environmental and exploration geophysics ii

Tom Wilson, Department of Geology and Geography

Environmental and Exploration Geophysics II

[email protected]

Department of Geology and GeographyWest Virginia University

Morgantown, WV

Common MidPoint (CMP) Records Common MidPoint (CMP) Records and Stackingand Stacking


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.

Stack Trace

Pure signal

Greenbrier

Huron

Onondaga

1

n

iji

a

Where i is the trace

number and j is a specific time


+1-1

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.

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

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

See Feynman Lectures on Physics, Volume 1.


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


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 2

ND

The average is taken over several repeated trials.


21DAfter 1 step will always equal 1 ( the

average

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

212

12

2 1or 1 DDD

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

1or 1 11 NNN DDD

121 12

12

1 NNN DDD

121 12

12

1 NNN DDD


121 12

12

1 NNN DDD

121 12

12

1 NNN DDD

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

121

2 NN DD

from the starting point.

Since 2

1D =1, it follows that

NDN 2

and therefore that NDN


The results of three sets of random coin toss experiments

See Feynman Lectures on Physics, Volume 1.


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


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

N

Hence, the ratio of signal to noise is N

Nor just

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

N


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.


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

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


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


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

Average Amplitude

Stack = Summation


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

between traces in the sum.

If the stacking velocities are incorrect ….


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

Are they also hyperbolic?

The real world: multilayer reflections


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

layer.

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


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.


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.

Greenbrier Limestone

Big Injun

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


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

significance.


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.


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


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.


Water Bottom Reflection

Reflection from Geologic intervalWater Bottom

Multiple

Normal Incidence Time Section ….


DEPTH

Interbed Multiples


Interbed Multiples


The Power of Stack extends to multiple attenuation


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


Multiple attenuation

Multiple Multiple

Primary Reflections


Buried graben or multiple

Examples of multiples in marine seismic data


Multiples are considered “coherent” noise or unwanted signal


Interbed multiples or Stacked pay zones


Waterbottom and sub-bottom multiples


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.


Offset (m) Reflection1 Reflection2 Reflection3

x t1 (ms) t2 (ms) t3 (ms)

3 21.4 62.3 79.4

6 25 62.4 79.5

9 30.1 62.6 79.6

12 36.1 62.9 79.9

15 42.5 63.2 80.1

18 49.2 63.6 80.5

21 56.2 64.1 80.9

24 63.3 64.7 81.3

27 70.4 65.4 81.8

30 77.6 66.1 82.4

33 84.9 66.9 83

36 92.2 67.7 83.7

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.


0 5 10 15 20 25 30 35 40

Source Receiver Offset (meters)

0

20

40

60

80

100

Arr

ival

Tim

e (m

s)

Note hyperbolic moveout of the three reflection events.


22 2

0 2rms

xt t

V

Recall -

The variables t2 and x2 are linearly

related.20

2

is the intercept &

1 is the slope

rms

t

V


0

2000

4000

6000

8000

10000

Tim

e2

0 200 400 600 800 1000 1200 1400

X2

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!


Start with definition of the RMS velocity

n

ii

n

iii

nRMS

t

tVV

1

1

2

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


n

ii

n

iii

nRMS

t

tVV

1

1

2

2

n

iintt

10Let

the two-way travel time of the nth reflector


n

iiinnRMS tVtV

1

20

2

1

1

220

2n

iiinnnnRMS tVtVtV

hence


102

1022

nnRMSnnRMSnn tVtVtV

1

1

210

21

n

iiinnRMS tVtVSince

102

12

02

nnRMSnnnnRMS tVtVtV

Vn is the interval velocity of the nth layer

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


102

1022

nnRMSnnRMSnn tVtVtV

n

nnRMSnnRMSn t

tVtVV 10

210

22

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.


n

nnRMSnnRMSn t

tVtVV 10

210

22

n

iitt

n1

0 the two-way travel time to the nth reflector surface

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

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

actually NMO velocities.

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

n-1

See Berger et al. page 173


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


•Multiples

•Refractions

•Air waves

•Ground Roll

•Streamer cable motion

•Scattered waves from off line

Stacking helps attenuate random and coherent noises


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?


Without Extrapolation


With Extrapolation


Increased projection distance


Time Surface


Wells > Edit > Time Depth Charts


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


Time horizon


Conversion to depth


• 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.

environmental and exploration geophysics ii

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