Palmer.03.Digital Processing Of Shallow Seismic Refraction Data.pdf

8/10/2019 Palmer.03.Digital Processing Of Shallow Seismic Refraction Data.pdf

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Chapter 2

Inversion of Shallow SeismicRefraction Data A Review

2.1 - Summary

All methods for inverting shallow seismic refraction data require reversed and

redundant data in order to resolve wavespeeds and structure within each

refractor, and to identify the wavespeed stratification above the target refractor.

However, there are fundamental limitations in accurately determining the

wavespeed stratification from even the most complete sets of data. Not all layers

are necessarily detected in the traveltime data, because some layers are either

too thin, or the wavespeeds are less than that in the overlying layer.

Furthermore, the wavespeed stratification cannot be determined with high

precision within those layers which are detected, because the refracted rays do

not penetrate deeply enough, or because the horizontal rather than the vertical

wavespeed is measured.

The difficulties in accurately determining the inversion model indicate that asmuch of the data processing as possible should be carried out in the time

domain, rather than in the depth domain. The wavespeed analysis and the time-

depth algorithms of the group of processing techniques known as the reciprocal

methods, satisfy these requirements.


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In addition, there is another fundamental issue of non-uniqueness in determining

lateral variations in wavespeeds in the refractor. This requires the use of

refraction migration in order to accommodate the offset distance. However,

incorrect migration distances which would result from the use of incorrect

wavespeeds in the layers above the target refractor, can still generate results

which satisfy the traveltime data. This problem can be overcome with the use of

multiple migration distances with the generalized reciprocal method (GRM) and

the use of the minimum variance criterion.

The GRM is a logical advancement of pre-existing refraction inversion methods.

It combines the horizontal layer approximations of the intercept time method, the

wavespeed analysis and time-depth algorithms of the traditional reciprocal

methods, and the accommodation of the offset distance with refraction migration

of the delay time and Hales methods. The variable migration of the GRM

provides a useful approach to the treatment of undetected layers, wavespeed

reversals, variable wavespeed media, anisotropy and non-uniqueness.

2.2 - Introduction

The refraction method was the first seismic technique to be used in petroleum

exploration, and in the 1920s, it achieved spectacular success in Iran and the

Gulf Coast of the USA. Although refraction methods were soon superseded by

reflection methods, they were still commonly used in many areas where single

fold reflection methods were not effective. However, with the development of

common midpoint methods in the 1950s, the use of refraction methods in

petroleum exploration decreased even further.

Today most seismic refraction surveys are carried out to map targets in the near

surface region for geotechnical, groundwater and environmental applications,


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and for statics corrections for seismic reflection surveys. On a line kilometre

basis, statics corrections clearly constitute the greatest use of the method.

The 1950s represent a significant period in the development of refraction

techniques. Almost all of the major issues had been identified and many

advances had been achieved in the years prior to that date. They include the

mapping of irregular refractors, complex wavespeed functions in the layers above

the target refractor, undetected layers, wavespeed reversals, anisotropy, and

refraction migration.

In the last fifty years, the development of the refraction method has been virtually

stagnant and most research has tended to focus on the various methods for

inverting traveltime data. However, in many cases, it is apparent that the models

used for inversion are not cognizant of the realities of the near surface

environment and that implausible assumptions are often made.

This study reviews the major issues associated with the inversion of seismic

refraction traveltime data, especially that acquired in the near surface

environment, where geological conditions can change rapidly. I conclude that

the generalized reciprocal method (GRM) (Palmer 1980, 1986) is a logical

evolution of the major inversion methods, which can usefully address the issues

of resolution, ambiguity and non-uniqueness.

2.3 - Field Data Requirements

The first stage of the inversion of the traveltime data is the determination of an

appropriate model. Generally, this is a qualitative stage in which an assessment

is made of the number of layers that can be recognized confidently in the

traveltime data, and in which each arrival is assigned to a particular refractor. It

requires reversed traveltime data for which there are shot points in both the


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forward and reverse directions, in order to resolve lateral variations in depths to

and wavespeeds within each refractor. In addition, redundant data in which there

are several shot points on either side of the array of detectors, are also essential.

Hinge points or changes in slope which shift horizontally with each graph indicate

new layers, while hinge points which shift vertically indicate changes in depth or

wavespeed within the same layer. These requirements are routinely satisfied

with shallow refraction operations which employ a high density of shot points

(Walker and Win, 1997), and they are described in more detail in Palmer (1986),

Palmer (1990), and Lankston (1990).

2.4 - Undetected Layers

However, this process is only effective if there is a monotonic increase in

wavespeeds from layer to layer with increasing depth and if the thickness of each

layer is greater than a minimum value. Layers, which are thin in relation to the

thicknesses and wavespeeds of the surrounding layers, can escape detection

(Maillet and Bazerque, 1931; Soske, 1959). Furthermore, even layers which are

thick are not detected if there is a reversal in wavespeed from the layer above

(Domzalski, 1956; Knox, 1967). These are the well-known undetected layer

problems and various methods for determining maximum errors have been

described by many authors (Merrick et al, 1978; Whiteley and Greenhalgh,

1979).

2.5 - Incomplete Sampling of Each Layer

The difficulties in accurately specifying the inversion model extend to the

determination of the wavespeed within each layer. In Hagedoorn (1955),

traveltimes are computed for a simple two layer model, in which the wavespeed


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in the upper layer varies linearly with depth. A variety of other wavespeed

functions are then fitted to the traveltime graphs with an accuracy of better than

0.5%, but nevertheless the errors in the computed depths to the refractor are

between 10% and 29%.

Hagedoorns (1955) study is of fundamental significance to the inversion of all

refraction data using anyapproach. It demonstrates that even in the absence of

undetected layers, the wavespeed model in the each layer and therefore its

thickness, cannot be accurately determined with the traveltimes from that layer

alone. It also demonstrates that the selection of the correct wavespeed model is

essential for accurate depth determinations.

The difficulties in accurately determining the parameters of each layer are related

to the inherent errors of extrapolation. The parameters of the wavespeed

function are computed from arrivals which rarely penetrate more than 30% of the

thickness for realistic wavespeed functions. These parameters are then

extrapolated to the remainder of the layer where each wavespeed function can

behave quite differently.

2.6 - Implications for Model-Based Methods of Inversion

Hagedoorns (1955) study is especially applicable to model-based inversion or

tomography (Zhu et al., 1992). With these methods, the parameters of a model

of the subsurface are refined by comparing the traveltimes of the model with the

field data. When the differences between the computed and field traveltimes area minimum, the model and parameters are taken as an accurate representation

of the wavespeeds in the subsurface.

The performance of refraction tomography has been continually improved

through more efficient inversion and forward modeling routines, (see Zhang and


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Toksoz, 1998 for an overview of these advances). However, the choice of the

model has yet to receive widespread attention, since the role of model-based

inversion is to provide information about the unknown numerical parameters

which go into the model, not to provide the model itself(Menke, 1989, p3).

Perhaps the most common model has been the linear increase of wavespeed

with depth (Zhu et al.,1992; Stefani, 1995; Miller et al., 1998; Lanz et al., 1998),

possibly because of mathematical convenience. However, this model is of

questionable validity as most theoretical (Iida, 1939; Gassman, 1951, 1953;

Brandt, 1955; Paterson, 1956; Berry, 1959), laboratory (Birch, 1960; Wyllie et al.,

1956, 1958), and field studies (Faust, 1951, 1953; White and Sengbush, 1953;

Acheson, 1963, 1981; Hall, 1970; Hamilton, 1970, 1971; Jankowsky, 1970),

suggest a more gentle increase for clastic sediments, such as a one sixth power

of depth function.

Furthermore, the gradients obtained range from 0.342 and 2.5 m/s per metre

(Stefani, 1995), and 2.68 and 4.67 m/s per metre (Zhu et al., 1992), to as high as

40 m/s per metre (Lanz et al, 1998). These values are generally much larger

than those applicable to the compaction of clastic sediments (Dobrin, 1976), but

they are rarely justified on geological or petrophysical grounds.

The combination of the linear increase of wavespeed with depth and the high

gradients probably contributes to instability in the inversion process. The

example of the somewhat paradoxical situation of the poor determination of

wavespeeds in the refractor, despite the fact that over 90% of traveltimes are

from that layer (Lanz et al., 1998, Figure 8), is at variance with the experiences of

most seismologists using more traditional methods of refraction processing.

Furthermore, the use of linear wavespeed functions where constant wavespeed

layering is applicable can result in large gradients which in turn can result in the

ubiquitous ray path diagrams demonstrating almost complete coverage of the


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are neither a complete, an accurate nor a representative indication of the

inversion model should be viewed as a fundamental geophysical reality which

must be accommodated in any approach to refraction inversion.

2.9 - The Large Number of Refraction Inversion Methods

In view of the many applications over the last eight decades, it is not surprising

that the refraction method is characterized by the existence of numerous

approaches for inverting the field data. Standard texts such as Musgrave (1967),

Dobrin (1976), and Sheriff and Geldart (1995), describe almost a score of

techniques which have been used at some time in the past. Each method

represents a compromise between the desire for mathematical exactness and

the realities of geophysical robustness and computational convenience.

Most of these methods have not seen regular use and are more of curiosity

value, rather than being practical inversion methods. The more commonly used

methods have been wavefront reconstruction, the intercept time, the reciprocal

method and the group which employ refraction migration, viz. the delay time.

Hales and the generalized reciprocal methods.

2.10 - Wavefront Reconstruction Methods

Perhaps the earliest techniques to be used were the wavefront reconstruction

methods (Thornburg, 1930; Rockwell, 1967; Aldridge and Oldenburg, 1992).

These methods retrace the emerging forward and reverse wavefronts down into

the subsurface. The refractor interface is located at the positions where the sum

of the forward and reverse wavefronts is equal to the reciprocal time. Wavefront

reconstruction methods are generally considered to be the most precise because


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they make few assumptions or approximate Snells law. However, they operate

in the depth domain and therefore require a detailed and accurate knowledge of

the wavespeeds above the target refractor. As discussed above, this is probably

one of the most difficult requirements to satisfy.

2.11 - The Intercept Time Method

Another longstanding technique is the intercept time method (ITM), (Ewing et al,

1939). This method is essentially a ray tracing approach applied to a subsurface

model consisting of homogeneous layers with uniform wavespeeds separated by

plane dipping interfaces. The angle of emergence of each ray is readily

determined from the travelime graphs, and its trajectory in the subsurface is then

computed with the simple application of Snells law.

Although the ITM is mathematically precise, it is not geophysically robust.

Discordant dips produce large changes in slope on the traveltime graphs and as

a result, there can be difficulties in recognizing individual layers. Furthermore,

dipping interfaces eventually intersect, thereby resulting in layers which do not

register in the traveltime graphs below a minimum thickness.

Under most circumstances, the horizontal layer approximations are of sufficient

accuracy (Palmer, 1986). These approximations are (i) the use of the law of

parallelism to obtain intercept times (Sjogren, 1980), which are a measure of the

depth to the refracting interface in units of time, (ii) the horizontal layer value of

the depth conversion factor which relates intercept times and layer thicknessesand (iii) the harmonic mean of the forward and reverse apparent wavespeeds to

obtain a measure of the refractor wavespeeds.


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2.12 - The Reciprocal Methods

The approximations of the ITM are identical to those which are integral to the

group of techniques known as the reciprocal methods (Hawkins, 1961). This

group had its origins in the 1930s when it was known as the method of

differences (Edge and Laby, 1931, p.339-340; Heiland, 1963, p.548-549). These

methods are also known as the ABC method in the Americas, (Nettleton, 1940;

Dobrin, 1976), Hagiwara's method in Japan, (Hagiwara and Omote, 1939), and

the plus-minus method in Europe, (Hagedoorn, 1959). There are no fundamental

mathematical differences between each of these methods, and usually the

choice of a particular version is a function of geography. Mathematically, the

reciprocal methods can be demonstrated to be simple extensions of the ITM

whereby depths and wavespeeds, which are determined at the shot points with

the ITM, are also computed at each detector position between the shot points

(Palmer, 1986).

2.13 - Data Processing in the Time Domain

The reciprocal methods employ two fundamental algorithms. The first, the

wavespeed analysis function tV, employs the subtraction of forward and reverse

traveltimes at each detector position. There can be other operations, such as the

addition of the reciprocal time, which is the traveltime from one shot point to the

other, and the halving of the result. However, the essential feature is the

subtraction operation, which effectively removes the effects of any variations in

the thicknesses of the layers above the refractor. The gradient of this functionwith respect to distance is the reciprocal of the wavespeed in the refractor, Vn.

tV= (tforward treverse+ treciprocal)/2 (2.1)

d/dx tV= 1 / Vn (2.2)


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The second algorithm employs the addition of the forward and reverse

traveltimes at each detector position, in order to obtain a measure of the depth to

the refracting interface in units of time. This function, known as the time-depth tG,

can also include other operations, such as the subtraction of the reciprocal time,

and the halving of the result.

tG= (tforward+ treverse- treciprocal)/2 (2.3)

The two algorithms of the reciprocal methods represent major advances in the

processing of shallow seismic refraction data. The processing is carried out in

the time domain and therefore it does not require an accurate knowledge of the

wavespeeds in the layers above the target refractor. Although accurate

wavespeeds are necessary for the final conversion to a depth cross-section,

nevertheless, many useful processing operations can be conveniently carried out

in the time domain prior to that step. This advantage is not shared with methods

which operate in the depth domain, such as the wavefront reconstruction

methods and tomography.

The depth zG, is computed from the time-depth and the wavespeeds in the

refractor and the layer(s) above with equation 4, viz.

zG= tGDCF (2.4)

where the DCF, the depth conversion factor relating the time-depth and the

depth, is given by:

DCF = V Vn/ (Vn2- V2) (2.5)

or

DCF = V / cos i (2.6)

where


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sin i = V / Vn (2.7)

and where V is the average wavespeed above the refractor.

2.14 - Accommodation of the Offset Distance with RefractionMigration

The offset distance is the horizontal separation between the point of emergence

of the ray on the refractor interface and the point of detection at the surface. The

offset distance is implicitly accommodated in all refraction techniques which use

a depth conversion factor similar to the horizontal layer approximations of the

ITM in equation 2.5.

In addition, there are several inversion techniques which explicitly accommodate

the offset distance. These methods seek to employ the process known as

refraction migration whereby any traveltime anomalies are laterally shifted by the

offset distance so that they are positioned above their source on the refractor.

They include the delay time method (Gardner, 1939; Barthelmes, 1946; Barry,

1967), Hales method (Hales, 1958; Sjogren, 1979, 1984) and the generalized

reciprocal method (GRM) (Palmer, 1980, 1986).

These methods represent a systematic evolution of the refraction migration

concept. In the delay time method, refraction migration is applied individually to

the forward and reverse traveltime graphs, and after a series of adjustments and

corrections, an averaged delay time profile is generated. Hales method

essentially achieves the same results more readily with a graphical approach

using reversed traveltime data. In addition, the use of the reversed traveltime

data within a single operation reduces the effects of dip on the offset distance (as

well as the time-depths) to the horizontal layer value.


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However, both of these methods ideally require an accurate knowledge of the

wavespeeds in the layers above the target refractor, in order to compute the

offset distance. This problem is addressed with the GRM through the use of a

series of offset distances (known as XY distances), and then selecting the

optimum value with a minimum variance criterion (Palmer, 1991). This is a

unique and useful feature of the GRM because under certain conditions, it can

permit the computation of the gross or average wavespeed model above the

refractor for a wide range of models using the optimum XY value. These models

include the single layer with a constant average wavespeed, two layers one of

which may be undetected, variable wavespeed media, and simple transverse

isotropy (Palmer 1981, 1992, 2000b, 2001a).

2.15 - Using Refraction Migration to Recognize Artifacts

The use of refraction migration was once an important part of refraction inversion

when the method was applied to deep targets in petroleum exploration. In those

applications, the offset distances could be hundreds or even thousands of

metres, and refraction migration was essential to ensure that any boreholes were

accurately sited with respect to the target.

However, with the restriction of refraction methods to predominantly shallow

targets in the last fifty years, the use of refraction migration has not always been

considered necessary because the offset distances are commonly only a few

metres or a few tens of metres at most. Furthermore, any improvements in the

resolution of the depths to the refractor were often quite subtle, especially withlarge detector intervals, and so it was usually considered difficult to justify the

extra effort in using refraction migration.

The major benefit of using refraction migration in shallow investigations is in the

determination of wavespeeds in the refractor where they are commonly used as


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a measure of rock strength. It is especially important to detect narrow zones with

low wavespeeds which can be representative of shear zones. However, the

wavespeed analysis function of the reciprocal methods generates narrow zones

with high and low wavespeeds, which are artifacts of inversion algorithm, where

there are changes in depth to the refracting interface.

The use of the GRM to separate genuine lateral variations in the refractor from

artifacts which are a product of the inversion algorithm is described in Palmer

(1991) and Palmer (2001b).

2.16 - Non-uniqueness in Determining Refractor Wavespeeds

The presentations of the wavespeed analysis function and the time-depths for a

range of XY or offset distances, represent families of geologically acceptable

starting models (Palmer, 2000c; 2000c) which satisfy the original traveltime data

(Palmer, 1980, p.49-52; 1986, p.106-107) to better than a millisecond. This is

simply another statement of the fundamental problem of non-uniqueness

common to all inversion processes (Oldenburg, 1984; Treitel and Lines, 1988),

but it is rarely if ever, addressed satisfactorily with refraction methods.

The problems of non-uniqueness are important to all refraction inversion

methods but especially so with model-based methods or tomography. The family

of starting models generated with the GRM can be useful for examining the

extent of the non-uniqueness problem with data obtained during routine surveys.

In many cases, the minimum variance criterion of the generalized reciprocal

method (GRM) can resolve whether lateral variations in the refractor wavespeeds

are genuine or if they are artifacts. However, this approach usually requires

good quality data and small detector intervals in relation to the depth of the

refractor. Commonly, detector intervals of less than about one quarter of the


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target depth are recommended. In those cases where the effective application of

the GRM is not possible, the use the amplitudes (Palmer, 2001c) is proposed.

2.17 - Fundamental Requirements for Refraction Inversion

In summary, the performance of all methods for inverting shallow seismic

refraction data depends upon the quality of the field data, and the applicability of

the inversion model to the geological realities. Good quality redundant data are

essential for resolving many basic ambiguities. However, there are fundamental

limitations in accurately determining the wavespeed stratification from even the

most complete sets of data. Not all layers are necessarily detected in the

traveltime data, because some layers are either too thin, or the wavespeeds are

less than that in the overlying layer. Furthermore, the wavespeed stratification

cannot be determined with high precision within those layers which are detected,

because the refracted rays do not penetrate deeply enough, or because the

horizontal rather than the vertical wavespeed is measured.

The difficulties in accurately determining the inversion model indicate that as

much of the data processing as possible should be carried out in the time

domain, rather than in the depth domain. The wavespeed analysis and the time-

depth algorithms of the group of processing techniques known as the reciprocal

methods, satisfy these requirements.

In addition, there is another fundamental issue of non-uniqueness in determining

lateral variations in wavespeeds in the refractor. This requires the use ofrefraction migration in order to accommodate the offset distance. However,

incorrect migration distances which would result from the use of incorrect

wavespeeds in the layers above the target refractor, can still generate results

which satisfy the traveltime data. This problem can be overcome with the use of


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multiple migration distances with the GRM and the use of the minimum variance

criterion.

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Documents

Palmer.03.Digital Processing Of Shallow Seismic Refraction Data.pdf