero intercept and slope 1, indicating perfect correlation. The actual correlation and error are printed at the top, and we can see that the result of using 7 attributes is to achieve a correlation of almost 62%.

点击Dominant Frequency 选中第七个属性, 点击Apply按钮, 显示出用多属性变换进行目标预测的结果. 点击View / Zoom, 看到以下图示:

Highlight the words Dominant Frequency again to select the seventh attribute, and click on the Apply button. A plot appears, showing the results of applying the multi-attribute transform along with the target logs. After using the View / Zoom option, the plot will look like this:

slide88
练习3: 多属性列表

点击Attribute / Display Single Attribute List , 选择第一个单属性, 1/Inversion Result , 点击Apply, 对比上示结果.

You may want to compare this result with the prediction using the single attribute. To do that, click on, select the first single attribute, 1/Inversion Result, and click on Apply.

从数学角度上讲, 相关系数从51%提高到62%.

Mathematically, we have increased the correlation from 51% to 62%.

再次选中Dominant Frequency点击List按钮, 下表显示出来:

Once again, highlight the words Dominant Frequency, and click on the List button. The following table appears:

该表列出了7个属性的权重, 都设为常数.This table lists all the weights for each of the seven attributes, as well as the constant.(练习3毕).

(End of Exercise 3)

slide89

褶积因子

目前为止, 多属性分析即是使每个目标和相应的地震属性二者相关.

The Multi-Attribute analysis so far correlates each target sample with the corresponding samples on the seismic attributes:

因为井位和地震属性之间存在很大的频率差(如下所示), 但是目前的属性分析方法忽略了这个事实.

This approach is limited because it ignores the fact that there is a big difference in frequency content between logs and seismic data, as shown in this zoomed display:

slide90

褶积因子

利用褶积因子, 交汇图扩大到对样点附近的点进行回归.

The convolutional operator extends the cross plot regression to include neighboring samples:

  • 通过样本集合的平均权重来预测每个目标曲线.平均权重通过褶积实现.
  • Each target sample is predicted using a weighted average of a group of samples on each attribute. The weighted average is convolution.
  • 以前的公式The previous equation:
  • P = w0 + w1A1 + w2A2 +….+ wNAN
  • 改为: is now replaced by:
  • P = w0 + w1*A1 + w2*A2 +….+ wN*AN
  • 其中 * 表示褶积. where * represents convolution by an operator.
slide91

褶积因子

以由两个属性预测孔隙度为例说明:

Consider the example of predicting porosity from two attributes:

  • 此时, 权wi 变为三个点的褶积因子:
  • Now let the weights, wi, become 3-point convolutional operators:
  • wi = [wi(-1), wi(0), wi(1)]
  • 上面的矩阵方程变为: The new matrix equation becomes:
  • 第二项变换如下: The second term can be re-arranged to give:
  • 这是一个新的线性方程, 其中的每个权重wi 都由三个权重wi(-1), wi(0), wi(1)来取代. 可通过最小二乘法求解. 与前面不同的是, 这种权重的方法针对两个属性, 共有3+3+1 = 7 个参数.
  • This is a new system of linear equations in which each weight, wi, has been replaced by three weights, wi(-1), wi(0), wi(1). This can be solved by least-squares regression just as before. The only difference is that for two attributes, we now have 3+3+1 = 7 parameters.
slide92

褶积因子

运用褶积因子就像增加了属性个数, 总是会改善预测误差, 但是过于约束的危险性也会增加, 校验误差可能得不到改善.

Using the Convolutional Operator is like adding more attributes: it will always improve the Prediction Error, but the Validation Error may not improve – the danger of over-training is increased.

slide93

褶积因子

上面的例子说明随着褶积因子长度的增加, 训练误差总是降低.

This example shows that as the operator length is increased, the Training Error always decreases.

而随着褶积因子长度的增加,校验误差降低到最低点, 之后会增加.

The Validation Error decreases to a minimum and then increases again for longer operators.

slide94
练习4: 褶积因子

本练习应用褶积因子来进行多属性分析.

In this exercise, we apply Multi-Attribute analysis to the data set using a convolutional operator.

多属性分析 Performing Multi-Attribute Analysis

点击Attribute / Create Multi Attribute List, 启动多属性分析, 以下菜单出现:

To initiate the multi-attribute transform process, click on Attribute / Create Multi Attribute List to get this menu:

与前几个练习不同的是, 因子长度改变了.

Notice that the only change from the previous exercise is to modify the Operator Length.

slide95
练习4: 褶积因子

填好上述菜单后, 点击Ok. 几分钟后, 多属性变换和预测误差如下就会显示出来. When the menu has been filled in as shown above, click on OK. This analysis will take several minutes. When it is complete, you will see the list of multi-attribute transforms and the display of the prediction errors:

slide96
练习4 褶积因子

以第6个属性为例, 选中Amplitude Weighted Frequency, 而后点击Cross Plot按钮, 可以看到第6个多属性因子的交汇图 , 如下:

To see a cross-plot of one of the multi-attribute operators, highlight the words Amplitude Weighted Frequency, selecting the sixth attribute, and click on the Cross Plot button. The following plot appears:

褶积因子的加入使得相关系数从62%上升到72%.

Notice that the effect of the convolutional operator is to increase the correlation from 62% to 72%.

slide97
练习4: 褶积因子

再次选中Amplitude Weighted Frequency , 即第6个属性后, 点击Apply按钮, 显示出运用多属性变换而得到的目标井的原始曲线和模拟曲线. 运用放大功能后, 下图显示出来:

Again, highlight the words Amplitude Weighted Frequency, selecting the sixth attribute, and click on the Apply button. A plot appears, showing the results of applying the multi-attribute transform along with the target logs. After using the Zoom option, the plot will look like this:

slide98
练习4: 褶积因子

以第6属性为例, 选中该属性(Amplitude Weighted Frequency), 点击 Validate / Selected Attribute, 多属性回归算法的有效性显示如下:

Another useful display can be seen if you select the sixth row on the multi-attribute transform list (with the name Amplitude Weighted Frequency), and click on Validate / Selected Attribute.

每个预测的井曲线韵的褶积因子都从其它的井曲线而得. 该图显示出了这个过程如何对新井起作用, 以后会做这方面的训练.

This display is like the previous one, but as the annotation points out, each predicted log has used an operator calculated from the other wells. Effectively, this display shows how well the process will work on a new well, yet to be drilled.

(End of Exercise 4)(练习4毕)

5 3 d exercise 5 processing the 3d volume
练习5: 3D数据体的处理Exercise 5: Processing the 3D Volume

本练习中, 我们将把多属性变换应用于三维地震体中, 用以创建一个新的P波速度体.

In this exercise, we apply the multi-attribute transform to the 3D volume to create a new volume of P-wave velocity.

三维地震体多属性分析

我们已经导出了地震道和目标井曲线的多属性关系, 现在点击Display / Seismic, 将该结果运用到整个三维数据体中. 地震分析窗口出现.

Now that we have derived the multi-attribute relationship between the seismic and target logs, we will apply the result to the entire 3D volume.

To start this, click on Display / Seismic. This causes the Seismic Analysis window to appear, if it is not already on the screen:

上述窗口显示出三维体的inline1. 弯曲的地震道为原始的地震数据, 而彩色背景则显示了反演结果.

This window currently shows Inline 1 of the 3D volume. The wiggle traces are the raw seismic data and the color background is the Inversion Result.

5 3 d
练习5: 3D数据体的处理

点击View / Parameters 后, 出现以下界面:

Click on View / Parameters to get this menu which allows you to modify the display:

可以在该菜单中改变数据的显示方式. 如: 将目前的inline数 改为95, 移动垂向的滚动条, 我们会看到inline95的目标带: 沙河道.

This menu can be used to display the data in various forms. For example, by changing the Current Inline to 95, as shown above, and moving the vertical scroll bar, we can see the sand channel which is the target zone for this data.

5 3 d1

显示如下:

练习5: 3D数据体的处理

点击Process/Apply EMERGE , 对三维体应用所导出的多属性变换, 菜单如下:

To apply the derived multi-attribute transform to the 3D volume, click on Process/Apply EMERGE to get this menu:

在此菜单上, 可以指定输出文件的文件名和路径, 也可以指定数据的处理范围. 点击Next, 保持默认选项.

Note that this menu allows you to specify the output file name and location, as well as specify the range of data to process. Click on Next >> to accept these defaults.

5 3 d2

下一页菜单如下: The next page appears:

练习5: 3D数据体的处理

在此菜单上, 点击Type of transform,我们可以指定应用那种多属性变换, 同时也可以选择是应用一种单属性变换还是应用神经网络(如果能够的话).

This page specifies which multi-attribute transform we wish to apply. Also, by clicking on Type of transform, you can choose to apply one of the single-attribute transforms or a Neural Network (if one has been created). We will use this in a later exercise.

在EMERGE窗口中, 变换列表中的每一行均为用于属性的一种变换. 举例: 当我们选择了其中的Amplitude Weighted Frequency , 便是要进行6个属性的多属性变换,校验分析表明该变换的效果最好.

As with the EMERGE list window, each line in the table is a transform using all of the attributes above it. For example, by selecting Amplitude Weighted Frequency above, we are choosing the transform with 6 attributes. This was the one that the Validation Analysis showed to be the best.

5 3 d3

点击History 得到以下窗口, 它用来检验变换中所用的参数.

To examine the parameters used in creating this transform, click on to get this window:

练习5: 3D数据体的处理

选中Amplitude Weighted Frequency 后, 点击Next >>后得到以下所示的菜单: After selecting Amplitude Weighted Frequency, click on Next >> once again to get this menu:

5 3 d4

在输出格式菜单中, 可以控制输出文件的格式. 通常情况下系统默认的是最好的格式. 点击Next>>, 有以下菜单:

This Output Format menu allows you to control the format of the output file. Usually, the defaults are best.Click on Next >> once again to get this menu:

练习5: 3D数据体的处理

以上菜单显示出随SEGY文件的创建而生成的历史记录文件. 您可以在User Description 栏中写批注. 点击Ok.

This page shows all the information that will be stored with the history file created along with the SEGY file. Note that you can type in your own comments under the field User Description. Now click on OK to apply the attribute.

整个三维体的多属性分析需要几分钟的时间, 在此过程中, 会显示出以下的进程监视.

The application can take several minutes for the entire 3D volume. While the process is running the following progress monitor appears:

5 3 d5
练习5: 3D数据体的处理

你随时都可以点击Stop终止该过程, 存储目前所计算出的SEGY文件.

At any time, you may click on Stop and the process will be terminated, saving the SEGY file calculated so far.计算完毕后, 显示下面所示的窗口:

When the calculation is complete, the following display appears:

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练习5: 3D数据体的处理

点击View / Parameters , 改善该图. 接着点击Color Key 键, 下面菜单显示出来:

To improve the plot, click on View / Parameters. When the menu appears, click on the Color Key tab at the top to get this page:

你可以在该菜单上随便修改色标.

This page gives you complete control over the color scale.

5 3 d7

点击Data Range , 如下图所示填上颜色的上下范围值来改变色标:

Click on Data Range and fill in the menu as shown to change the range of the color bar:

练习5: 3D数据体的处理

点击该菜单上的Ok和Seismic View Parameters菜单上的Ok, 得到新的显示:

Then click on OK on this menu and on the Seismic View Parameters menu to get the new display:

我们注意到河道主要在该图的中心位置.

Note the channel prominently visible in the center of the display.

5 3 d8

创建切片也是观察该结果的一个很有趣的方法. 点击显示computed_P-wave result的地震窗口中的Process / Slicing / Create Data Slice后, 下面菜单出现:

Another interesting way of looking at this result is to produce a data slice. To do this, click on Process / Slicing / Create Data Slice on the seismic window showing the computed_P-wave result. The following menu appears:

练习5: 3D数据体的处理

你可以在该菜单中选择所要显示的三维体, 此处采用默认选项, 点击Next, 有以下菜单:

This menu allows you to select the volume that you are displaying along with the Plot Attribute. We will use the defaults, so click on Next >> to get the following menu:

5 3 d9
练习5: 3D数据体的处理

填好上面的菜单后, 我们就创建了一个以1065ms为中心的, 平均时窗为10ms的切片. 点击Next >> 直至点击 OK, 显示出该切片:

By filling in the menu as shown, we are creating a slice by averaging a 10 ms window centered on the time of 1065 milliseconds. When you have set up the menu as shown above, click on Next >> and OK to produce this data slice:

该切片显示出低速河道穿过多口井的测线沿水平方向延伸的特征. The data slice shows a low-velocity channel feature extending horizontally across the survey through many of the wells in the project.

分析完毕, 点击EMERGE 主窗口中的File / Exit退出程序.

This completes the analysis of the first data set. To close the EMERGE program, click on File / Exit on the EMERGE main window.

系统会提示是否存储该工区, 点击Yes.

When you see the question:

Do you want to save the project?

Click on Yes.

(End of Exercise 5) (练习5毕)

emerge1
EMERGE中的神经网络: 为什么要用神经网络

我们希望能够解释井曲线与地震属性之间的非线性关系.

We want to account for non-linear relationships between logs and attributes.

线性预测: Linear prediction

Log

Attribute属性

非线性预测 Non-linear prediction

Log

属性 Attribute

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EMERGE中的神经网络

EMERGE 中运用了三类神经网络:

EMERGE has three types of Neural Network:

MLFN 多层正向反馈, 类似于传统的误差 反向传播 .

Multi-Layer Feed Forward Similar to traditional back- propagation.

PNN 概率神经网络, 可用于数据分类, 与聚类分 析相同, 也可以用于数据的预测, 此时与回归 分析相同.

Probabilistic Neural Network Can be used to classify data, in which case it is similar to Discriminant analysis, or to predict data, in which case it is similar to regression analysis.

Discriminant 一种线性分类方法

A linear classification system.

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EMERGE中的神经网络

学习样本包括输入属性和特定的时间样本的已知目标值.

Each training example consists of the input attributes plus the known target value for a particular time sample.

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MLFN 神经网络学习参数

MLFN Neural Network Training Parameters

MLFN 的学习过程就是确定各节点的最佳连接权重.

The training of MLFN consists of determining the optimum set of weights connecting the nodes.依定义, 能用最低的最小二乘误差来预测已知的学习样本的那些权重便是最佳的权重.

By definition, the “best” set of weights is the one which predicts the known training data with the lowest least-squares error.

这是个非线性的最优化问题. EMERGE通过结合模拟退火和共轭梯度来解决这个问题.

This is a non-linear optimization problem. EMERGE solves this by a combination of simulated annealing and conjugate-gradient.总的迭代次数决定着运行时间的主要参数. 对每个迭代过程而言, 都存在一个特定的共轭梯度迭代次数能够达到局部的最小误差.

The main parameter controlling the training time is the number of Total Iterations. Within each one of these iterations, there is a fixed number of Conjugate-Gradient Iterations to find the local minimum.

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MLFN 神经网络学习参数

对每个迭代过程而言, 模拟退火可以通过搜寻其它的参数空间来优化迭代过程. 迭代过程中是否运用模拟退火取决于该工区是否适于用此方法以及模拟退火在前面的迭代中所起到的优化程度.

Within each of the Total Iterations, simulated annealing may be used to look for improvements by searching in other areas of the parameter space. The decision about whether to perform simulated annealing in any iteration is controlled by the program and depends on the degree of improvement in the previous iteration.

理论上讲, 由于随着迭代次数的增加, 可以在更多的空间搜寻全局最小误差, 所以迭代次数多总是好的.

Theoretically, more iterations is always better than fewer because it allows more scope for finding the global minimum.

学习过程中,随时监测预测误差.

While the training is going on, the prediction error may be monitored:

点击“Stop”随时终止学习过程.

Pressing “Stop” on this menu allows the training to be terminated at any time.

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MLFN 神经网络学习参数

隐层的节点数控制着神经网络预测学习样本的成效.

The parameter which controls how well the network predicts the training data is the Number of Nodes in the Hidden Layer:

默认的节点数遵循大拇指规则, 即等于输入属性个数的2/3. (输入属性的个数等于属性的个数与褶积因子长度的乘积).

The default value follows the rule-of-thumb that it should be equal to 2/3 the number of input attributes. (Note that the number of input attributes equals the number of actual attributes times the operator length).

增加隐层节点的个数一般会提高预测的精度, 同时也会带来过于学习的后果.

Increasing the Number of Nodes in the hidden layer will always predict the training data more accurately, but the danger of over-training is increased.

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隐层节点数的影响

此节讨论改变隐层的节点数对单属性预测的影响.

These displays show the effect of changing the number of hidden layer nodes for the simple 1-attribute case:

两个节点时的情形: 2 nodes in hidden layer:

5个节点时的情形: 5 nodes in hidden layer:

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隐层节点数的影响

此节讨论改变隐层的节点数对单属性预测的影响.

These displays show the effect of changing the number of hidden layer nodes for the simple 1-attribute case:

5个节点时的情形: 5 nodes in hidden layer:

10 个节点时的情形10 nodes in hidden layer:

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MLFN 神经网络

优点: Advantages:

(1) 关于神经网络的书中都谈到了传统的格式;

Traditional form is well described in all Neural Network books.

(2) 一旦学习完毕, 应用到大量数据体中速度相对较快.

Once trained, the application to large volumes of data is relatively fast.

缺点: Disadvantages:

(1) 神经网络趋向于“黑箱”, 无法解释权重的取值.

The network tends to be a “black box” with no obvious way of interpreting the weight values.

(2)由于模拟退火采用一个随机数的产生器来搜寻全局误差, 所以对于同一个参数的学习过程可能会产生不同的结果.

Because simulated annealing uses a random number generator to search for the global optimum, training calculations with identical parameters may produce different results.

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概率神经网络 (PNN)

概率神经网络(PNN)是用于EMERGE中的第二类神经网络, 它能用于分类或绘图.

The Probabilistic Neural Network, or PNN, is a second type of neural network used in EMERGE. The PNN can be used either for classification or for mapping.

EMERGE将一个输入地震样本分为N类(如: 沙岩, 页岩, 石灰岩, 或, 油, 气, 水, 等等).

In classification, EMERGE classifies an input seismic sample into one of N classes (e.g. sand, shale, carbonate, or oil, gas, water, etc.).

后面我们会看到, EMERGE通过线性聚类分析(LDA)实现分类. PNN实际上是LDA的非线性延伸.

As we shall see later, this can also be done using Linear Discriminant Analysis (LDA) in EMERGE, and PNN can be thought of as the non-linear extension of LDA.

EMERGE将输入地震属性样本转化成储层参数如孔隙度来绘图, 这与多线性回归, MLFN都是相同的. 但是, PNN用的是另外一种方法.

In mapping, EMERGE maps an input seismic sample into a reservoir parameter such as porosity. This is the same thing that we did with multi-linear regression and MLFN, but PNN uses a different approach.

广义的回归神经网络(GRNN)将PNN用于绘图是最成功. 此处我们用PNN来绘图和分类.

The more correct term for PNN applied to mapping is the Generalized Regression Neural Network, or GRNN, but we will use the term PNN for both mapping and classification.)

为了说明PNN, 我们先来看属性的空间距离, 接下来探讨分类问题.

To understand PNN, we will first look at the concept of “distance” in attribute space, and then start with the classification problem.

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概率神经网络(PNN)

假定X-Y平面上三点(p1, p2, p3), 我们想通过三点与p0的距离来建立它们之间的关系式, 如下:

Assume we have three points (p1, p2, and p3) on a map that are functions of the coordinates X and Y, and we want to relate them to point p0.

y2

p1

p2

y1

d2

d1

p0

y0

d3

Y

p3

y3

x0

x3

x2

x1

X

This can be done using the distances from point p0 to each of the other points:

d12 = (x1-xo)2 + (y1-yo)2d22 = (x2-xo)2 + (y2-yo)2

d32 = (x3-xo)2 + (y3-yo)2

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概率神经网络(PNN)

Log

Seismic Attributes

X

Y

y1

x1

x2

y2

x3

y3

x0

y0

我们来回顾一下前面那张井与属性的图片, 当时去掉了第三个属性. 现在我们将两个属性X, Y标出来, 分别选四个点, 我们就可以从二维属性空间内平均距离的角度来重新解释前面那张图.

Now let us revisit the earlier picture showing the log and attributes, where we have dropped the third attribute. If we label the two attributes X and Y, and show four points on the attributes, we can now re-interpret the previous plot as meaning “distance” in 2D attribute space.

(如果加上第三个属性, 我们就能得到可视化的三维空间. N个属性则会创建N维空间). 目前为止我们还未考虑井的数据.

(If we add the third attribute, we get 3D space, which can still be visualized. More attributes creates an N-dimensional space). Note that we have not yet considered the log.

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概率神经网络(PNN)

Log

Seismic Attributes

X

Y

y1

x1

x2

Class A

y2

x3

y3

x0

y0

y4

y5

x4

Class B

x5

x6

y6

我们只能用井来标识两类属性A和 B(可能为砂岩和页岩, 或者是含气砂岩和湿砂岩)何处不同而已. 前三个点都在A类中, B类中则加入了更多的点. 下面来看一下X-Y坐标中的图:

Now, we will use the log only to indicate where there are two different classes, A and B (maybe sand and shale, or gas sand and wet sand). The first three points are in Class A. Three more points have been added, in class B.

Let us see what this would look like on an X-Y plot.

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概率神经网络(PNN)

p1

Class A

p3

p2

d1

d3

d2

Class B

d5

p0

d4

p5

p4

Y

d6

p6

X

上图中, 6个点都画在了属性空间内, 各点与p0的“距离”都已标出来. 我们看到, A类距离点p0比B类近. (该图只是示意图, 与前面的图不成比例).

In the above figure, all six points have been plotted in attribute space, and the “distances” between point p0 and all the other points have been annotated. Notice that point p0 is “closer” to Class A than it is to Class B. (Note that this is simply a cartoon, and is not scaled properly with the previous figure).

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概率神经网络(PNN)的权重函数

Probabilistic Neural Network (PNN) The Weighting Function

事实上, PNN不是采用各点到p0的距离, 而是对距离进行指数权重函数运算(Parzen estimator). 对两种类而言, 有:

In fact, PNN does not use distance on its own, but applies an exponential weighting function to the distance (called the Parzen estimator). For the two classes, we can write:

这样就会推导出著名的贝叶斯公式, 其中每类的概率为:

This leads us to the famous Bayes’ theorem, which allows us to assign a probability to each class, as follows:

类A和B的判定十分简单. 当PA > PB时, p0 点属于A类; 反之, p0 点属于B类.

The decision is then simple. If PA > PB, the point p0 is in Class A, and If PA < PB, the point p0 is in Class B.

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概率神经网络的(PNN)权重函数

为了更好地说明权重函数的影响, 我们举个例子, 与前面提到的相同, 是关于6个点的例子. A类, B类分别有自己的函数.

To visualize the effect of the weighting functions, here are the functions for Class A on its own and Class B on its own, and the two classes together. This is for a 6 point problem similar to the one shown earlier.

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概率神经网络的(PNN)权重函数

下面显示出搜寻A类和B类的概率函数. 这只是一个针对两种属性的简单的线性问题, 但是大多数情况下的应用都非常复杂.

Here are the probability functions for finding Classes A and B. Note that this is a simple 2 class linear problem with only two attributes, and most applications are much more complex.

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概率神经网络的(PNN)权重函数

下图显示了不同希格玛值时对A类与B类的影响. 上幅图, 希格玛值太低, 结果过于“起伏”, 下幅图,希格玛值太高了, 结果过于平滑.

Here is the effect of varying sigma for both classes. In one case, the value is too low, and the result is too “spiky”. In the other, the value is too high, and the result is too smooth.

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概率神经网络的(PNN)绘图

地震属性

X

Y

p1至 pN已知 p1 to pN known

p1

y1

x1

x2

y2

p2

x3

y3

p3

pN

xN

yN

p0

x0

y0

从x0和 y0中预测未知 p0 .

p0, unknown, predict from x0 and y0.

已知值

All values known

我们再来看前面的那幅关于井和地震属性的图. 令pi为 测井曲线值, 其中只有p0是未知的. 预测未知井的公式是仅仅是分类的一个延伸, 如下:

Now let us once again look at the earlier picture showing the log and attributes. Now we will let the pi values be the log values themselves, where only p0 is unknown. Let us look at the formula for predicting the unknown log value, which is simply an extension of classification.

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概率神经网络的(PNN)权重函数

设有3个点, 称为学习点:

Consider the first 3 points, which we will call the training points:

井曲线值Log value

地震属性值Attributes

已知x0和 y0的情况下, 希望得到新的输出点p0.

We wish to get a new output point, p0, where we know the values of x0 and y0:

与分类相似, 通过与p0 相关的属性和与p1 , p3相关的属性之间的比较来求解p0 .

As in classification, we solve for p0 by comparing the “attributes” associated with p0

with the “attributes” associated with p1 to p3:

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概率神经网络的(PNN)权重函数

将每个学习点的指数函数乘以已知的井曲线值, 再除以指数函数的和. 别忘了, 距离与点x0和 y0都有关.

But now, we multiply the exponential functions from each training point with the known log values, and divide by the sum of the exponential functions. Remember that the distances all relate to points x0 and y0.

我们可以看到, 上式与多线性回归方程有些相像. 但是,多线性回归方程中的协方差矩阵是井点值与相应的属性的叉乘, 而不是与权重函数的运算.

Notice the similarity of the above equation to the multi-linear regression equations. However, in multi-linear regression, the covariance matrix contains cross-products of the log values with the attributes themselves rather than with the weighting functions.

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概率神经网络的(PNN)权重函数

在概率神经网络分析中, 属性往往多于2个:

In PNN, we usually have many more than 2 attributes:

瞬时振幅Instantaneous amplitude

瞬时频率Instantaneous frequency

同样计算出距离: But the “distances” are calculated the same way:

d12 = (x1-xo)2 + (y1-yo)2 + (A1-Ao)2 + (F1-Fo)2

这样, 权重函数均可用于分类和绘图了.

And so are the weighting functions used in both classification and mapping.

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概率神经网络的(PNN)小结

EMERGE中的PNN用于分类和绘图.

The PNN is used in EMERGE for both classification and mapping.

对分类而言, 只需要权重, 它取决于目标点和学习点之间的距离.

In classification we need only the weights that depend on the “distance” from the desired point to the training points.

“距离”是多维属性空间的概念, 由希格玛值来标定. 希格玛值由交叉验证自动确定.

The “distance” is measured in multi-dimensional attribute space.The “distance” is scaled by smoothers (the sigma values), which are determined automatically by cross-validation.

对绘图而言, 用加权函数乘以已知的井点值来确定未知的井点值.

In mapping, the weighting functions are multiplied by the known log values to determine the unknown log values.

下面来看EMERGE菜单中的选项.

We will now look at the specific menu items in EMERGE.

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概率神经网络(PNN)学习参数

PNN的学习过程便是搜寻每个属性的最佳希格玛值的过程.

Training the PNN means finding the“best” set of sigma values for each attribute.定义: 产生最小的校验误差值的希格玛便是最佳选择.

By definition, the “best” set of sigmas is the one which produces the minimum cross-validation error.

交叉验证意为基于井-井和点-点之上隐藏数据. 通常是缺省井-井:

Cross validation means hiding data on a well-by-well basis or on a point-by-point basis.

The well-by-well default is always recommended:

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概率神经网络的学习参数

搜寻最佳希格玛值是个非线性优化问题. EMERGE中, 分两步:

Finding the optimal set of sigmas is a non-linear optimization problem. In EMERGE, it is handled in two stages:

(1) 在一定的范围内处理, 拾取最小校验误差的希格玛值, 便是最佳的单个希格玛值. 并假定所有的希格玛值都等于该值.

Find the single best sigma, assuming that all the sigmas have the same value. This is handled by trying a range of sigmas and picking the one with the lowest validation error:

由于输入的属性都已经标定到0.1标准方差, 所以最佳的希格玛值通常在0.5到1.5之间.

Since the input attributes are scaled to a standard deviation of 1.0, the best sigma is usually in the range of 0.5 to 1.5.

(2) 以全局统一的希格玛值作为起始点, 通过共轭梯度算法来搜寻每个属性相应的希格玛值, 该值能够使有效误差最小化.

(2) Using the single global sigma as a starting point, use a conjugate-gradient algorithm to search for the individual sigmas for each attribute which minimize the validation error:

经验表明, 改变系统的默认的参数通常不会产生什么效果.

Experience has shown that there is rarely any benefit in changing these default parameters.

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概率神经网络中的希格玛值

学习了概率神经网络之后, 相应的希格玛值就会显示出计算结果:

After the PNN Network is trained, the calculated sigma’s may be displayed:

这些值可以手动修改: They may also be modified manually:

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改变希格玛值对概率神经网络所产生的效果

下面的图片显示了在单属性情况下, 改变希格玛值所产生的不同的效果:

These displays show the effect of changing the single sigma value for the simple 1-attribute case:

当希格玛值被自动优化时: Sigma optimized automatically:

当希格玛值减小到优化值的1/10时:

Sigma reduced to 1/10 the optimized value:

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改变希格玛值所产生的概率神经网络的效果

下面的图片显示了在单属性情况下, 改变希格玛值所产生的不同的效果:

These displays show the effect of changing the single sigma value for the simple 1-attribute case:

当希格玛值被自动优化时: Sigma optimized automatically:

当希格玛值减小到优化值的1/2时:

Sigma reduced to 1/2 the optimized value:

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改变希格玛值所产生的概率神经网络的效果

下面的图片显示了在单属性情况下, 改变希格玛值所产生的不同的效果: These displays show the effect of changing the single sigma value for the simple 1-attribute case:

当希格玛值被自动优化时: Sigma optimized automatically:

当希格玛值增加到优化值的2倍时:

Sigma increased to 2 times the optimized value:

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概率神经网络

优点:

(1) 因为PNN的算法是个数学上的内插问题, 导出的希格玛值可以作为每个属性的相对权重;

(1) Because the PNN is a mathematical interpolation scheme, the derived sigma’s may be interpreted as the relative weight given to each attribute.

(2) 与MLFN不同的是, PNN的学习过程可以复制;

(2) Unlike the MLFN, the training process is reproducible.

(3) 分类模式中, PNN可以产生概率估计值;

(3) In classification mode, the PNN may produce probability estimates.

缺点:

(1) 由于PNN 对所有学习数据进行了复制, 三维体的运行时间会非常长. 运行时间与学习的样本数成正比. 如果应用于小的目标体情况会有所改善.

(1) Because the PNN keeps a copy of all the training data, the application time to the 3D volume may be very large. This application time is proportional to the number of training samples. This problem may be alleviated by applying to a small target window.

6 exercise 6 predicting porosity logs
练习6: 预测孔隙度井Exercise 6: Predicting Porosity Logs

本练习中, 我们将利用EMERGE从地震属性方面来预测孔隙度井.

In this exercise, we use EMERGE to predict porosity logs from seismic attributes.

数据为7口井的资料, 包括其孔隙度测井曲线seismic.sgy和相应的地震道文件inversion.sgy.

The analysis data will consist of seven wells with measured porosity logs, along with the seismic files seismic.sgy and inversion.sgy.

点击Database / Open, 加载一个新的数据库到GEOVIEW, 菜单如下:

To load a new database into GEOVIEW, click on Database / Open. The menu will look like this:

选中数据库porosity.wdb后, 点击OK.

Select the database porosity.wdb as shown above and click on OK.

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GEOVIEW 界面如下: GEOVIEWwill now look like this:

练习6: 预测孔隙度井

如上图所示, 7口井都已被加载进来. 双击第一个图标01-08, 检验其测井曲线, 显示如下:

As you can see, seven wells have now been loaded. To examine the logs within one of the wells, double click on the first icon, 01-08, to produce this display:

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该井包括一条孔隙度测井曲线,命名为den-porosity, 还有其它的测井曲线.

This well contains a porosity log, called den-porosity, along with the other logs.启动EMERGE 程序, 选中“Start a New Project”, 该工区命名为porosity, 如下所示: Restart the EMERGE program and select Start a New Project. Call the project porosity as shown below:

练习6: 预测孔隙度井

EMERGE 主窗口显示如下:

The EMERGE main window will now appear:

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练习6: 预测孔隙度井

加载数据的过程与前面的练习相同, 此处不再赘述. 点击Wells / Read From Database, 如下所示填好前三页:

The steps for loading the data into this project are identical to the previous exercise, so they will be summarized briefly here. Click on Wells / Read From Database and fill in the first three pages as shown below:

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练习6: 预测孔隙度井

现在点击OK. 因为数据库中不止一条P波测井曲线, 所以下面的菜单出现了.

Now click on OK. Once again this menu appears, because there is more than one P-wave log within the database:

即便我们将孔隙度测井曲线作为目标曲线, P波测井曲线也仍需要进行深时转换. 点击OK, 激活P波测井曲线.

Even though we are using the porosity log as the target, the P-wave log is still required to perform depth-to-time conversion for EMERGE analysis. Click on Ok on this menu to accept the active P-wave logs.

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练习6: 预测孔隙度井

EMERGE的主窗口内显示出目标测井曲线(孔隙度曲线):

The EMERGE main window will now look like this, showing the target (porosity) logs:

点击Seismic / Add Seismic Input / From File, 选中所有的文件, 加载地震数据, 如下所示:

To load the seismic data, click on Seismic / Add Seismic Input / From File and select both files, as shown below:

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练习6: 预测孔隙度井

设置常规信息: Set the general information:

指定属性类型和文件的名字:

Specify the attribute type and name for both files:

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练习6: 预测孔隙度井

设置文件格式(选择默认):

Set the file format (the defaults are correct):

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练习6: 预测孔隙度井

设置几何结构(选择默认):

Set the geometry information (the defaults are correct):

之后, 点击OK. Click Ok on this menu.

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练习6: 预测孔隙度井

设置井-地震图(选择默认):

Set the well-to-seismic mapping (the defaults are correct):

提取井位处的地震道(系统默认):

Extract the traces at the wells (the defaults are correct):

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练习6: 预测孔隙度井

EMERGE主窗口现在显示出所提取的地震道和来自于外部属性(反演结果)的合成波阻抗地震道:

The main window now shows the extracted seismic trace and the composite impedance trace from the external attribute (Inversion Result):

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练习6: 预测孔隙度井

数据加载完毕, 可以进行分析了. 第一步, 检验单属性变换. 点击Attribute / Create Single Attribute List, 得到下图:

The data is now loaded and ready for analysis. The first step is to examine the single-attribute transforms. To do this, click on Attribute / Create Single Attribute List to get this menu:

注意我们要对目标曲线(孔隙度曲线)和外部属性(反演结果)进行非线性变换. 而这是由二者之间显著的负相关所决定的.

Note that we are choosing to test non-linear transforms applied to both the target (porosity) and the external attribute (Inversion Result). This is suggested by the obvious negative correlation between these two data sets.

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在上面的菜单上,点击Ok, 得到下面的列表:

With the menu set as shown above, click on Ok to get the list:

练习6: 预测孔隙度井

由上表我们可以看出最好的相关系数29%也不是太合适. 原因之一, 尽管经过check shot 校正, 目标孔隙度曲线和地震数据之间仍然存在着剩余时移. 点击Wells / Shift Target Logs 来验证此点:

We note that the best correlation of about 29% is rather poor. One reason for this may be that there are residual time-shifts between the target porosity logs and the seismic data, in spite of the check shot corrections. One way to check this is to click on Wells / Shift Target Logs to get this menu:

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练习6: 预测孔隙度井

该菜单用来输入时移, 将其用于每条目标曲线. 当然了, 我们不知道输入多大的数字, 但我们可以通过点击Optimize估计时移, 得到下面的菜单:

This menu allows you to enter time-shifts to be applied to each of the target logs. Of course, we don’t know what numbers to enter. To estimate these shifts, click on Optimize to get this menu:

在优化时移菜单中, 我们可以选择任一种变换, 此处选择单属性变换: 1/(Inversion Result). 程序会对每口井进行一系列的时移变换, 找到能够产生最大相关系数的时移, 最大时移不超过10ms. 上面所示菜单显示出来后,点击Ok.

The Optimize Shifts menu allows you to select any one transform – in this case, the single attribute transform: 1/(Inversion Result). The program then tries a series of time shifts for each well to find the set of shifts that will maximize the correlation, subject to a Maximum Shift of 10 milliseconds. With the menu set as shown above, click on Ok.

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这时, 时移菜单显示出所建议采用的时移:

The Shift Logs menu now shows the suggested shifts:

练习6: 预测孔隙度井

接受这些时移,点击Ok. EMERGE主窗口中会显示出经过时移后的测井曲线. 然后, 点击Attribute / Create Single Attribute List, 重新计算单属性变换. 采用系统默认的参数, 新的变换列表如下:

To accept these shifts, click on Ok. The EMERGE main window will be updated to show the shifted logs. Now recalculate the single attribute transforms by clicking on Attribute / Create Single Attribute List. Using the default values on this menu, the new list will look like this:

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练习6: 预测孔隙度井

注意到, 最大的相关系数上升到近乎44%.

Note that the maximum correlation has now increased to nearly 44%.点击Attribute / Create Multi Attribute List , 创建多属性列表, 如下:

Now create the multi-attribute list by clicking on Attribute / Create Multi Attribute List and filling in the menu as shown below:

分析完毕后,显示出多属性列表和预测误差图.

When the analysis completes, the multi-attribute list and the prediction error plot are displayed.

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练习6: 预测孔隙度井

由上图看出, 四个属性时的情况最佳.

From this display, we see that it is best to use only four attributes.

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练习6: 预测孔隙度井

选中多属性列表中的第四行, 点击Apply, 看效果如何:

To see the application, select the fourth row of the Multi-Attribute List (Integrate) and click on Apply:

此时, 预测曲线与目标曲线的相关系数达到了59%. 另外, 平均RMS误差为0.054, 即, 5.4%的孔隙度.

Note that we have now achieved a 59% correlation between the predicted logs and the target logs. In addition, the average RMS error is 0.054, i.e., 5.4% porosity.

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练习6: 预测孔隙度井

回到地震显示窗口, 点击Process / Apply EMERGE. 按照下面所示填写第一个菜单:

Now apply this result to the SEGY data. Go to the Seismic Display window and click on Process / Apply EMERGE. Fill in the first menu as shown below:

注意: 为了节省时间, 我们只处理一段数据(单inline方向) . Note that we are choosing to process a segment of the data – a single inline – to save time in this process.

点击Next >> , 得到 下一个菜单:

With the menu filled in as shown above, click on Next >> to get the next menu:

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练习6: 预测孔隙度井

如上面所示, 选中第四个多属性变换. 点击Next>>和Ok, 启动. 处理完成后, 所计算的孔隙度显示如下:

Select the fourth multi-attribute transform, as shown above. Click on Next >> and then OK to start the process.

When the processing is complete, the computed porosity volume appears:

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点击View / Parameters修改显示参数. 在颜色页上, 改变色标为Lithology :

To improve the display parameters, click on View / Parameters. On the Color Key page, change the Color Scheme to Lithology and clear the Normalized Scale box:

练习6: 预测孔隙度井

点击Data Range, 改变各个数值范围, 设置如下:

To change the numerical range, click on Data Range, and set the menu as shown:

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练习6: 预测孔隙度井

点击OK, 显示预测孔隙度如下:

Click on OK on both menus to set the new display of predicted porosity:

1065ms附近的高孔隙度带与练习1中的砂岩带相对应.

Note the predicted high porosity zone at around 1065 ms corresponding to the sand channel from Exercise 1.

(End of Exercise 6)(练习6毕)

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神经网络学习

在该菜单中创建一个新的神经网络, 覆盖原有的:

This menu allows you to create a new network or to overwrite an existing one.

一个EMERGE工区中不限制所存储的神经网络个数.

There is no limit to the number of networks stored in an EMERGE project.

也可以将学习数据写到一个ASCII文件, 然后从另一个神经网络中去读.

You may also choose to write out the training data to an ASCII file for another Neural Network program to read.

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神经网络学习

输出的ASCII文件有两种格式:

The output ASCII file may be in either of two formats.

(1) 预测格式. 该格式用于通过神经软件来进行预测的程序中.

The Predict format is the one used by the program “Predict” from NeuralWare:

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神经网络学习

(2) 神经格式, 此种格式用于许多神经网络中.

The Neural format is used by many other Neural Network programs:

属性 1

目标

属性 2

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神经网络学习

该菜单决定那些井能够用于学习.

This page determines which wells to use in the training.

剔除一些井, 有以下几个原因:

Note that there may be two reasons to leave a well out of the training:

(1) 井与地震的约束太差;

The well-to-seismic tie is poor.

(2) 可以留出一口井作为“隐藏井”, 以便用于校验.

You may wish to use the well for “blind well testing” or validation later.

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神经网络学习

该菜单决定以前创建的多属性变换是否可以用作模板来建立神经网络. This page determines whether a previously calculated multi-attribute transform is used as a “template” for setting up the neural network.

选择“yes” 意味着该神经网络将拥有与所选择的多属性变换完全相同的属性和因子长度.

Choosing “yes” here means that the neural network will have exactly the same attributes and the same operator length as the selected multi-attribute transform.

因为step-wise回归能够确定最佳采用的属性, 所以推荐使用这种方法.

This is usually recommended since step-wise regression is the best way to determine which attributes to use.

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神经网络学习

当多属性变化不被用成模板时, 此页才显示出来.

This page is used only if a multi-attribute transform is not being used as a template.

必须在此指定可选的任一属性的非线性变换.

In that case, any attributes with (optional) non-linear transforms may be specified here.

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神经网络学习

该页决定重要的常规网络特性.

This page determines important general network properties.

第一个参数是网络类型:

The first parameter is the type of network:

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神经网络学习

These parameters control the option to Cascade the neural Network with the trend from the multi-attribute transform.

This option exists because Neural Networks usually work best with stationary data containing no long period trend.

有时候, 最好去掉来自目标体的趋势, 用神经网络去预测已经去掉趋势的数据.

Sometimes it is best to remove the trend from the target data, and use the Neural Network to predict the residual data which is left after trend removal.

选中该选项后, In this option, the following steps are followed:

(1) 多属性变换用于预测目标测井曲线.

The multi-attribute transform is used to predict the target logs.

(2) 被预测的曲线经过平滑.

The predicted logs are smoothed using a running average.

(3) 从原始的测井曲线中抽取出被预测的曲线, 而该曲线已经过平滑处理.

The smoothed predicted logs are subtracted from the original logs.

(4) 神经网络是基于残差或差分之上的学习.

The Neural Network is then trained on the residual or difference.

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神经网络学习

由多属性变换预测的趋势

Trend predicted from multi-attribute transform

PNN的剩余误差的预测

PNN Prediction of residual

未经过串联的PNN预测

PNN Prediction without cascading

检验该选项是否有用的唯一途径是用两种方法创建一个神经网络, 查看学习过程和校验误差.

The only way to tell if this option is helpful is to create Neural Networks both ways and look at the training and validation errors.

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神经网络学习

Mapping在EMERGE中是默认选项, 它是个预测数目的过程.

Mapping is the process of predicting numbers. This is the default option in EMERGE.

Classification则意味着预测数据的类或类型. 选中了这个选项, 必须提供目标数据分类的依据.

Classification means to predict classes or types of data. If this option is chosen, parameters must be supplied which tell EMERGE how the target data is to be classified:

如果目标曲线已经被分过类, 那么它们必须以数值的形式读入EMERGE. 其中的数值代表类别.

If the target logs have been classified previously, they must still be read into EMERGE as numerical values, where the numbers represent the classes.

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神经网络学习

即使对数值型数据而言, 它可以通过分类对数据进行块化, 减小可能的输出值的范围, 有时候这是很有用的.

Classification can sometimes be useful even for numerical data, by blocking the data and reducing the range of possible output values:

Mapping绘图

分类Classification

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神经网络学习

对一个以分类模式来学习的神经网络而言, 存在一个选项来计算和输出一个与各个类别都相关的概率.

For a network trained in classification mode, the option exists to calculate and output the probability associated with each class:

discriminant analysis
聚类分析Discriminant Analysis

Discriminant Analysis is a mathematical clustering technique which is applied in Classification mode.

聚类分析是应用于分类模式的一种数学聚类方法. 举例说明: 假设两个属性X和Y, 我们知道存在两类A和B:

As an example, assume we have 2 attributes X and Y and we know there are 2 clusters A and B:

分界线

Discriminant

Line

聚类分析则是寻找那条直线, 它能够恰当地将两类分开. 多于两个属性时, 线就变成了多维空间内的超平面.

Discriminant Analysis finds the single line which best separates the two clusters. For more than two attributes, the line becomes a hyper-plane in multi-dimensional space.

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聚类分析

由于聚类分析假设类别之间是线性分割, 那如果分割是非线性的话, 聚类分析则不灵了.

Because discriminant analysis assumes a linear separation between clusters, it can fail if the real separation is non-linear:

Attribute

1

Attribute

2

在这种情形下, PNN之类的神经网络会有效一些.

In this case, a Neural Network such as PNN can be expected to work better.

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聚类分析

优点:

(1) 学习和应用时间都比别的神经网络方法快得多.

Both training and application times are much faster than any Neural Network.

(2) 该算法非常稳健, 几乎不存在过于约束的趋势. 这意味着交叉有效误差可以与学习误差相比较.

The algorithm is very robust, with little tendency to over-train. This means that cross-validation errors are usually comparable to training errors.

不足:

(1) 只在分类模式中起作用;

Only works in Classification mode.

(2) 假设类别之间为线性分割;

Assumes linear separation between classes.

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练习7: 神经网络的应用

本练习中, 我们将要用神经网络的兼容性来改善前面练习中的孔隙度的预测.

In this exercise, we will use the Neural Network capabilities of EMERGE to improve the porosity prediction from the previous exercise.

点击Neural / Train Neural Network开始神经网络分析. 下面的窗口出现:

To start the Neural Network analysis, click on Neural / Train Neural Network. The following menu appears:

接受默认的选项, 我们将创建一个新的网络, 命名为Network_1.

We will accept these defaults, which will cause a new network to be created with the name Network_1.

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点击Next >> , 得到下面的菜单:

Click on Next >> to get the next page of the menu:

练习7: 神经网络的应用

多属性学习时, 我们可以在该菜单上选择将要用于神经网络学习的井的集合. 系统默认使用所有的井. 点击Next>> , 得到下页:

As with the multi-attribute training, this page allows us to select the subset of wells to be used in training the Neural Network. The default is to use all the wells. Click on Next>> to get the next page:

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该菜单上最上面的问题是: 是否希望用以前计算所得的多属性变换来创建神经网络. 通常回答“是”. 这是因为多属性的筛选过程已经决定了对于预测目标孔隙度曲线来说最好的属性. 选中第四种变换(积分变换), 我们创建一个与前面完全相同的神经网络.点击Show Transform History, 我们可以看到多属性变换的细节. 填好上述菜单, 点击Next>>, 得到下面的菜单:

The question at the top of this page asks if we wish to use one of the previously calculated multi-attribute transforms to structure the Neural Network. Usually, the answer to this is “Yes”. This is because the multi-attribute selection process has determined which attributes are best for predicting the target porosity log. By selecting the fourth transform (called Integrate), we are constructing a Neural Network with precisely the same attributes as those used in that transform. To see the details of that multi-attribute transform, click on Show Transform History. With the menu filled in as shown above, click on Next >> to get this page:

练习7: 神经网络的应用

我们可以看到, 这个菜单完全是不可以激活的. 这是因为该页上的参数已经由以前的多属性变换自动设置好了. 只有在你选择不用以前的多属性变换来创建网络时,该页上的参数才能被激活. 那时, 可以随意地设置神经网络的属性.

As you can see, this page is entirely “grayed out”. This is because the parameters for this page have been set automatically by using the multi-attribute transform on the previous page. This page will only be active if you choose not to use a previously generated multi-attribute transform to structure the Neural Network. In that case, this page will enable you to arbitrarily set the attributes for the Neural Network.

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练习7: 神经网络的应用

点击Next >> , 得到右图:

Click on Next >> to get the next page:

我们将要来创建一个概率神经网络, 如上所示. 此处我们不对多属性变换进行分级(串联). 在后面的练习中我们会进行分级. 最后, 选择分析类型为Mapping, 指定预测数值型的孔隙度, 而不是分类类型的孔隙度.

We will start by creating a Probabilistic Neural Network, as shown above. For this network, we will not cascade with the trend from the multi-attribute transform. We will do this in a later example, and the process will be explained then. Finally, by choosing the type of analysis as Mapping, we are specifying that we wish to predict numerical values for the porosity and not classification types.

点击 Next >>, 得到以下菜单: Click on Next >> to get the final page:

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点击OK, 接受所有默认选项. 这其中需要花费几分钟, 下面的进度指示会出现:

Accept the defaults for the PNN training process by clicking on OK. This process will take several minutes, during which the Progress Monitor can be seen:

练习7: 神经网络的应用

这个过程结束后, 显示出所预测的井曲线:

If you click Stop before the process has completed you can optionally save the partially trained network. However, we recommend that you allow the training to finish. When the training has been completed, the predicted logs appear:

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我们注意到0.87的相关系数远比利用多属性回归得到的相关系数高. 通常都是这样的结果, 这是由因子的非线性特性决定的.我们还注意到神经网络只用于学习时窗中, 这样做有两个原因:

  • Note that the correlation of 0.87 is much higher than that achieved with multi-attribute regression. This is usually the case with Neural Networks because of the non-linear nature of the operator. Note also that the Neural Network has been applied only within the training windows. This is done for two reasons:
    • (1) 如果将神经网络用于整个时窗, 学习时间会很长.
    • The application time for the Neural Network can be very long if applied to the entire window.
    • (2) 神经网络在学习时窗外不善于进行外插. 在学习时窗外的部分, 较多属性回归而言, 神经网络的有效性更差.
    • The Neural Network is not very good at extrapolating beyond the bounds of the training data. For this reason, it is expected to be less valid outside the training windows than the multi-linear regression.
  • 放大之后, 结果如下: After zooming, the result looks like this:
练习7: 神经网络的应用

现在我们想看神经网络的有效性. 这就要求我们隐藏其中的一部分井, 然后通过神经网络的方法利用别的井来预测他们的值.

Now we would like to see how the network performs in Validation Mode. This means that we will hide wells and use the trained network to predict their values.

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点击Neural / Validate Neural Network开始, 得到下面的菜单:

To start this, click on Neural / Validate Neural Network. The following menu appears:

练习7: 神经网络的应用

点击Next >> 后, 选中已经学习过的网络, 下一页如下所示:

Click on Next >> to select the network which has been trained. The next page appears:

因为所有的井都已用于学习, 所以只有第一个选项是合适的. 这意味着每个井都会轮流被“隐藏”起来, 用剩下的井来预测. 点击OK, 开始执行.

Since all the wells were used for training, only the first selection is appropriate. This means that each of the training wells will be “hidden” in turn and predicted using the remaining wells. Click on OK to start this process.

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该过程完成后, 下面的图出现了:

When completed, the following plot appears:

练习7: 神经网络的应用

我们注意到此次的相关系数相当低, 只有0.48. 这几乎等同于多属性回归分析的结果(0.49). 点击View / Error Plot 查看误差的分布情况, 如下所示:

Note that the correlation is now considerably lower (0.48). It is about the same as the validation error for the multi-attribute regression, which was 0.49. To see how the errors are distributed over the wells, click on View / Error Plot. The following plot appears:

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练习7: 神经网络的应用

校验曲线(红色)表明如果去掉第一口井(01-08)结果可能会好些. 将第一口井的校验曲线放大, 结果如下:

The validation curve (in red) suggests that the process might be improved by omitting the first well (01-08) from this analysis. However, if you zoom in closely on the first well on the validation display, the result looks like this:

仔细地观察该曲线, 我们发现被预测的曲线有正确的波峰波谷, 相对于真实的孔隙度测井曲线而言一些部分有些轻微的时移. 因为是高频预测, 相关系数对深时转换的精确度十分敏感. 实际上, 这导致了校验误差的极度悲观. 基于此, 我们剔除了校验误差高的井位.

Looking closely at this display, we can see that the predicted curve has the correct events, but some of them are slightly shifted in time with respect to the real porosity log. Because of the very high frequency prediction, the correlation calculation is very sensitive to the precise depth-to-time calculation, and in fact, this can cause the validation errors to be overly pessimistic for Neural Network calculations. For this reason, we will leave in the well with high validation errors.

**改善PNN结果的另一种方法是利用多线性回归所计算的趋势. 这种方法有时候是有用的, 因为神经网络针对具有稳定统计意义的数据, 即, 没有长周期趋势的数据.

Another possibility for improving the PNN result is to use the trend from the multi-linear regression calculation. This is sometimes useful because Neural Networks operate best on data with stationary statistics, i.e., data sets without a significant long period trend.

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练习7: 神经网络的应用

为了评价这个选项, 点击Neural / Train Neural Network创建一个新的网络. 菜单出现后, 点击Next >>, 接受默认的神经网络命名:

To evaluate this option, we will create a new network. Click on Neural / Train Neural Network. When the menu appears, click on Next >> to accept the default new network name:

第二页上, 点击Next >> , 用所有的井:

On the second page, click on Next >> to use all the wells:

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练习7: 神经网络的应用

**第三页上, 点击Next >> , 用相同的多属性变换:

On the third page click on Next >> to use the same multi-attribute transform with four attributes as the basis for this network:

属性菜单未能激活, 点击Next>>.

Once again, the Attribute Details page is disabled, so click on Next >>

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练习7: 神经网络的应用

最后, 下一页上, 第二个参数必须改变.

Finally, on the next page, we come to the parameter which must be changed:

注意: 你希望对多属性变换的趋势实行分级吗? 我们的回答为: “是”.

Note that we have answered “Yes” to the question:

Do you wish to cascade with the trend from the multi-attribute transform?

该参数的影响下面再解释. 现在, 点击Next >> , 然后点击OK, 开始学习新的神经网络.

The effect of this parameter will be explained below. For now, click on Next >> and then OK to start training the new network.

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学习完成后, 下面的图显示出来:

When the training is completed, the following plot appears:

练习7: 神经网络的应用

首先, 我们注意到分析时窗之外的目标测井曲线的低频趋势确实也被预测出来了. 在此模式中, 第一步便是要进行多线性回归. 然后用神经网络学习菜单中的一个平滑因子去平滑用于预测的测井曲线. PNN神经网络用于预测剩余误差, 它是曲线的高频分量, 不能控制在平滑趋势内. 将多线性回归趋势和神经网络的预测剩余误差相结合就得到最终的预测结果.

The first thing you can see is that the low-frequency trend from the target logs has actually been predicted outside the analysis windows. In this mode, the first calculation that the network performs is the multi-linear regression with the same four attributes. The predicted log from that calculation is then smoothed with a smoother length given on the Neural Network training menu. The PNN Neural Network is then used to predict the residual, which is the high-frequency component of the logs which is not contained within the smooth trend. The final predicted log is obtained by adding the trend from the multi-linear regression and the predicted residual from the Neural Network.

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正如我们所看到的, 与第一次神经网络得到的相关系数相比, 这次的有点低. 点击Neural / Validate Neural Network, 计算其校验误差. 在第一页菜单上点击Next >>, 接受创建新的神经网络.

As we can see the correlation is somewhat lower than that obtained with the first Neural Network. To calculate the validation error for this network, click on Neural / Validate Neural Network. On the first page of the menu, click on Next >> to validate the new network, which has just been created:

练习7: 神经网络的应用

在第二页上, 点击OK. On the second page, click on Ok to begin the validation calculation:

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练习7: 神经网络的应用

新的校验结果如下: The new validation result appears:

这次的相关系数是0.44, 仍然低于第一次的结果(0.48). 这表明第一次的神经网络比较合适.

Note that the correlation of 0.44 is also lower than the validation correlation of 0.48 for the first network, confirming that the first network was better.

接下来, 我们将创建一个多层前馈神经网络(或简写为MLFN). 它是一种常规的网络, 有时被称为“向前传播”的神经网络.

Finally, we will create one more Neural Network. This will be a multi-layer feedforward Neural Network or MLFN. This is the conventional network, which is sometimes called a “back-propagation” network.

现在从点击Neural / Train Neural Network开始.

To start this process, click on Neural / Train Neural Network.

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首页菜单上, 点击Next>>接受系统默认的新的神经网络的命名.

On the first page, click on Next >> to accept the new network name:

练习7: 神经网络的应用

以下的几页内, 不停地点击Next >>, 直到下面这一页为止:

On the subsequent pages, click Next >> to accept all the same parameters until you reach this page:

在网络的类型选项中, 选择MLFN. 然后点击Next, 得到下面所示的菜单:

Now for the type of network, select MLFN, as shown.

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Click on Next >> to get the parameters page:

练习7: 神经网络的应用

此过程中有两个非常重要的参数. 一为隐藏层的节点数, 它控制着神经网络与被学习的数据之间的拟和程度; 另一个为总的迭代次数, 它决定着网络搜寻目标权重所需要的时间. 该过程完成后, 下面所示的菜单显示出来:

There are two important parameters for this process. The number of Nodes in Hidden Layer controls the extent to which the network accurately models the training data. The second important parameter is the number of Total Iterations. This controls how long the network will search for optimum weights. Now click on OK to perform the MLFN training. When the process has completed, the following display appears:

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我们看到, 这次的相关系数比前几次都低, 所以我们不再进一步研究该网络. 点击Neural / Display Neural Network List , 我们来看一下到目前为止所创建的神经网络:

As we can see, the training correlation is lower than either of the previous networks, so we will not pursue this network any further. Now click on Neural / Display Neural Network List to get a list of all networks created so far:

练习7: 神经网络的应用

选中名为Network_1 作为例子, 点击Cross Plot 按钮, 下图显示出来:

As an example of the capabilities of this list, click on the name Network_1 and click the Cross Plot button. The following display appears:

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练习7: 神经网络的应用

同样, 点击History按钮就会得到该神经网络的详细资料.

Similarly, click on the History button to get the detailed history of how this network was created:

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神经网络应用于三维体

Applying the Neural Network to the 3D Volume

当我们有了一个已经学习好的神经网络时, 就要将其结果应用于三维体中. 如果地震分析窗口不在屏幕上的话,点击Display / Seismic , 它就会出现.

Now that we have a trained network, we will apply the result to the 3D volume. To start this, click on Display / Seismic. This causes the Seismic Analysis window to appear if it is not already on the screen:

点击Process / Apply EMERGE. 为节省时间, 我们只在单测线(inline95)上应用神经网络因子. 同时创建了一个SEGY输出文件, 命名为pnn_result.

Now click on Process / Apply EMERGE. To save time, we will apply the Neural Network operator to a single inline (95). Also, we will create an output SEGY file called pnn_result.

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神经网络应用于三维体

接着点击Next >>, 如下所示:

When you have completed the menu as shown, click on Next >> to get this page:

现在我们选择应用Network_1 . 由于我们正在应用网络, 菜单的下半部分不能激活, 只能选择神经网络的应用时窗范围. Note that we have chosen to apply Network_1. Also, because we are applying a Neural Network, the lower part of the menu is enabled, allowing us to set an Application Window for the Neural Network.

如果该工区中有水平层位, 它们会引导神经网络应用步骤. If horizons had been entered into the project, these could have been used to guide the Neural Network application window.

因为没有水平层位, 我们对1000~1200 ms应用神经网络.按照上图填好, 点击Next >>和OK.

Since there are no horizons, we will apply the network from 1000 to 1200 ms. When the menu has been filled in as shown above, click on Next >> and OK to start the process.

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神经网络应用于三维体

计算完毕后, 结果如下:

When the calculation has completed, the result appears:

Because of the large trace excursion, this plot may be easier to see if the wiggle traces are turned off.

To do that, click on View and Wiggle Traces: Unshown:

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神经网络应用于三维体

如前所述, 能够在井位处观察到高孔隙度的通道.

As before, the high porosity channel can be seen at the well location:

最后, 点击Project / Save存储该工区.

Finally, save this project by clicking on on the EMERGE main window.

(End of Exercise 7) (练习7毕)

8 exercise 8 predicting logs from logs
练习8: 由井到井的预测Exercise 8: Predicting Logs from Logs

本练习中, 我们将利用EMERGE通过一些井的多属性变换来预测未知井.

In this exercise, we apply EMERGE to the problem of predicting logs using a multi-attribute transform calculated from other logs.

本例的数据来自于四口井, 每口井包括几条测井曲线. 回到GEOVIEW主窗口中

会看到这些资料. 目前的窗口显示的是孔隙度的数据库.

The data for this example consists of a series of four wells, each containing several log curves. To see this data, go back to the GEOVIEW main window. That window currently contains the porosity database:

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点击Database / Open将新的数据库导入. 在文件选择菜单中, 选中logs 数据库(如下所示)之后, 点击OK.

To change to the new database containing the data for this example, click on Database / Open. On the File Selection menu, select the logs database, as shown below, and click OK:

练习8: 由井到井的预测

GEOVIEW 窗口如下所示:

The GEOVIEW window will now look like this:

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练习8: 由井到井的预测

该数据库中包含四口井. 双击B_Yates_11图标, 可以看到第一口井的测井曲线, 显示如下:

As you can see, there are four wells in this database. To see the log curves in the first well, go to the B_Yates_11 icon and double-click. This display will appear:

移动滑动条, 看到该井的8条测井曲线, 其中包括一条声波测井曲线(DLT). 点击Display Well List按钮也可以看到每口井的测井曲线.

By moving the scroll bar, you can see eight logs in this well, including a sonic log (DLT). Another way of examining the logs within a well is to click the Display Well List button on the GEOVIEW main window.

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练习8: 由井到井的预测

列表如下: This list appears:

在上表中, 选中B_Yates_11, 点击Display Logs, 菜单显示如下:

From this list, select the name B_Yates_11, and click on Display Logs. This list appears:

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练习8: 由井到井的预测

这次, 我们仍能看到B_Yates_11 井有8条曲线, 另外还有一条声波测井曲线. 另外我们可以看到B_Yates_18D 也有一条声波曲线, 而另外两口井, B_Yates_13 and B_Yates_15 , 并不包含声波曲线. 其目的在于用别的井来预测其声波曲线.

Once again, we can see that this well, B_Yates_11, contains eight logs, including a sonic log. By examining the other wells, you will find that one other well, B_Yates_18D, also contains a sonic log, while two of the wells, B_Yates_13 and B_Yates_15 do not contain sonic logs. The objective of this part of the guide is to predict sonic logs using the other log curves.点击EMERGE, 选中Start a New Project, 命名为 logs , 如下所示:

Start the EMERGE program by clicking the EMERGE button on the GEOVIEW main window and select Start a New Project. Call the new project, as shown below:

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练习8: 由井到井的预测

点击Wells / Read From Database, 从数据库中加载井曲线. 然后点击Add all >>, 加在所有的井(4口井).

To load the analysis logs from the database, click on Wells / Read From Database. When the menu appears, click on Add all >> to select all four wells from the database:

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练习8: 由井到井的预测

点击Next>>, 第二页菜单按照下图填写:

Click Next >> at the bottom of the menu. The second page is filled in as follows:

注意到我们选择了P波(即声波)曲线作为目标曲线. 作用域选为深度域. 这是因为这个例子中没有地震信息, 测井曲线全部都在深度域中, 因此没必要进行深-时转换. 必须在此页上设置采样率.

wave (or sonic) log Notice that we have selected the P-wave (or sonic) log as the target. Also notice that the Processing Domain has been selected as Depth. This is because all the logs are in depth – there is no seismic in this example, so there is no need to convert from depth to time. The Processing Sample Rate must also be set before you can access the next page of this menu.

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练习8: 由井到井的预测

之后, 点击Next >> , 显示出分析窗口:

When this page of the menu is completed as shown above, click on Next >> to show the Analysis Window page:

本例中, 我们已经创建了两个层位, 分别命名为Start和End. For this example, we have created two tops called Start and End. Select these for the analysis window.

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练习8: 由井到井的预测

点击Next >> , 直到出现外部属性页:

Finally, click on Next >> to show the External Attributes page:

外部属性列表给出了GEOVIEW数据库中所有的测井曲线. 点击Add all >>选择EMERGE中所用的属性. 之后出现两个对话框, 其一是通知你正在创建的井曲线, 其二是显示4口井中不存在的井曲线. EMERGE将会建立剩下的6条曲线与目标声波曲线之间的关系.

The list of possible External Attributes shows all of the log curves present in at least one well of the GEOVIEW database. Click on Add all >> to select the attributes that will actually be used by EMERGE. You will see two dialogs appear as the database is analyzed. The first informs you that a list of logs is being built, and the second shows the logs that are not found in all four wells. EMERGE will look for a relationship between the remaining six logs and the target sonic log.

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练习8: 由井到井的预测

点击OK之后. EMERGE主窗口显示如下:

After you click OK, the EMERGE main window will look like this:

移动滚动条, 可以看到4口井的测井曲线, 其中的两口井不包含目标曲线.

By moving the scroll bar, you can see each of the four wells and their associated logs. You will also notice that two of the wells do not contain target logs.

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练习8: 由井到井的预测

点击Display / Crossplot . 填写该菜单如下所示:

Now click on Display / Crossplot. Fill in the menu as shown below:

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练习8: 由井到井的预测

交绘图结果如下: The resulting plot looks like this:

显然, P波曲线和伽玛曲线显示出极强的线性关系, 相关系数为0.82.

Obviously, the P-wave logs and the Gamma Ray show a strong linear relationship with a correlation of 0.82.

再回到EMERGE的主窗口, 点击Display / Crossplot , 选中属性RILD:

Now go once again to the EMERGE main window and select Display / Crossplot. This time select RILD as the attribute:

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练习8: 由井到井的预测

新的交绘图如下所示: The new cross plot looks like this:

很清楚,它们的关系不是线性的.再回到EMERGE的主窗口, 点击Display / Crossplot , 将目标曲线(声波曲线)求对数, 然后计算它与属性RILD之间的关系:

Clearly, this relationship is not linear. Instead, go back to the EMERGE main window once again and click on Display / Crossplot. On the menu, choose the option to apply the Log transform to both the target (sonic log) and attribute (RILD):

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练习8: 由井到井的预测

交会图如右图所示: Now the cross plot looks like this:

分析表明, 这种变换有时有助于目标曲线与属性之间的非线性变换. 更为幸运的是, EMERGE能够确定用哪种变换. 点击Attribute / Create Single Attribute List, 可以看到单属性变换. 填该菜单, 如下:

This analysis demonstrates that sometimes it helps to apply a nonlinear transform to either the target or the attribute or both. Fortunately, EMERGE can help determine which transform to apply. To see the single-attribute transforms, click on Attribute / Create Single Attribute List. Fill in the menu as shown:

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练习8: 由井到井的预测

注意到选项“Test Non-Linear Transforms of Target”和“Test Non-Linear Transforms of External Attributes”被核查. 这意味着所选择的外部属性诸如Caliper, Gamma Ray, 等等经过一系列非线性变换之后会成为一些新的属性.

Notice that the options “Test Non-Linear Transforms of Target” and “Test Non-Linear Transforms of External Attributes” are checked. This means that for each of the selected External Attributes, Caliper, Gamma Ray, etc. EMERGE will create a series of new attributes by applying a set of non-linear transforms.点击Ok, 下面的列表会出现:

Click on Ok on this menu, and the following table will appear:

上表表明, 1/(P-wave) 与Log(RILM)之间的误差最小. 相关系数达到0.87.

This table shows that the lowest error is obtained by cross plotting 1/(P-wave) against Log(RILM). The correlation for this transform is 0.87.

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在第一行选中any cell, 点击Cross Plot, 交会图如下:

To see this cross plot, select any cell in the first row and click on Cross Plot. The following display appears:

练习8: 由井到井的预测

在第一行选中any cell, 点击Apply, 菜单显示如下:

Now once again, select any cell in the first row and click on Apply. The following display appears:

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练习8: 由井到井的预测

该图显示了4条预测的声波曲线(红色标识). 包含目标曲线的两口井则用黑色表识所预测的声波曲线. 点击View / Zoom features会看出运用RILM 曲线预测声波曲线的效果.

This display shows all four predicted sonic logs in red. Two of the wells, which contain target logs, show those logs in black. By using the View / Zoom features, you can see how well the target sonic log has been predicted using the RILM curve:

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点击Attribute / Create Multi Attribute List, 进行多属性分析. 在第一页菜单上, 选中所有的井, 点击Next>>, 按照下面所示填充第二页:

Now start the multi-attribute analysis by clicking on Attribute / Create Multi Attribute List. On the first page, select all the wells for analysis, and click on Next >>. Fill in the second page as shown below:

练习8: 由井到井的预测

对于从井到井的预测, 我们倾向于使用作用因子的长度为1, 常规的多回归算法中即如此. 我们还要验证目标曲线与外部属性之间的非线性变换.

Note that for the log prediction from other logs, we tend to use an Operator Length of 1, which is conventional multi-regression. We are also testing the non-linear transforms of both the target and the external attributes. When the analysis is complete the following table appears:

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与前面一样, 每条线代表着一个多属性变换, 其中包含的属性各不相同. 举例: 第三条线,属性(Density)**2 代表着它与Log(RILM),Gamma Ray, (Density)2的变换. 上面的曲线显示着校验误差. 显然, 本例中的最佳属性个数应为3.

Just as before, each line on this table represents a multi-attribute transform containing all the attributes down to that line. For example, the third line, with the attribute (Density)**2, represents the transform with Log(RILM),Gamma Ray, and Square of (Density). As before, the upper curve on the prediction error plot shows the validation error for the log that was hidden during the analysis. Clearly, the proper number of attributes to use in this case is three.

练习8: 由井到井的预测

选择第三个属性(Density)**2 , 绘制交会图, 如下:

Now, select the name (Density)**2 (the third attribute) from the list and click on Cross Plot. This display appears:

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该交会图显示出预测得到的P波曲线与真实的P波曲线之间的相关性, 相关系数为0.93, 拟合的非常好.

This plot shows that the correlation between the Predicted and Actual P-wave logs is 0.93, indicating a very good fit.选中属性(Density)**2, 点击List, 列表如下:

Now, select the name (Density)**2 (the third attribute) from the list and click on List. This table appears:

练习8: 由井到井的预测

上表显示出了各个属性应用于变换时的权重大小.

The table shows the actual weights to be applied to each of the logs in order to predict the sonic log.

最后, 选中属性(Density)**2, 点击Apply, 显示如下:

Finally, select the name (Density)**2 (the third attribute) from the list and click on Apply. This display appears:

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练习8: 由井到井的预测

点击File / Export to Database, 将所预测的曲线到会GEOVIEW数据库中. 点击Add all >>输出声波曲线.

On this display, click on File / Export to Database. This will cause the predicted logs to be sent back to the GEOVIEW database, where they can be used just like any other log. Click on Add all >> to export the sonic log from EMERGE to every well in the database.

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练习8: 由井到井的预测

回到GEOVIEW主窗口, 双击B_Yates_13图标. 新的曲线Emerge_DLT 出现了.

To verify that this happened, go back to the GEOVIEW main window, and double-click on the second well icon (B_Yates_13). The new log Emerge_DLT now appears:

点击File / Exit, 退出EMERGE程序.

This completes the analysis of the third data set. To close the EMERGE program, click on on the EMERGE main window.

When you see the question:

Do you want to save the project?

Click on Yes.

(End of Exercise 8)(练习8毕)

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EMERGE课程总结

Summary of the EMERGE Course

  • EMERGE是由地震属性来预测井的特性的一个程序.
  • EMERGE is a program that predicts log properties from seismic attributes.
  • 属性可以是由EMERGE产生的内部属性, 也可以是由别的程序产生的外部属性.
  • Attributes may be internal (generated by EMERGE) or external (generated by other programs).
  • EMERGE 将运用井位处的学习数据来确定一种关系, 然后将其应用于地震体.
  • EMERGE uses training data at well locations to determine a relationship, which is then applied to a seismic volume.
  • EMERGE不是假定某一特定的模型, 而是运用统计分析的方法去确定属性与井之间的关系.
  • EMERGE does not assume any particular model, but uses statistical analysis to determine the attribute/log relationship.
  • EMERGE利用 step-wise回归来确定属性的最佳个数.
  • EMERGE uses step-wise regression to determine the optimal ordering of attributes.
  • EMERGE 利用有效性来确定属性的最佳个数.
  • EMERGE uses validation to determine the optimal number of attributes.
  • EMERGE的交会图中包括褶积因子, 它可以解释目标体与属性之间的频率差.???
  • EMERGE extends cross plotting to include the convolutional operator, which accounts for frequency differences between target and attributes.
  • EMERGE 算法可以用于从井到井的预测.
  • The EMERGE algorithm may be used to predict logs from other logs.
  • EMERGE通过运用神经网络来提高高频分辨率和进行分类.
  • EMERGE uses Neural Networks to enhance the high frequency resolution and perform classification.