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Environmental and Exploration Geophysics II. Common MidPoint (CMP) Records and Stacking. tom.h.wilson tom.wilson@mail.wvu.edu. Department of Geology and Geography West Virginia University Morgantown, WV. Stack Trace. Pure signal.

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slide1

Environmental and Exploration Geophysics II

Common MidPoint (CMP) Records and Stacking

tom.h.wilson

tom.wilson@mail.wvu.edu

Department of Geology and Geography

West Virginia University

Morgantown, WV

Tom Wilson, Department of Geology and Geography

slide2

Stack Trace

Pure signal

If we sum all the noisy traces together - sample by sample - we get the trace plotted in the gap at right. This summation of all 16 traces is referred to as a stack trace.

Note that the stack trace compares quite well with the pure signal.

Greenbrier

Huron

Onondaga

Wherei is the trace number and j is a specific time

Tom Wilson, Department of Geology and Geography

slide3

Noise

Noise comes in several forms - both coherent and random. Coherent noise may come in the form of some unwanted signal such as ground roll. A variety of processing and acquisition techniques have been developed to reduce the influence of coherent noise.

Random noise can come in the form of wind, rain, mining activities, local traffic, microseismicity ...

+1

-1

The basic nature of random noise can be described in the context of a random walk -

See Feynman Lectures on Physics, Volume 1.

Tom Wilson, Department of Geology and Geography

slide4

The random walk attempts to follow the progress one achieves by taking steps in the positive or negative direction purely at random - to be determined, for example, by a coin toss.

+1

-1

Tom Wilson, Department of Geology and Geography

slide5

Does the walker get anywhere?

Our intuition tells us that the walker should get nowhere and will simply wonder about their point of origin.

However, lets take a look at the problem form a more quantitative view.

It is easy to keep track of the average distance the walker departs from their starting position by following the behavior of the average of the square of the departure. We write the average of the square of the distance from the starting point after N steps as

The average is taken over several repeated trials.

Tom Wilson, Department of Geology and Geography

slide6

After 1 step

will always equal 1 ( the average

of +12 or -12 is always 1. After two steps -

which is 0 or 4 so that the average is 2. After N steps

Tom Wilson, Department of Geology and Geography

slide7

Averaged over several attempts to get home the wayward wonderer gets on average to a distance squared

from the starting point.

Since

=1, it follows that

and therefore that

Tom Wilson, Department of Geology and Geography

slide8

The results of three sets of random coin toss experiments

See Feynman Lectures on Physics, Volume 1.

Tom Wilson, Department of Geology and Geography

slide9

The implications of this simple problem to our study of seismic methods relates to the result obtained through stacking of the traces in the common midpoint gather.

The random noise present in each trace of the gather (plotted at left) has been partly but not entirely eliminated in the stack trace.

Just as in the case of the random walk, the noise appearing in repeated recordings at the same travel time, although random, does not completely cancel out

Tom Wilson, Department of Geology and Geography

slide10

The relative amplitude of the noise - analogous to the distance traveled by our random walker- does not drop to zero but decreases in amplitude relative to the signal.

If N traces are summed together, the amplitude of the resultant signal will be N times its original value since the signal always arrives at the same time and sums together constructively.

The amplitude of noise on the other hand because it is a random process increases as

Hence, the ratio of signal to noise is

or just

where N is the number of traces summed together or the number of traces in the CMP gather.

Tom Wilson, Department of Geology and Geography

slide11

In the example at left, the common midpoint gather consists of 16 independent recordings of the same reflection point.

The signal-to-noise ratio in the stack trace has increased by a factor of 16 or 4.

The number of traces that are summed together in the stack trace is referred to as its fold – i.e. 16 fold.

Tom Wilson, Department of Geology and Geography

slide12

N=80

To double the signal to noise ratio we must quadruple the fold

Question -

If you had a 20 fold dataset and wished to improve its signal-to-noise ratio by a factor of 2, what fold data would be required?

Square root of 20 = 4.472

Square root of N(?) = 8.94

What’s N

Tom Wilson, Department of Geology and Geography

slide13

The reliability of the output stack trace is critically dependant on the accuracy of the correction velocity.

Tom Wilson, Department of Geology and Geography

slide14

Stack = Summation

Average Amplitude

Accurate correction ensures that the same part of adjacent waveforms are summed together in phase.

Tom Wilson, Department of Geology and Geography

slide15

If the stacking velocities are incorrect ….

then the reflection response will be “smeared out” in the stack trace through destructive interference between traces in the sum.

Tom Wilson, Department of Geology and Geography

slide16

The real world: multilayer reflections

Are they also hyperbolic?

The two-term approximation to the multilayer reflection response is hyperbolic. The velocity in this expression is a root-mean-square velocity.

Tom Wilson, Department of Geology and Geography

slide17

A series of infinite terms – but we just ignore a bunch of them

The sum of squared velocity is weighted by the two-way interval transit times ti through each layer.

Tom Wilson, Department of Geology and Geography

slide18

The approximation is hyperbolic, whereas the actual is not. The disagreement becomes significant at longer offsets, where the actual reflection arrivals often come in earlier that those predicted by the hyperbolic approximation.

Tom Wilson, Department of Geology and Geography

slide19

Refraction into high velocity layers brings the events in along paths that don’t have hyperbolic moveout.

Greenbrier Limestone

Big Injun

The reason for this becomes obvious when you think of the earth as consisting of layers of increasing velocity. At larger and larger incidence angle you are likely to come in at near critical angles and then will travel significant distances at higher than average (or RMS) velocity.

Tom Wilson, Department of Geology and Geography

slide20

Different kinds of velocity

VRMS VAV and VNMO are different. VNMO does not equal VRMS. Each of these 3 velocities has different geometrical significance.

Tom Wilson, Department of Geology and Geography

slide21

The VNMO is derived form the slope of the regression line fit to the actual arrivals.

In actuality the moveout velocity varies with offset.

The RMS velocity corresponds to the square root of the reciprocal of the slope of the t2-x2 curve for relatively short offsets.

Tom Wilson, Department of Geology and Geography

slide22

The general relationship between the average, RMS and NMO velocities is shown at right.

Tom Wilson, Department of Geology and Geography

slide23

Geometrically the average velocity characterizes travel along the normal incidence path.

The RMS velocity describes travel times through a single layer having the RMS velocity. It ignores refraction across individual layers.

Tom Wilson, Department of Geology and Geography

slide24

Other benefits derived from Stacking

Seeing double?

Tom Wilson, Department of Geology and Geography

slide25

Normal Incidence Time Section ….

Water Bottom Reflection

Reflection from Geologic interval

Water Bottom Multiple

Tom Wilson, Department of Geology and Geography

slide26

Interbed Multiples

DEPTH

Tom Wilson, Department of Geology and Geography

slide27

Interbed Multiples

Tom Wilson, Department of Geology and Geography

slide28

The Power of Stack extends to multiple attenuation

Tom Wilson, Department of Geology and Geography

slide29

Velocities associated with primary reflections are higher than those associated with multiples. The primaries are flattened out while residual moveout remains with the multiple reflection event.

The NMO Corrected CDP gather

Tom Wilson, Department of Geology and Geography

slide30

Multiple attenuation

Primary Reflections

Multiple

Multiple

Tom Wilson, Department of Geology and Geography

slide31

Examples of multiples in marine seismic data

Buried graben or multiple

Tom Wilson, Department of Geology and Geography

slide32

Multiples are considered “coherent” noise or unwanted signal

Tom Wilson, Department of Geology and Geography

slide33

Interbed multiples or Stacked pay zones

Tom Wilson, Department of Geology and Geography

slide35

Waterbottom and sub-bottom multiples

Tom Wilson, Department of Geology and Geography

slide36

Other forms of coherent “noise” will also be attenuated by the stacking process.

The displays at right are passive recordings (no source) of the background noise.

The hyperbolae you see are associated with the movement of an auger along a panel face of a longwall mine.

Tom Wilson, Department of Geology and Geography

slide37

Problem 4.4

Table 1 (right) lists reflection arrival times for three reflection events observed in a common midpoint gather. The offsets range from 3 to 36 meters with a geophone spacing of 3 meters.

Conduct velocity analysis of these three reflection events to determine their NMO velocity. Using that information, determine the interval velocities of each layer and their thickness.

Tom Wilson, Department of Geology and Geography

slide38

Note hyperbolic moveout of the three reflection events.

Tom Wilson, Department of Geology and Geography

slide39

Recall -

2

2

t - x

The variables t2 and x2 are linearly related.

Tom Wilson, Department of Geology and Geography

slide40

Estimates of RMS velocities can be determined from the slopes of regression lines fitted to the t2-x2 responses.

Keep in mind that the fitted velocity is actually an NMO velocity!

Then what?

Tom Wilson, Department of Geology and Geography

slide41

Dix Interval Velocity

Start with definition of the RMS velocity

The Vis are interval velocities and the tis are the two-way interval transit times.

Tom Wilson, Department of Geology and Geography

slide42

Let

the two-way travel time of the nth reflector

Tom Wilson, Department of Geology and Geography

slide43

hence

Tom Wilson, Department of Geology and Geography

slide44

Since

Vn is the interval velocity of the nth layer

tn in this case represents the two-way interval transit time through the nth layer

Tom Wilson, Department of Geology and Geography

slide45

Hence, the interval velocities of individual layers can be determined from the RMS velocities, the 2-way zero -offset reflection arrival times and interval transit times.

Tom Wilson, Department of Geology and Geography

slide46

Review: terms in the Dix Equation

See Berger et al. page 173

The

terms represent the velocities obtained from the best fit lines. Remember these velocities are actually NMO velocities.

the two-way travel time to the nth reflector surface

the two-way interval transit time between the n and n-1 reflectors

is the interval velocity for layer n, where layer n is the layer between reflectors n and n-1

Tom Wilson, Department of Geology and Geography

slide47

Dix Interval Velocity

The interval velocity that’s derived from the RMS velocities of the reflections from the top and base of a layer is referred to as the Dix interval velocity.

However, keep in mind that we really don’t know what the RMS velocity is.

The NMO velocity is estimated from the t2-x2 regression line for each reflection event and that NMO velocity is assumed to “represent” an RMS velocity.

You put these ideas into application when solving problems 4.4 and 4.8

Tom Wilson, Department of Geology and Geography

slide48

Coherent Noise

Stacking helps attenuate random and coherent noises

  • Multiples
  • Refractions
  • Air waves
  • Ground Roll
  • Streamer cable motion
  • Scattered waves from off line

Tom Wilson, Department of Geology and Geography

slide49

Back to your computer projects. Please review the Summary Activities and Report Handout. We are at the mid point in the semester and time will run out quickly.

Questions about gridding and math on two maps topics covered in the last lecture?

Tom Wilson, Department of Geology and Geography

slide50

Conversion to Depth

Tom Wilson, Department of Geology and Geography

slide51

Average velocity map

Tom Wilson, Department of Geology and Geography

slide52

Without Extrapolation

Tom Wilson, Department of Geology and Geography

slide53

With Extrapolation

Tom Wilson, Department of Geology and Geography

slide54

Increased projection distance

Tom Wilson, Department of Geology and Geography

slide55

Time Surface

Tom Wilson, Department of Geology and Geography

slide57

Wells > Edit > Time Depth Charts

Tom Wilson, Department of Geology and Geography

slide58

Interval Velocity

Tom Wilson, Department of Geology and Geography

slide59

Formation top approach (times derived from TD chart and formation top depths from well file)

Tom Wilson, Department of Geology and Geography

slide60

Time horizon

Tom Wilson, Department of Geology and Geography

slide61

Conversion to depth

Tom Wilson, Department of Geology and Geography

slide62

Time vs. Depth

Tom Wilson, Department of Geology and Geography

slide63

Mark your calendar

  • Problem 4.1 is due today
  • Problems 4.4 and 4.8 are due 1st Wednesday following Spring Break.
  • Look over Exercises IV-V. These will be due 1st Monday after Spring Break.
  • Exercise VI will be due Wednesday after Spring Break
  • For the remainder of today – Conversion to depth and project work.
  • Mid Term Reports are due the Monday March 23rd.

Tom Wilson, Department of Geology and Geography