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Hampson-Russell Software Services Ltd. EMERGE WORKSHOP. Theory and Exercises. EMERGE Course Outline. EMERGE 简介 3 Exercise 1: Setting up an EMERGE Project7 地震属性 32 交会图 54 Exercise 2: The Single-Attribute List59 多属性 69 验证属性 76

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Hampson russell software services ltd

Hampson-Russell Software Services Ltd.

EMERGE

WORKSHOP

Theory and Exercises


Emerge course outline

EMERGE Course Outline

  • EMERGE 简介 3

  • Exercise 1: Setting up an EMERGE Project7

  • 地震属性32

  • 交会图54

  • Exercise 2: The Single-Attribute List59

  • 多属性69

  • 验证属性76

  • Exercise 3: The Multi-Attribute List82

  • 使用褶积算子89

  • Exercise 4: The Convolutional Operator94

  • Exercise 5: Processing the 3D Volume99

  • EMERGE 里的神经网络110

  • Exercise 6: Predicting Porosity Logs140

  • 训练神经网络162

  • Exercise 7: Using Neural Networks177

  • Exercise 8: Predicting Logs from Logs200

  • EMERGE 课程总结222


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EMERGE 简介

EMERGE 程序的目标:

  • EMERGE 是一个分析分析井曲线和地震数据的程序。

  • 它寻找井点处的地震数据与测井曲线之间的关系。

  • 它利用这个关系在地震数据体内“预测”或估算测井曲线属性。

    EMERGE 使用的数据:

  • 一个地震数据体(通常是三维的)。

  • 一些与地震数据标定好了的井。

  • 每一口井包含一个将要预测的“目标”曲线,例如孔隙度。

  • 每一口井也要包含时深转换信息,通常是时深校正过的声波曲线。

  • (可选的):一种或多种3D地震属性。


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EMERGE简介

测井曲线必须加载到 GEOVIEW 数据库中:

这张图显示了单口井的数据:


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EMERGE简介

理论上来说,任何类型的测井曲线属性都可以作为 EMERGE 预测的目标。

实际上,下面的曲线类型都已经成功地预测过:

  • P波速度

  • 孔隙度

  • 密度

  • 伽玛曲线

  • 水饱和度

  • 岩性曲线

    唯一的要求是:每一口井必须有目标曲线作为样板。

    因为 EMERGE 假设目标曲线是不含噪声的,在应用EMERGE 前编辑目标曲线是很重要的。

    因为 EMERGE 把目标曲线与地震数据作相关,正确的时深转换是很关键的。因此,时深校正和手工相关是必要的。


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EMERGE 简介

EMERGE 可以被认为是常规迭后反演的扩展:


Exercise 1 setting up an emerge project

Exercise 1: Setting up an EMERGE Project

Estimating P-Wave Velocity from Seismic Attributes

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.

The data set consists of the following:

  • A SEGY file, seismic.sgy, which is a 3D post-stack data set.

  • A SEGY file, inversion.sgy, which is the 3D result of performing inversion on the input seismic data.

  • 12 wells that tie the two SEGY files. Each of these wells contains a sonic log and a check-shot file.

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


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Loading the Data

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

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


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Loading the Data

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:

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


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Starting EMERGE

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:

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):


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Starting EMERGE

The EMERGE main window now appears:

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. 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.


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Starting EMERGE

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:

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.

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 >>.


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Starting EMERGE

The menu now looks like this:

Now click on the Next >> button at the bottom of the menu. The new page will now appear:


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Starting EMERGE

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. 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.Click on the Next >> button at the bottom of the menu. The new page will now appear:


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Starting EMERGE

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. 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.

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:


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Starting EMERGE

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:

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.


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Starting EMERGE

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.Now we will read in the seismic training data. To do this click on Seismic / Add Seismic Input / From File. The following menu appears:


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Starting EMERGE

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

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


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Starting EMERGE

The next menu that appears is this one:

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.


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Starting EMERGE

Click on Next >> to get this menu:

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.


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Starting EMERGE

Click on Next >> again to get this menu:

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.

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.


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Starting EMERGE

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:


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Starting EMERGE

The second window shows the seismic data:

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.


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Starting EMERGE

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 Neighbourhood 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.


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Starting EMERGE

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:


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Starting EMERGE

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:

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


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Starting EMERGE

Specify the general format:

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

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.


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Starting EMERGE

Describe the geometry:

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:


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Starting EMERGE

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:

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.


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Starting EMERGE

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.


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Starting EMERGE

To examine (and possibly change) the analysis window, click on Wells / Set Analysis Windows to get the following table:

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

(End of Exercise 1)


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地震属性

地震属性是地震道的变换,通常是非线性的。

两种类型的属性:

基于采样的:地震道上一个样点一个样点的计算出来的。

例如:振幅包络。

基于层位的:由两个层位之间的平均值计算出来 。

例如:两层之间的平均孔隙度

对EMERGE而言,所有的属性必须都是基于采样的。

地震属性的例子:


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地震属性

EMERGE 能够计算下列的内部属性:

振幅包络

振幅加权的相位余弦

振幅加权的频率

振幅加权的相位

平均频率

视极性

瞬时相位余弦

差分

瞬时振幅的差分

主频

滤波切片

瞬时频率

瞬时相位

积分

绝对振幅积分

二阶差分

瞬时振幅的二阶差分


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地震属性

EMERGE 也可以输入外部属性。 这些是不能通过内部计算得来的地震属性, 因为:

它们是特有的–比如: 相关性。

它们太复杂–比如地震反演, AVO属性, 等等。

内部属性可以归为以下几类:

瞬时属性

加窗的频率属性

滤波切片

差分属性

积分属性

时间(线性渐变)

以地震数据为例,现在来了解一下关于每一组属性的理论。


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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)的概念。瞬时属性从复地震道C(t)导出, C(t) 由地震道s(t)和它相应的Hilber变换 h(t)组成, h(t) 相当于将s(t)进行90 °相移。复数道以极坐标形式表示如下,我们得到了两个基本属性:振幅包络A(t)和瞬时相位f(t),(注意: 瞬时振幅与振幅包络表示同一个意思)。


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瞬时属性

第三个基本属性是瞬时频率,它是瞬时相位对时间的导数。 方程如下:

EMERGE中,其它的瞬时属性便是以上三种瞬时属性的组合, 如下所示:

视极性属性是振幅包络乘以地震道样点在波峰的极性符号而得,应用于波峰两边波谷之间的一段地震样点。


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瞬时属性

现在,我们来看一下应用于所输入的3D数据体inline95线的每一个瞬时属性的例子。下面这条线用颜色表示振幅值上面覆盖了波形道,08-08井的声波测井曲线也覆盖在地震数据上了。


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瞬时属性

inline 95线的瞬时相位

inline 95线的振幅包络


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瞬时属性

inline95线的瞬时相位余弦

inline 95 振幅的加权相位余弦


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瞬时属性

inline 95线的振幅加权相位

inline 95线的视极性


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瞬时属性

inline 95线的瞬时频率

inline 95线的振幅的加权频率


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加窗的频率属性

EMERGE中另一组属性是基于对地震道加窗的频率分析。在这个过程中,每一个地震道的付立叶变换时窗取为64个样点(缺省值)。在这个时窗里,或者选择平均频率振幅,或者选择主频振幅,这个值放在窗口中间。下一个窗口选择32个样点(缺省值),计算新的频率属性,如此进行下去。注意缺省值可以在Attribute/Attribute Parameters 菜单里改变,如下所示。


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加窗的频率属性

inline 95线的主频

inline 95线的平均频率


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滤波切片属性

EMERGE的第三组属性由地震道的窄带频率切片组成。 使用以下6个切片

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

下一张片子上的数字表示最低和最高的频率切片。


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滤波切片属性

inline 95 线的5/10 – 15/20 Hz滤波切片

inline 95 线的55/60 – 65/70 Hz 滤波切片


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导数属性

EMERGE中的第四组属性是基于地震道的一、二阶导数或振幅包络( 或瞬时振幅,瞬时振幅的同义词)。导数用以下的方式计算,这里, si =第 i 个地震或振幅包络样点,d1i =第 i 个一阶导数,d2i =第 i个二阶导数,and Dt =采样率:

下两张片子是inline 95线地震数据的导数的例子:


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导数属性

inline 95线的导数

inline 95线的振幅包络的导数


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导数属性

inline 95线的二阶导数

inline 95 线的振幅包络的二阶导数


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积分属性

EMERGE的第五组属性是基于地震道或振幅包络的(或瞬时振幅,振幅包络的同义词)。积分值用以下方式计算,这里 si =第 i 个地震或振幅包络样点,Ii =积分值。注意这是一个连续求和。

在连续求和之后,对积分地震道应用了确省值为50个样点的圆滑滤波,并去除了结果中的低频趋势。通过除以总样点的最大最小值的差,对积分振幅包络进行归一化。注意确省值可以在 Attribute / Attribute Parameters 菜单里改变,前面已经介绍过了。

下张片子上的积分的例子来自于 inline 95线


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积分属性

inline 95 线的道积分

inline 95 线的振幅包络积分


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时间属性

最后的属性是时间属性。这仅仅是地震道的时间值,它形成了一个渐变函数,给计算的油藏参数加上了一个趋势。

这里有一张时间属性图

inline 95 线的时间属性(注意:在数据体上的任意一条线上看起来都是一样的


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地震属性

EMERGE 实际上是试图寻找目标测井曲线与地震道属性组合之间的关系

井旁道的所有属性


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交会图

度量目标数据与一个属性之间相关程度的方法就是作它们两个的交会图。

这个图显示了目标曲线,地震道,和一个外部属性:


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交会图

这是一个交会图,显示了目标值--P波(垂直轴)与一个特别属性的交会。


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交会图

回归线是这个形式

y = a + b*x

这条线最小化预测总误差:

协方差定义为:

这里的均值是:


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交会图

归一化的协方差定义为:

把回归直线应用到地震数据上得到目标属性的预测曲线:

预测误差是实际目标曲线与预测目标曲线之间的均方根误差。


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交会图

有时可以通过对目标变量或属性变量或两者作非线性变换提高相关值:


Exercise 2 the single attribute list

Exercise 2: The Single-Attribute List

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

Cross plotting:

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

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.


Exercise 2 the single attribute list1

Click on Ok to get this plot:

Exercise 2: The Single-Attribute List

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


Exercise 2 the single attribute list2

Exercise 2: The Single-Attribute List

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

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.


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Performing Single-Attribute Analysis

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:

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.


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Performing Single-Attribute Analysis

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

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.


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Performing Single-Attribute Analysis

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

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:


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Performing Single-Attribute Analysis

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. The Shift Logs menu now shows the suggested shifts:

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.


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Performing Single-Attribute Analysis

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

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).

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


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Performing Single-Attribute Analysis

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

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.


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Performing Single-Attribute Analysis

The resulting plot will look like this:

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. 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. 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.

(End of Exercise 2)


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多属性

使用多属性就是对传统的交会图的扩展。

与一个属性的交会图

与两个属性的交会图


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多属性

多属性线性回归:

在每一个时间样点处,目标曲线被几个属性的线性组合所拟合。


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多属性

用三个属性预测孔隙度:

(t) = w0 + w1I(t) + w2E(t) + w3F(t)

其中 (t) = 孔隙度

I(t) = 声阻抗

E(t) = 振幅包络

F(t) = 瞬时频率

用线性方程组表示为:

1 = w0 + w1I1 + w2E1 + w3F1

2 = w0 + w1I2 + w2E2 + w3FN

. . . . .

N = w0 + w1IN + w2EN + w3FN

矩阵形式为:

  • 或者:P = AW


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多属性

用最小二乘法解此方程组

W = [ATA]-1ATP

展开形式为:

or:

这些系数最小化预测总误差:


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多属性

减小预测误差

N+1个属性的预测误差决不会大于N个属性的预测误差。

我们怎麽这样有把握哪?

如果上述观点不正确的话,我们通过把最后的系数设为零,总能使得预测误差减小。


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多属性

挑选属性的组合:

所有的内部属性和外部属性都已给出了,我们怎麽找到用于预测目标曲线多属性组合?

EMERGE使用所谓的单步回归法的过程:

(1)第1步:通过试验的方法和误差的大小寻找最好的单个属性。对于在属性表里的每个属性,

振幅加权相位

平均频率

视极性等,

计算预测误差。有最低预测误差的属性就是最好的属性。把这个属性称为 attribute1.

(2)第二步:寻找最好的属性对,假设第一个成员是attribute1.对于在表里面的每一个其它属性,形成所有的属性对,

(attribute1,振幅加权相位)

(attribute1,平均频率),等。

有最低预测误差的属性对就是最好的属性对。把这第二个属性称为 attribute2.


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多属性

(3)寻找最好的三属性组,假设前两个成员是attribute1 和 attribute2 .对于在属性表里的每一个其它的属性,形成所有的三属性组,

(attribute1, attribute2,振幅加权相位),

(attribute1, attribute2,平均频率),等。

有最低预测误差的三属性组就是最好的三属性组。把这第三个属性称为 attribute3.

持续进行这个过程,直到满意为止。

减小预测误差:

不管用哪些属性, 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 EN-1。


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多属性的验证

我们怎麽知道何时停止增加属性?

增加属性类似于使用不断增加次数的多项式拟合一条通过一系列点子的曲线。


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多属性的验证

对于每一个多项式,我们能够计算预测误差,也就是实测值与预测值之间的均方根误差。

  • 当多项式次数增加时,预测误差总是减小。

  • 问题是,虽然高次多项式预测训练数据较好,在内插和外插如下所示的数据范围以外的部分时,效果较差。这被称为“过训练”:


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多属性的验证

为了确定多属性的验证误差,EMERGE 使用以下的验证过程:

(1)把整个数据库分为两组:

训练数据库

验证数据库

(2)当用回归方法确定系数时,使用训练数据库。

(3)当度量预测误差时,使用验证数据库。

如上图所示,拟合训练数据训练数据较好的高次多项式,拟合验证数据反而差。这表明多项式的次数太高了。


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多属性的验证

EMERGE通过系统地隐藏掉一些井作验证。

假设我们有5口井:

{Well1, Well2, Well3, Well4, Well5}

假设我们有3个属性:

{Impedance, Envelope, Frequency}

按照这个思路做验证:

(1)隐藏掉 Well1.仅仅使用来自于{Well2, Well3,Well4, Well5}的数据求解回归系数,这就意味着求解方程组系统,包含Well1的这些列没有数据::

1 = w0 + w1I1 + w2E1 + w3F1

2 = w0 + w1I2 + w2E2 + w3FN

. . . . .

. . . . .

N = w0 + w1IN + w2EN + w3FN


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多属性的验证

(2)有了导出的系数,计算 Well1的预测误差。这意味着计算下式:

  • 这里仅仅使用Well1的数据点。我们得到了 Well1的验证误差 E1。

  • (3) 对 Well2, Well3,等重复这个过程,每一次在计算回归系数的过程中隐藏掉选择的井,这口井只是在误差计算中使用。

  • (4)计算所有井的平均验证误差:

  • EA = (E1+E2+E3+E4+E5) / 5


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多属性的验证

这是一张EMERGE 分析的验证图:

水平轴表示在预测中使用的属性数。垂直轴表示均方根预测误差。.

黑色的曲线(下面一点的)表示使用训练数据计算的误差。

红色的曲线(上面一点的)表示使用验证数据计算的误差。

上图表明,当使用5个或更多的属性时,验证误差增加了,意味这这些额外的属性是“过拟合”的。


Exercise 3 the multi attribute list

Exercise 3: The Multi-Attribute List

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

Performing Multi-Attribute Analysis

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

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 >>.


Exercise 3 the multi attribute list1

Exercise 3: The Multi-Attribute List

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

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.


Exercise 3 the multi attribute list2

Exercise 3: The Multi-Attribute List

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

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.

Also, as we did with the Single-Attribute Analysis, we will be testing non-linear transforms on both the target and the external attributes. To verify that these options have been selected, click on Next >> to display the final page of this menu.

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:


Exercise 3 the multi attribute list3

Exercise 3: The Multi-Attribute List

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

You will also see a display of the prediction errors:


Exercise 3 the multi attribute list4

Exercise 3: The Multi-Attribute List

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

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

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:


Exercise 3 the multi attribute list5

Exercise 3: The Multi-Attribute List

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%.

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:


Exercise 3 the multi attribute list6

Exercise 3: The Multi-Attribute List

You may want to compare this result with the prediction using the single attribute. To do that, click on Attribute / Display Single Attribute List, select the first single attribute, 1/Inversion Result, and click on Apply. Mathematically, we have increased the correlation from 51% to 62%.

Return to the Multi-Attribute List table and highlight the words Dominant Frequency, and click on the List button. The following table appears:

This table lists all the weights for each of the seven attributes, as well as the constant.

(End of Exercise 3)


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使用褶积算子

至此,多属性分析把目标曲线上的每一个样点与相应的地震属性上的样点建立了关系:

这个方法是有局限性的,因为它忽略了这个事实,那就是在测井曲线和地震数据间存在着较大的频率成分差别,就像在下面放大的图里所显示的那样:


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使用褶积算子

褶积算子对交会图回归进行了扩展,包含临近的样点:

  • 每一个目标样点都是由利用每一个属性上的一组样点的加权平均预测出来的。这里的加权平均就是褶积。

  • 前一个方程:

  • P = w0 + w1A1 + w2A2 +….+ wNAN

  • 现在替换为:

  • P = w0 + w1*A1 + w2*A2 +….+ wN*AN

  • 这里* 代表被一个算子褶积。


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使用褶积算子

考虑使用两个属性预测孔隙度的例子:

  • 现在让权wi,变成3点褶积算子:

  • wi = [wi(-1), wi(0), wi(1)]

  • 新的矩阵方程变为:

  • 第二项重新整理,得到:

  • 这是一个新的线性方程组系统,在这个系统里每一个权 wi,都被三个权 wi(-1), wi(0), wi(1)替换了。这个线性方程组象以前那样,用最小二乘法求解。 唯一的差别是:对于两个属性,我们现在有 3+3+1 = 7 个参数。


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使用褶积算子

使用褶积算子就像加上了更多的属性:仍然总是改进预测误差, 但是验证误差可能不会改进– “过训练”的风险也增加了。


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使用褶积算子

这个例子表明:当算子长度增加时,训练误差总是减小。

验证误差减小到最小,当算子较长时又增加了。


Exercise 4 the convolutional operator

Exercise 4: The Convolutional Operator

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

Performing Multi-Attribute Analysis

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

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


Exercise 4 the convolutional operator1

Exercise 4: The Convolutional Operator

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:


Exercise 4 the convolutional operator2

Exercise 4: The Convolutional Operator

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:

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


Exercise 4 the convolutional operator3

Exercise 4: The Convolutional Operator

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:


Exercise 4 the convolutional operator4

Exercise 4: The Convolutional Operator

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.

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)


Exercise 5 processing the 3d volume

Exercise 5: Processing the 3D Volume

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

Applying Attributes to the 3D Volume

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:

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.


Exercise 5 processing the 3d volume1

Exercise 5: Processing the 3D Volume

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

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.


Exercise 5 processing the 3d volume2

The display will look like this:

Exercise 5: Processing the 3D Volume

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

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.


Exercise 5 processing the 3d volume3

The next page appears:

Exercise 5: Processing the 3D Volume

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.

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.


Exercise 5 processing the 3d volume4

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

Exercise 5: Processing the 3D Volume

After selecting Amplitude Weighted Frequency, click on Next >> once again to get this menu:


Exercise 5 processing the 3d volume5

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:

Exercise 5: Processing the 3D Volume

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.

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


Exercise 5 processing the 3d volume6

Exercise 5: Processing the 3D Volume

At any time, you may click on Stop and the process will be terminated, saving the SEGY file calculated so far.When the calculation is complete, the following display appears:


Exercise 5 processing the 3d volume7

Exercise 5: Processing the 3D Volume

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:

This page gives you complete control over the color scale.


Exercise 5 processing the 3d volume8

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

Exercise 5: Processing the 3D Volume

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

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


Exercise 5 processing the 3d volume9

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:

Exercise 5: Processing the 3D Volume

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:


Exercise 5 processing the 3d volume10

Exercise 5: Processing the 3D Volume

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:

The data slice shows a low-velocity channel feature extending horizontally across the survey through many of the wells in the project.

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

Do you want to save the project?

Click on Yes.

(End of Exercise 5)


Emerge

在EMERGE里使用神经网络:为什麽使用神经网络?

我们要考虑测井曲线和属性之间的非线性关系:

线性预测

Log

Attribute

非线性预测

Log

Attribute


Emerge1

在EMERGE里使用神经网络

EMERGE里有三种类型的神经网络:

MLFN多层前馈网络,类似于传统的误差反传播。

PNN概率神经网络可以用于作数据分类(类似于聚类分析),或者预测数据(类似于回归分析)。

Discriminant线性分类系统


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MLFN神经网络

每一个训练样本包含输入的属性以及特定时间样点的已知目标值。


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MLFN神经网络训练参数

MLFN训练包括确定优化的节点联结权系数集。根据定义,“最好的”权系数集是那些能够以最小方差预测已知的训练数据的权系数。

这是一个非线性优化的问题。EMERGE 利用模拟退火和共轭梯度法相结合来解这个问题。影响训练时间的主要参数是总迭代次数。在每一次迭代里,有一个固定的共轭梯度迭代次数寻找局部极小。


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MLFN神经网络训练参数

在每一次总迭代中,模拟退火通过在其它的参数空间中进行搜索来改进收敛效果。在任何一次迭代中,是否使用模拟退火是由程序控制的,并且依赖于上一次迭代对收敛效果的改进程度。

从理论上来说,更多的迭代次数总是比较少的迭代次数好,因为程序能够搜索更大的范围寻找全局极小。

在训练进行的过程当中,预测误差是可以看到的:

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


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MLFN神经网络训练参数

控制神经网络预测训练数据的优劣程度的参数是隐蔽层的节点数:

按照经验的做法确省值应该等于输入属性的2/3 。(注意输入的属性数等于实际的属性乘以算子长度)。

增加隐蔽层的节点数总是能更精确地预测训练数据,但是“过训练”的风险性也增加了。


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改变隐蔽层节点数的效果

这些图显示了在利用1个属性进行预测的时候改变隐蔽层节点数的效果:

隐蔽层里有2个节点:

隐蔽层里有5个节点:


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改变隐蔽层节点数的效果

这些图显示了在利用1个属性进行预测的时候改变隐蔽层节点数的效果:

隐蔽层里有5个节点:

隐蔽层里有10个节点:


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MLFN神经网络

优点:

(1)传统形式在所有的有关神经网络的书籍里已经讲解的很清楚了。

(2)一旦训练好了,当应用到大数据体上时,相对要快一些。

缺点:

(1)这个网络趋向于是一个“黑匣子” ,没有办法明显的解释权系数。

(2)因为模拟退火使用随机数发生器搜索全局优化,用同一个参数进行训练可能会产生不同的结果。


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概率神经网络 (PNN)

概率神经网络PNN,是在EMERGE 中所使用的第二类神经网络。PNN 既可以用于分类也可以用于映射。

PNN用于分类方面,EMERGE 把输入的地震样点分成N类( 例如:砂、泥、碳氢、油、气、水等) 。我们以后就会看到,在EMERGE里,也可以使用线性聚类分析(LDA),而PNN 可以被看作LDA的非线性扩展。

PNN用于映射方面,EMERGE 把输入的地震数据映射成像孔隙度这样的油藏参数。这与我们利用多线性回归和MLFN所作的预测是相同的,但是,PNN 使用不同的方法。用于映射的PNN更准确的名称应该是广义回归神经网络GRNN,但是我们对映射和分类统一使用名称PNN 。)

为了理解PNN,我们首先了解一下属性空间中的“距离”的概念,然后开始解决分类的问题。


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概率神经网络 (PNN)

假设在一张图上有三个点 (p1, p2, 和 p3)它们是X 、Y 坐标的函数,我们要建立它们与 p0点的关系:

y2

p1

p2

y1

d2

d1

p0

y0

d3

Y

p3

y3

x0

x3

x2

x1

X

我们可以利用每一点到 p0的距离建立这个关系:

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

现在我们再看一看前面的测井曲线和地震属性图,这张图上我们去掉了第三个属性。如果我们把这两个属性标成X和Y,每个属性上标出了四个点,我们现在把前一张图重新解释为2D属性空间的“距离”。 (如果我们加上第三个属性,我们得到了一个3D空间,3D空间仍然是可以直接观察的。更多的属性产生一个N维空间)。注意我们尚未考虑测井曲线。


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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

现在,我们将仅仅使用测井曲线表示出有两个不同的类A和B, (也许是砂岩和泥岩,或含气砂岩和含水砂岩)。前三个点属于A类,又加了三个点属于B类。

我们看一看在X-Y平面图上是什麽样的。


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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

在上面的图中,所有的六个点都画在属性空间里了,p0点与其它点之间的“距离”都加了标注。注意p0点与A类之间的距离比与B类之间的距离更近。 (注意这仅仅是一张卡通画,与前一张图的比例不一致。)


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概率神经网络 (PNN) 权函数

事实上,PNN 本身并不使用距离,但是给距离加上了指数权函数 (称为Parzen 估算子)。对于这两个类,方程式为:

这里引用著名的 Bayes’ 定理,我们给每一类分配一个概率,如下所示:

判别是很简单的,如果 PA > PB, 那麽 p0点属于A类,如果 PA < PB, 那麽 p0属于B类。


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概率神经网络 (PNN) 权函数

为了直观地观察权函数的结果,这里画出了A类单独的权函数,B类单独的权函数,以及两类放在一起时的权函数。这里的6个点的例子类似于以前的那一个6点的例子。


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概率神经网络 (PNN) 概率函数

这里画出了区分A类和B类的概率函数。注意这是简单的两个属性的2个类的线性问题,大部分的实际应用情况是相当复杂的。


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概率神经网络 (PNN) Sigma值的影响

这里是改变两类的 sigma 值的结果。一种情况下,值太低,结果太“尖”。另一种情况下,值太高,结果太圆滑。


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概率神经网络 (PNN) 映射

Log

Seismic Attributes

p1 to pN known

X

Y

p1

y1

x1

x2

y2

p2

x3

y3

p3

pN

xN

yN

p0

x0

y0

p0 unknown, predict from x0 and y0.

All values known

现在我们再看一看前面的那张测井曲线和地震属性图。现在我们令 pi值等于测井曲线值, 这里只有 p0是未知的。我们看一下预测未知曲线值的公式,它只是分类的扩展。


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概率神经网络 (PNN) 映射

考虑前3个点,我们称之为训练点:

曲线值

属性

我们希望得到一个新的输出点 p0,然而我们知道x0和 y0的值:

就象在分类里一样,我们通过比较与之有关系的属性来求解 p0。

with the “attributes” associated with p1 to p3:


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概率神经网络 (PNN) 映射

现在,把每一个已知的测井曲线训练值乘以指数函数,然后除以指数函数的和。注意所有与x0和 y0有关的距离。

注意上面的方程与多线性回归方程的相似性。然而,在多线性回归里面,协方差矩阵包含测井曲线值与属性本身的交叉乘积,而不是与权函数的乘积。


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概率神经网络 (PNN) 映射

在PNN里,我们通常使用的属性要多于2个:

瞬时振幅

瞬时频率

但是“距离” 以同样的方式计算:

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

而且在分类与映射里使用的权函数也以同样的方式计算。


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概率神经网络 (PNN) 概述

在EMERGE 里PNN 用于分类和映射。

在分类应用里面,我们只需要由未知点与已知点间“距离”决定的权。

“距离”是在多维属性空间中度量的。“距离”被圆滑因子(sigma值)所归一化,sigma值由交叉验证自动确定。

在映射应用里面,权函数乘以已知的测井曲线值,用于求取未知的测井曲线值。

我们现在来EMERGE的特定的菜单项:


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概率神经网络的训练参数

训练PNN 意味着寻找与每个属性的有关的“最好的”sigma值。根据定义,“最好的”sigma值就是具有最小交叉验证误差的那些sigma值。

交叉验证意味着基于井对井隐藏数据,或者基于点对点的隐藏数据。建议井对井的交叉验证为确省值:


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概率神经网络的训练参数

寻找优化的sigma值是一个非线性优化的问题。在EMERGE 里分两步解决:

(1)寻找单个最好的sigma,假设所有的sigma都有相同的值。通过试验一系列的sigma值,找出具有最小验证误差的sigma作为这个sigma值:

因为输入属性都归一化为标准偏差为1.0,最好的 sigma 通常在 0.5 到 1.5 之间。

(2)使用这个单个的全局sigma作为起始点, 使用共轭梯度算法搜索能够最小化验证误差的与每个属性有关的sigma值:

经验表明:改变这些确省参数没有多大益处。


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概率神经网络 显示Sigmas

PNN 训练以后,计算的sigma 可以显示出来:

也可以手工改动这些sigma值:


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概率神经网络 改变 Sigma 的效果

这些图显示了在只有1个属性时改变单个sigma值的效果:

Sigma 自动地优化:

Sigma 减小到优化值的 1/10 :


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概率神经网络 改变 Sigma 的效果

这些图显示了在只有1个属性时改变单个sigma值的效果:

Sigma 自动地优化:

Sigma 减小到优化值的 ½:


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概率神经网络 改变 Sigma值的效果

这些图显示了在只有1个属性时改变单个sigma值的效果:

Sigma 自动地优化:

Sigma 增加到优化值的 2 倍:


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概率神经网络

优点:

(1)因为 PNN 采用数学内插的机制,导出的 sigma 可以解释为给每个属性分配的相对权。

(2)与 MLFN 不一样,训练过程可以重新产生。

(3)在分类模式里,PNN 可以产生概率估计。

缺点:

(1)因为 PNN 保存所有训练数据的拷贝,在3D数据体上的应用处理时间可能很长。应用处理时间与训练样点数成正比。通过应用到一个小的目标窗口的办法部分地解决这个问题。


Exercise 6 predicting porosity logs

Exercise 6: Predicting Porosity Logs

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

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

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

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


Exercise 6 predicting porosity logs1

GEOVIEW will now look like this:

Exercise 6: Predicting Porosity Logs

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:


Exercise 6 predicting porosity logs2

This well contains a porosity log, called den-porosity, along with the other logs.Restart the EMERGE program and select Start a New Project. Call the project porosity as shown below:

Exercise 6: Predicting Porosity Logs

The EMERGE main window will now appear:


Exercise 6 predicting porosity logs3

Exercise 6: Predicting Porosity Logs

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:


Exercise 6 predicting porosity logs4

Exercise 6: Predicting Porosity Logs

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

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.


Exercise 6 predicting porosity logs5

Exercise 6: Predicting Porosity Logs

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

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


Exercise 6 predicting porosity logs6

Exercise 6: Predicting Porosity Logs

Set the general information:

Specify the attribute type and name for both files:


Exercise 6 predicting porosity logs7

Exercise 6: Predicting Porosity Logs

Set the file format (the defaults are correct):


Exercise 6 predicting porosity logs8

Exercise 6: Predicting Porosity Logs

Set the geometry information (the defaults are correct):

Click Ok on this menu.


Exercise 6 predicting porosity logs9

Exercise 6: Predicting Porosity Logs

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

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


Exercise 6 predicting porosity logs10

Exercise 6: Predicting Porosity Logs

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


Exercise 6 predicting porosity logs11

Exercise 6: Predicting Porosity Logs

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:

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.


Exercise 6 predicting porosity logs12

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

Exercise 6: Predicting Porosity Logs

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:


Exercise 6 predicting porosity logs13

Exercise 6: Predicting Porosity Logs

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:

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.


Exercise 6 predicting porosity logs14

The Shift Logs menu now shows the suggested shifts:

Exercise 6: Predicting Porosity Logs

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:


Exercise 6 predicting porosity logs15

Exercise 6: Predicting Porosity Logs

Note that the maximum correlation has now increased to nearly 44%.Now create the multi-attribute list by clicking on Attribute / Create Multi Attribute List and filling in the menu as shown below:

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


Exercise 6 predicting porosity logs16

Exercise 6: Predicting Porosity Logs

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


Exercise 6 predicting porosity logs17

Exercise 6: Predicting Porosity Logs

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

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.


Exercise 6 predicting porosity logs18

Exercise 6: Predicting Porosity Logs

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:

Note that we are choosing to process a segment of the data – a single inline – to save time in this process.

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


Exercise 6 predicting porosity logs19

Exercise 6: Predicting Porosity Logs

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:


Exercise 6 predicting porosity logs20

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:

Exercise 6: Predicting Porosity Logs

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


Exercise 6 predicting porosity logs21

Exercise 6: Predicting Porosity Logs

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

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

(End of Exercise 6)


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训练神经网络

这个菜单允许你产生一个新网络或覆盖一个已经存在的网络。

在EMERGE 工区里不限制储存多少个网络。

你也可以把训练数据写成ASCII文件,以便其它的神经网络程序读取。


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训练神经网络

可以用两种格式输出ASCII文件。

(1)预测格式,在神经元里程序进行“预测”使用的格式:


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训练神经网络

(2)神经格式:许多其它神经网络程序可以使用的格式:

Attribute 1

Attribute 2

Target


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训练神经网络

这一页确定哪些井用于网络训练。

注意,有两个原因把某些井从训练数据中剔除:

(1)井与地震的标定不好。

(2)你可能要使用这口井作“盲测试”,或者以后验证。


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训练神经网络

这一页确定是否前边计算的多属性变换用于作为建立神经网络的模板。

在这里选择 “yes” 意味着神经网络与选择的多属性变换有完全相同的属性和算子长度。

通常建议选择“yes”,因为单步回归法是最好的确定使用哪些属性的方法。


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训练神经网络

这一页只在多属性变换不用作模板时使用。

在这种情况下,在这里可以指定是否使用某一属性或它的非线性变换。


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训练神经网络

这一页确定重要的一般神经网络的特性。

第一个参数是网络类型:


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训练神经网络

这些参数控制在神经网络里去除多属性变换当中的低频趋势这个选项。

这个选项存在的原因是:神经网络处理不包含有长波长趋势的稳定数据效果更好。

有时从目标数据里移去低频趋势会更好,使用神经网络预测移走了低频趋势之后的剩余数据。

在这个选项里,按照以下的步骤进行:

(1)多属性变换用于预测目标测井曲线。

(2)预测的测井曲线使用连续平均进行圆滑。

(3)从原始测井曲线中减去圆滑过的预测曲线。

(4)在剩余或差曲线上作神经网络预测。


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训练神经网络

从多属性变换预测出来的趋势

PNN预测的剩余值

没有去趋势的PNN预测

确定这个选项是否有作用的唯一方法用两种方法产生神经网络,看一看训练误差和验证误差再作决定。


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训练神经网络

映射是预测数值的处理。 在EMERGE 里这是缺省的选项。

分类意味着预测类别或类型。 如果选择了这个选项,必须要提供一些参数,告诉 EMERGE 如何对目标数据进行分类:

如果在以前已经对目标曲线作了分类,目标曲线仍然作为数值读入 EMERGE ,这些数值代表类别。


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训练神经网络

即使对于数字值,有时分类也是有用的,通过分块把输出值的范围减小了:

Mapping

Classification


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训练神经网络

对于以分类模式训练的神经网络,有这样一个选项,它计算和输出与每一个类有关的概率:


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聚类分析

聚类分析是应用在分类模式里的一个数学分族的方法。

例如,假如我们有2个属性X 和 Y ,并且我们我们知道有2个族 A 和 B:

Discriminant

Line

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

因为聚类分析假设两族之间为线性分隔,如果分隔是非线性的,聚类分析可能就失败了:

Attribute

1

Attribute

2

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)训练时间和应用时间比任何其它的神经网络都少。

(2)算法是相当稳健的,很少有“过训练”的可能。这意味着通常交互验证误差与训练误差是很接近的。

缺点:

(1)只能以分类模式使用。

(2)类之间是线性分隔。


Exercise 7 using neural networks

Exercise 7: Using Neural Networks

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

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

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


Exercise 7 using neural networks1

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

Exercise 7: Using Neural Networks

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:


Exercise 7 using neural networks2

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:

Exercise 7: Using Neural Networks

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.


Exercise 7 using neural networks3

Exercise 7: Using Neural Networks

Click on Next >> to get the next page:

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.

Click on Next >> to get the final page:


Exercise 7 using neural networks4

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:

Exercise 7: Using Neural Networks

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:


Exercise 7 using neural networks5

  • 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) The application time for the Neural Network can be very long if applied to the entire window.

    • (2)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.

  • After zooming, the result looks like this:

Exercise 7: Using Neural Networks

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.


Exercise 7 using neural networks6

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

Exercise 7: Using Neural Networks

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

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.


Exercise 7 using neural networks7

When completed, the following plot appears:

Exercise 7: Using Neural Networks

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:


Exercise 7 using neural networks8

Exercise 7: Using Neural Networks

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:

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.

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.


Exercise 7 using neural networks9

Exercise 7: Using Neural Networks

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:

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


Exercise 7 using neural networks10

Exercise 7: Using Neural Networks

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

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


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Exercise 7: Using Neural Networks

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

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

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

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


Exercise 7 using neural networks12

When the training is completed, the following plot appears:

Exercise 7: Using Neural Networks

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.


Exercise 7 using neural networks13

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:

Exercise 7: Using Neural Networks

On the second page, click on Ok to begin the validation calculation:


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Exercise 7: Using Neural Networks

The new validation result appears:

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.

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.

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


Exercise 7 using neural networks15

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

Exercise 7: Using Neural Networks

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

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


Exercise 7 using neural networks16

Click on Next >> to get the parameters page:

Exercise 7: Using Neural Networks

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:


Exercise 7 using neural networks17

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:

Exercise 7: Using Neural Networks

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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Exercise 7: Using Neural Networks

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


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Applying the Neural Network to the 3D Volume

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:

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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Applying the Neural Network to the 3D Volume

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

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. If horizons had been entered into the project, these could have been used to guide the Neural Network application window. 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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Applying the Neural Network to the 3D Volume

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 / Wiggle Traces: Unshown:


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Applying the Neural Network to the 3D Volume

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

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

(End of Exercise 7)


Exercise 8 predicting logs from logs

Exercise 8: Predicting Logs from Logs

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

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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Exercise 8: Predicting Logs from Logs

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:

The GEOVIEW window will now look like this:


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Exercise 8: Predicting Logs from Logs

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:

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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Exercise 8: Predicting Logs from Logs

This list appears:

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


Exercise 8 predicting logs from logs4

Exercise 8: Predicting Logs from Logs

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


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Exercise 8: Predicting Logs from Logs

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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Exercise 8: Predicting Logs from Logs

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

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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Exercise 8: Predicting Logs from Logs

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

For this example, we have created two tops called Start and End. Select these for the analysis window.


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Exercise 8: Predicting Logs from Logs

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

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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Exercise 8: Predicting Logs from Logs

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

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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Exercise 8: Predicting Logs from Logs

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


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Exercise 8: Predicting Logs from Logs

The resulting plot looks like this:

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

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


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Exercise 8: Predicting Logs from Logs

The new cross plot looks like this:

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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Exercise 8: Predicting Logs from Logs

Now the cross plot looks like this:

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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Exercise 8: Predicting Logs from Logs

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

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.


Exercise 8 predicting logs from logs15

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

Exercise 8: Predicting Logs from Logs

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


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Exercise 8: Predicting Logs from Logs

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:


Exercise 8 predicting logs from logs17

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:

Exercise 8: Predicting Logs from Logs

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:


Exercise 8 predicting logs from logs18

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.

Exercise 8: Predicting Logs from Logs

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


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This plot shows that the correlation between the Predicted and Actual P-wave logs is 0.93, indicating a very good fit.Now, select the name (Density)**2 (the third attribute) from the list and click on List. This table appears:

Exercise 8: Predicting Logs from Logs

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

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


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Exercise 8: Predicting Logs from Logs

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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Exercise 8: Predicting Logs from Logs

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:

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

When you see the question:

Do you want to save the project?

Click on Yes.

(End of Exercise 8)


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EMERGE 课程总结

  • EMERGE 是一个利用地震属性预测测井曲线的程序。

  • 地震属性可以是内部的(由 EMERGE 产生的)或者是外部的 (由其它程序产生的)。

  • EMERGE 在每个井点使用训练数据寻找关系,然后把这个关系应用到地震数据体上。

  • EMERGE 不需要一个特定的模型,它使用统计分析确定属性与测井曲线的关系。

  • EMERGE 使用单步回归法确定优选的属性次序。

  • EMERGE 使用验证的方法确定最优的属性数目。

  • EMERGE 把交会图扩展为包含了褶积算子,考虑了目标曲线与地震属性之间的频率差别。

  • EMERGE 方法可以用于从一些测井曲线预测另一条曲线。

  • EMERGE 使用神经网络提高了高频成分,可以进行分类处理。


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