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Chapter 7

Effects Of Near-Surface LateralVariations On Refraction Amplitudes

7.1 - Summary

Increases in refracted amplitudes not related to changes in the head coefficient

are usually associated with increases in traveltimes in the near-surface layers,

while decreases in amplitudes are associated with decreases in traveltimes.

These correlations demonstrate that the amplitude variations are related to

variations in the near surface geology, rather than to variations in the coupling of

the detectors with the ground.

The change in amplitude can be described with the transmission coefficient of

the Zoeppritz equations. Correction factors can be applied for those surface

conditions which are sufficiently extensive to permit the measurement of the

wavespeed. Where this is not possible, then the lowest amplitude or amplitude

product is representative of the head coefficient for the main refractor.

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7.2 - Introduction

The generation of a refraction time section through the convolution of forward

and reverse seismic traces (Palmer, 2001a), provides a powerful and convenient

approach to resolving some of the ambiguities in the inversion of shallow seismic

refraction data (Palmer, 2001b). 2D and 3D case histories demonstrate that the

approach is efficacious with refractors exhibiting large variations in depths and

wavespeeds. The head coefficient is approximately the ratio of the specific

acoustic impedance in the upper layer to that in the refractor, while amplitudes in

the convolution section are the square of that ratio.

However, there can be geological situations where the refraction amplitudes are

not predicted by the head coefficient or its approximations. These situations

include lateral variations in the near surface layers and/or variations in the

coupling of the geophones with the ground.

The coupling of geophones, especially with the standard single geophone per

trace of most shallow seismic refraction operations, is a ubiquitous concern with

quantitative analysis of refraction amplitudes. Pieuchot (1984) reviewed earlier

work (Bycroft, 1956; Fail et al, 1962; Lamer, 1970), in which the effects of the

weight and diameter of geophones on coupling were considered. He concluded

that the size of modern geophones was adequate to produce satisfactory

coupling, and that the common geophone spike lengths of 50 mm to 100 mm

further guaranteed satisfactory coupling. Field trials (E J Polak, 1969) in which

the amplitudes of bunched geophones were measured, demonstrate that

variations in amplitudes related to planting are minor.

These conclusions are supported by a seismic refraction profile across a narrow

massive sulfide orebody at Mt Bulga in southeastern Australia. Originally, this

profile was recorded to observe whether there are any variations in refraction

amplitudes related to an unambiguous increase in density associated with the

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mineralization. However, it is a complex case history which combines lateral

changes in the wavespeeds in both the refractor and the weathered layer above,

as well the density changes associated with the mineralization. Furthermore, the

results provide a valuable insight into the relative importance of the effects of

near surface lateral variations and geophone coupling with the ground on the

measurement of seismic amplitudes with single detectors. In particular, there is

a consistent correlation between amplitude variations of the refracted signal and

minor traveltime variations in the near surface layers. These results indicate that

near-surface geology rather than geophone coupling is the dominant cause of

seismic amplitude “statics”.

7.3 - Traveltime Results

The Mt Bulga massive sulfide orebody is narrow with a width generally less than

about 10 m. Nine shots, each consisting of small explosive charges in shallow

hand augered shot holes, and nominally 30 m apart, were recorded with a 48

trace seismic system using single geophones which were 2.5 m apart.

The centre of the seismic line at station 49 was located on the crest of a small

ridge, which also marked the location of the sulfide orebody. The rocks on either

side of the mineralization are Ordovician meta-sediments. Between stations 25

and 49, these sediments crop out, and there was some difficulty in auguring the

shot holes to a satisfactory depth and in planting the geophones. Between

stations 49 and 73, there is no outcrop, and the production of the shot holes was

much easier, as was the planting of the geophones.

The traveltime graphs are shown in Figure 7.1. They show that a two layer

model of the wavespeeds is generally satisfactory, and that there is a significant

lateral change in the wavespeeds of the first layer. Between stations 25 and 48

where the Ordovician meta-sediments sediments crop out, the wavespeed of the

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first layer is 1500 m/s. Between stations 48 and 53 there is no outcrop, due

partly to the mining of the enriched supergene zone over a century ago and to

recent restoration of the site for a pine tree plantation. Here, the wavespeed of

the first layer is 900 m/s. On the other side of the orebody, between stations 53

and 72, the wavespeed of the first layer is 1000 m/s.

Figure 7.1: Traveltime data for a line crossing a narrow massive sulfide orebody

at Mt Bulga. The shot point interval is nominally 30 m.

Between stations 26 and 28, the traveltimes increase in both the forward and

reverse directions. This increase is inferred to be the result of an increase in the

thickness of surface layer of soil, because there is no lateral offset between the

increases in the forward and reverse traveltime graphs. A wavespeed of

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approximately 500 m/s can be obtained from the graph with the shot point at

station 25.

Between stations 69 and 71, the traveltimes decrease in both the forward and

reverse directions. As with the previous case, there is no lateral offset, and so

this decrease is inferred to be the result of a reduction in the thickness of the

surface layer of soil.

Figure 7.2: Time-depths computed from traveltime data with shot points at

stations 1 and 97. The shading highlights a distinctive pattern of time-depth

anomalies which are centred on station 56 and which have their origin in the very

near-surface soil layer.

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By contrast, the increases in the traveltimes in the forward and reverse directions

on either side of station 49 are offset by about two detector intervals, indicating

that the corresponding increases in depth occur in the main refractor. This

corresponds with an optimum XY value of 5 m, which is obtained from both the

wavespeed analysis function in Figure 7.3 and the offset in amplitudes in Figure

7.7.

The time-depths computed with the traveltimes for the shots at stations 1 and 97

and using a reciprocal time of 120 ms, and XY values from 0 to 10 m in

increments of 2.5 m which is the trace spacing, are presented in Figure 7.2. The

increase in the time-depths over the orebody is readily apparent.

The wavespeed analysis function is shown in Figure 7.3, using the traveltimes for

the shots at stations 1 and 97, and XY values from 0 to 15 m in increments of 2.5

m, the trace spacing. The optimum XY value has been taken as 5m, although it

may be a little less, possibly about 4m, because the graphs for the XY values of

2.5 m and 5 m are symmetrical about their average. The wavespeed in the

refractor is 5000 m/s between stations 25 and 48, 3430 m/s between stations 48

and 62, 2400 m/s between stations 62 and 68, and possibly about 5000 m/s

between stations 68 and 72. The region with the wavespeed of 2400 m/s is

along strike from the shear zone detected in another study (Palmer, 2001a;

chapter 3), and it is probably a continuation of that feature.

The depth section computed with these wavespeeds is shown in Figure 7.4. The

depths have been plotted vertically below the surface reference point and require

an additional operation (Palmer, 1986), which is equivalent to reflection migration

or imaging. The increase in the depth of weathering in the vicinity of station 50 is

probably caused by the more rapid breakdown of the sulfides or the removal of

ore and rock during mining.

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Figure 7.3: The generalized wavespeed analysis function for a range of XY

values from zero to 15 m in increments of 2.5 m, which is the station separation.

The values for a 5 m XY value show the least variation related to the increased

depth of weathering over the orebody, and at least four zones with different

wavespeeds can be recognized.

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Figure 7.4: Depth section computed with the time-depths shown in Figure 7.2.

The vertical to horizontal exaggeration is approximately 4:1.

7.4 - Effects of Near-surface Lateral Variations on Amplitudes

The two shot records with shot points at stations 1 and 97, are shown in Figures

7.5 and 7.6. They both show the large decrease in amplitude with increasing

shot-to-detector distance. In addition, there is a very obvious reduction in

amplitudes on the few traces centered on station 50, which is the location of the

massive sulfide orebody.

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Figure 7.5: Field record for shot point at station 1, presented at constant gain.

The large drop in amplitudes at stations 51 and 52 occurs near the location of the

massive sulfide orebody.

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Figure 7.6: Field record for shot point at station 97, presented at constant gain.

The large drop in amplitudes at stations 49 and 50 occurs near the location of the

massive sulfide orebody.

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Figure 7.7: Amplitudes of the first cycles of the field records with shot points at

stations 1 and 97.

The amplitudes of the first cycles are shown in Figure 7.7, and show the usual

decrease with distance from the shot point, together with the sudden decrease at

around station 50. The amplitudes are somewhat erratic for the forward shot

between stations 26 and 49, which is the region of outcrop and where some

difficulties were experienced in planting the geophones. In addition, there is

good correlation between similar features on the reverse shot point, such as at

stations 32 and 43.

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Figure 7.8: Uncorrected amplitude products of the first cycles of the field

records with shot points at stations 1 and97.

The product of the shot amplitudes, shown in Figure 7.8 with an XY separation of

zero, exhibits the same erratic nature as the shot amplitudes between stations 26

and 49. The amplitude products at stations 32 and 43 for example, are higher

than those at the adjacent stations.

A similar correlation is possible at station 56, where there is an increase in

amplitudes on both forward and reverse shots, and a corresponding increase in

the amplitude product. Furthermore, there is an increase in traveltime at this

station, and in turn, an increase in time-depths computed with a zero XY value as

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shown in Figure 7.2. An examination of Figure 7.1, shows that the increase in

the traveltime occurs at the same geophone location for both the forward and

reverse shots, that is, there is no lateral displacement. Therefore, the increase in

depth occurs in the surface soil layer, rather than in the main refractor. The near-

surface origin is also supported by the characteristic pattern produced the time-

depths with in Figure 7.2 (Palmer, 1986, p107-111).

These results indicate that the occurrence of the soil surface layer produces

increases in seismic amplitudes. This is clearly indicated at station 56, as well as

at stations 32, 35, 41 and 43. In the latter cases, the time-depth anomalies are

not as large, but nevertheless, they are consistent with the hypothesis.

The hypothesis is further supported by the large increase in the surface soil layer

at stations 26 and 27 which corresponds with an increase in amplitudes, as well

as the decrease in the surface layer at stations 70 and 71, which correlates with

a decrease in amplitudes.

The variations in amplitudes with varying surface layers can be explained with

the transmission coefficients of the Zoeppritz equations, viz.:

Trans Coeff = 2 v lower ρ lower / (v lower ρ lower + v upper ρ upper) (7.1)

where

v upper is the wavespeed in the upper or surface layer,

ρ upper is the density in the upper or surface layer,

v lower is the wavespeed in the lower layer, and

ρ lower is the density in the lower layer.

This form of the equation is a little different from the standard, because the signal

is travelling upwards from the refractor.

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In general, v upper < v lower and ρ upper < ρ lower. Therefore, the transmission

coefficient in equation 7.1 will vary from one, that is, there is no surface soil layer,

to two, that is, the surface soil layer wavespeed and density are much less than

those of the layer below. In those cases where there is a surface soil layer, there

will be an increase in amplitudes, because the transmission coefficient will

usually be greater than one.

The wavespeeds and densities in the upper soil layer can vary over quite large

ranges. Furthermore, it can be difficult to accurately map any rapid lateral

variations with for example, seismic methods. Therefore, it may not always be

possible to conveniently derive correction factors based on the Zoeppritz

equation.

In such situations where there is significant variation in the surface soil layer, it is

suggested that the minimum values, rather than the average values, be taken as

representative of that region. For example, the amplitude product for the region

between stations 30 and 48 will be taken as about 1.3, rather than the average of

about 2 or the maximum of about 2.5.

However, a wavespeed of approximately 500 m/s can be recovered for the

surface soil layer between stations 26 and 28. If the densities are ignored, then

the transmission coefficient computed with equation 7.1, is 1.5. Since the

amplitudes are multiplied in Figure 7.8, the transmission coefficient must be

squared, prior to application. The squared correction factor of 2.25 satisfactorily

accounts for the increase in amplitude, as shown in Table 1.

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7.5 - Relationships Between Amplitudes and RefractorWavespeeds

The normalized amplitude products are shown in Figure 7.9 for XY values from

zero to 10 m. The values shown include the addition of a constant, namely, 1 for

an XY value of 2.5 m, 2 for an XY value of 5 m, and so on, in order to separate

the graphs.

The anomalous amplitude product at station 56 is readily seen on the graph for

the zero XY value. As the XY value is systematically increased, the forward and

reverse amplitude anomalies are separated, with the result that the anomalous

product separates into two, which correspond with the forward and reverse shot

amplitude values. The forward amplitude systematically moves to the right, while

the reverse value moves to the left. The pattern is similar to that produced by

traveltime anomalies which originate in the near-surface (Palmer, 1986, p107-

111), as shown in Figure 7.2 for station 56.

This pattern with the amplitude products which can be seen clearly at station 56,

can also be recognized with some difficulty between stations 27 and 48.

Figure 7.7 shows that the very low amplitudes associated with the massive

sulfides, occur at stations 51 and 52 on the forward shot and 49 and 50 on the

reverse shot. The amplitude products in Figure 7.9, show that this interval is a

minimum for an XY value of 5 m, and that it occurs at stations 50 and 51. For

other XY values, this zone is wider.

The accompanying table summarizes the amplitude products and the correlation

with wavespeeds. In general, the agreement is good.

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Figure 7.9: Uncorrected products of the amplitudes of the first cycles of the field

records with shot points at stations 1 and 97 for a range of XY values from zero

to 10 m.

The normalized squared ratios of the wavespeeds in the final row have been

corrected for the additional near-surface layer of soil between stations 26 and 29,

and for an inferred density factor of 2.8 for the mineralized region in the centre

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between stations 50 and 51. If a density of 2.4 tonnes/m3 is assumed for the

meta-sediments, then the resulting density for the mineralization is 6.6

tonnes/m3. This density is a little high, but it is possible to reduce it using a

higher wavespeed in the mineralization. This is reasonable because the

measured wavespeeds may not be especially accurate over such a narrow

interval.

Station 26 – 29 29 – 50 50 – 51 51 – 62 62 – 68 68 -72NormalizedAmplitudeProduct

2.9 1.3 0.13 1.0 2.2 1.5

V1 (m/s) 1500 1500 900 1000 1000 ? 1600

V2 (m/s) 5000 5000 3430 3430 2400 ? 5000

(V1/ V2)2 0.09 0.09 0.07 0.07 0.17 ? 0.10

Normalized(V1/ V2)2

1.3 1.3 1 1 2.4 ? 1.5

Corrected(V1/ V2)2

2.9

(soil

layer)

1.3 0.13

(orebody

density)

1 2.4 ? 1.5

Table 1: Summary of amplitude products and wavesppeds.

7.6 - Discussion and Conclusions

This case history provides another good example of the correlation between

head wave amplitude products and the ratios of the wavespeeds. It is complex

with many large variations in depths as well as wavespeeds in both the refractor

and the layer above. Furthermore, it qualitatively confirms the importance of

densities on head wave amplitudes.

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The case history also provides a valuable insight into the importance of near-

surface variations and geophone coupling on the measured refraction

amplitudes.

Between stations 50 and 72 where there is no outcrop, the amplitudes and the

amplitude products are essentially a function of the wavespeeds in the refractor

and the layer above. However, at station 56, there is an increase in amplitudes

which correlates with an increase in traveltimes and time-depths. These results

indicate that the amplitude variation is related to the near-surface layering, rather

than to the coupling of the geophones with the ground.

The results for the region between stations 26 and 50, where there was

extensive outcrop, support this interpretation, because all of the amplitude

anomalies can be associated with traveltime anomalies.

The presentation of both amplitude products and time-depths for a range of XY

values from zero to more than the optimum value, provides a convenient and

effective method for recognizing near-surface anomalous zones of limited lateral

extent.

The increases in amplitudes are compatible with the transmission coefficients of

the Zoeppritz equations. As the seismic signal approaches the surface from the

refractor, there is an increase in seismic amplitude where there is another layer

with lower wavespeed and or density.

In general, this change in amplitude can be ignored when there are several

continuous layers above the refractor, because the same increase in amplitudes

occurs at each detector. In these situations, the amplitudes are adequately

described with the head coefficients, together with a geometric spreading factor.

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Where there are lateral changes in the surface layers, such as the irregular

development of a surface soil layer, there can be large variations in amplitudes

by a factor of between 1 and 2. If these layers have sufficient lateral extent so

that they can be mapped, such as the region between stations 26 and 28, then

an approximate correction factor can be computed with the transmission

coefficients of the Zoeppritz equations.

However, this is not always possible. Under these circumstances, the minimum

amplitudes are probably the most representative.

7.7 - References

Bycroft, G. N., 1956, Forced vibrations of a rigid plate on a semi-infinite elastic

space: Roy. Soc. London, 248, 327-368.

Fail, J. P., Grau, G., and Lavergne, M., 1962, Couplage des sismographes avec

le sol: Geophys. Prosp., 10, 128-147.

Lamer, A., 1970, Couplage sol-geophone: Geophys. Prosp., 18, 300-319.

Palmer, D., 1980, The generalized reciprocal method of seismic refraction

interpretation: Society of Exploration Geophysicists.

Palmer, D., 1986, Refraction seismics - the lateral resolution of structure and

seismic: Geophysical Press.

Palmer, D., 2001a, Imaging refractors with the convolution section: Geophysics

66, 1582-1589.

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Palmer, D., 2001b, Resolving refractor ambiguities with amplitudes: Geophysics

66, 1590-1593.

Pieuchot, M., 1984, Seismic instrumentation: Geophysical Press.

Polak, E. J., 1969, Attenuation of seismic energy and its relation to the properties

of rocks: Ph D thesis, University of Melbourne, p4.7-4.9.