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    Chapter 8

    Enhancement of Later Events in theRCS with Dip Filtering

    8.1 - Summary

    Later events, which occur in the shot records, are also treated in the same

    manner as first events with the convolution process. Both the addition of the

    traveltimes and the multiplication of amplitudes take place. However, there can

    be additional features in which cross-convolution artifacts are also generated.

    These artifacts which are formed by the convolution of events from different

    refractors, occur as relatively steeply dipping events in the refraction convolution

    section (RCS) and therefore, they can be removed by dip filtering. The filtered

    RCS shows better continuity of events than is the case with the unfiltered

    section.

    For events which have traveled through the surface layer, the filtered RCS shows

    a series of events which occur at a time which is a function of the distance

    between the two shot points and the wavespeed in the surface layer. The time of

    this event can be used to improve the estimates of the wavespeed in the surface

    layer.

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    8.2 - Introduction

    The generation of the refraction convolution section (RCS) (Palmer, 2000)

    produces a set of traces with the superficial appearance of a seismic reflection

    section. It has been demonstrated that the RCS reproduces the time structure of

    the refractor interface with first arrivals, while the amplitudes which are largely

    corrected for geometric spreading, are essentially a function of the square of the

    head coefficient. It has also been demonstrated that the head coefficient is given

    approximately by the ratio of the wavespeeds in the upper layer and refractor.

    The RCS amplitudes can be employed to image the refractor, to resolve some of

    the ambiguities in the determination of wavespeeds in the refractor, and to obtain

    a measure of azimuthal anisotropy with three dimensional methods.

    To date, research has focused primarily on the portion of the RCS which

    corresponds with the first arrivals, and little attention has been directed at later

    events. However, the convolution process performs the same operations on later

    arrivals as it does with the first events. These operations are the addition of the

    traveltimes in the forward and reverse directions, which replaces of moveout from

    trace to trace with a constant amount equal to the reciprocal time, the time from

    the forward shot point to the reverse shot point, and the multiplication of the

    amplitudes. The addition of the traveltimes produces the relative time structure

    on the refracting interface, while the amplitude product effectively compensates

    for the large geometric spreading which is characteristic of refraction data. The

    true time structure on the interface can be obtained by subtracting the reciprocal

    time. As the reciprocal time generally decreases with deeper layers, the

    shallower layers occur at later times in the RCS.

    One feature of the RCS is the generation of what will be termed cross-

    convolution events with later arrivals. In this case, the convolution operation

    adds arrivals from different refractors, and therefore generates artifacts which

    have no geophysical significance. For example, it is possible to produce an

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    event which is the addition of the traveltimes from the refractor in the forward

    direction, with the traveltimes from the surface layer in the reverse direction. In

    practice, these artifacts occur as pairs, that is there is also an event produced by

    the addition of the traveltimes from the surface layer in the forward direction, with

    the traveltimes from the refractor in the reverse direction. Because of the

    different moveouts or wavespeeds, these events appear as relatively steeply

    dipping features in the RCS.

    This study describes the use of dip filtering in the f-k domain (Sheriff and Geldart,

    1995), to remove the cross-convolution events, with the aim of enhancing those

    later events which may have geological significance.

    8.3 - Generation of Useful Events and Artifacts in the RCS

    The generation of useful later events in the RCS can best be demonstrated with

    the ground-coupled air wave. While it is recognized that the imaging of the air

    wave has minimal geological significance, it is employed in this study because its

    high amplitude improves its clarity in the RCS.

    Figure 8.1 is a shot record from a shallow seismic refraction survey at Mt Bulga,

    which has been described previously (Palmer, 2001). The record shows the first

    arrivals between about 70 ms and 130 ms as very low amplitude signals, and a

    very high amplitude event between 350 ms and 1000 ms. The first arrivals are

    refracted from the base of the weathering, while the second arrivals are the

    ground-coupled air wave.

    Figure 8.2 shows the shot record in the reverse direction. The same two events

    can be clearly identified, but in this case, the relative amplitude of the ground-

    coupled air wave is lower.

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    Figure 8.1: A shot record showing low amplitude first arrivals between about 70

    ms and 130 ms refracted from the base of the weathering, and the high

    amplitude ground-coupled air wave between 350 ms and 1000 ms.

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    Figure 8.3: The RCS generated with the two shots shown in Figures 8.1 and

    8.2. The sampling interval has been halved but there has been no subtraction of

    a reciprocal time.

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    The RCS generated with these two shots is shown in Figure 8.3. The sampling

    interval has been halved (Palmer, 2001), but there has been no subtraction of a

    reciprocal time. The presentation gain is low so that the portion of the RCS

    which corresponds with the convolved events from the refractor around 150 ms,

    becomes essentially featureless. However, the gain facilitates the recognition of

    the strong event at approximately 700 ms between stations 29 and 68. The

    limited lateral extent of this event occurs because the recording time of one

    second was insufficient to record the air wave at the distant detectors.

    In addition, the presentation gain highlights the cross-convolution events which

    start a few traces from the left side of the section at 300 ms and continue to

    about 550 ms near the right side of the section. The recognition of the

    companion artifact which starts on the right hand side and finishes on the left is

    not as clearly evident in Figure 8.3 and requires more careful inspection.

    8.4 - Removal of Cross-convolution Artifacts with Dip Filtering

    The transformation of the in RCS in Figure 8.3 from the time-distance domain to

    the frequency-wavenumber (fk) domain with the double Fourier transform, is

    shown in Figure 8.4. It shows signal centered on the frequency axis, which

    corresponds with the horizontal events, and signal spread out parallel to the

    wavenumber axis, which is inferred to correspond with the cross-convolution

    events.

    Figure 8.6 shows the fk domain after the application of a filter to remove all signalother than that centered on the frequency axis, while Figure 8.5 shows the RCS

    after the application of the filter. The event which corresponds with the time-

    depth of the ground-coupled air wave can be clearly seen at about 0.710 s.

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    Figure 8.4:The transformation of the in RCS in Figure 8.3 from the time-distancedomain to the frequency-wavenumber (fk) domain with the double Fouriertransform.

    Figure 8.6: The transformation of the in RCS in Figure 8.5 from the time-distance domain to the frequency-wavenumber (fk) domain with the doubleFourier transform.

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    Figure 8.5: Refraction convolution section in Figure 8.3 after dip filtering to

    remove cross-convolution events.

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    8.5 - Times for Near-surface Events in the Uncorrected RCS

    The RCS in Figure 8.5 which has not been corrected by the subtraction of a

    reciprocal time, facilitates the computation of wavespeeds for the near surface

    layers.

    The traveltime in the forward direction tforward, of a seismic signal travelling

    through a near-surface layer, that is, for which the depth can be ignored is

    tforward= x / V1 (8.1)

    Similarly, the traveltime in the reverse direction treverse, at the same detector is

    treverse= (d x) / V1 (8.2)

    where x is the forward shot-to-detector distance and d is the separation between

    the forward and reverse shot points, and V1is the wavespeed in the near-surface

    layer.

    In the RCS in Figure 8.5, these times are firstly summed, then halved, and they

    occur at a time tRCS, where:

    tRCS= d / 2 V1 (8.3)

    It can be readily shown that the ground-coupled airwaves in Figures 1 and 2 haswavespeeds of about 335 m/s. Using a value of d, the shot point to shot point

    distance, of 480 m, the value of tRCScomputed with equation is 0.716 s. This

    value is similar to that measured above in Figure 8.5.

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    Figure 8.7: Shot record with shot point at station 26.

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    8.6 - Near-surface Wavespeeds from the Uncorrected RCS

    Figures 8.7 and 8.8 are two shot records with shot points at the ends of the

    geophone spread at stations 26 and 73. The presentation gains are low to

    facilitate recognition of a series of events with a wavespeed of approximately 400

    m/s, that is, they arrive at the geophones most distant from the shot points after

    about 0.600 s. These events occur over an interval of about 0.15 s, and they are

    interpreted to be arrivals from the near-surface layer, rather than the ground-

    coupled airwave, because of their lower frequency and inferior continuity

    compared to the ground-coupled airwaves in Figures 8.1 and 8.2.

    A comparison of the unfiltered and filtered RCS in Figures 8.9 and 8.10, shows

    that the dip filtering has removed the cross-convolution events, and that the

    horizontal and near-horizontal events are emphasized.

    Using equation 8.3, it is readily demonstrated that the group of events with the

    wavespeeds of 400 m/s should occur at a time tRCS, of 0.3 s. Figure 8.10 shows

    a series of events from about 0.33 s to about 0.47 s with higher amplitudes than

    the adjacent events. These events are interpreted to represent signals which

    have traveled in the surface soil layer. Using the minimum time of 0.33 s and

    equation 8.3, the revised wavespeed for this layer is 360 m/s.

    It is also possible to recognize a series of events from about 0.18 s with higher

    amplitudes than the adjacent events. These events may correspond with arrivals

    which travel through the second layer with a wavespeed of approximately 700

    m/s.

    While the event associated with the ground-coupled air wave convincingly

    demonstrates the generation of meaningful later events in the RCS, the

    application to events from the near-surface layers is not as clear. It is likely that

    further processing, such as deconvolution may be useful. However initial

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    attempts at simple deconvolution methods were not successful, suggesting that

    considerably more research may be required to develop suitable techniques.

    Figure 8.8: Reverse shot record with shot point at station 73.

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    Figure 8.9: Unfiltered convolution section.

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    Figure 8.10: Dip filtered convolution section.

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    8.7 - Conclusions

    Later events, which occur in the shot records, are also treated in the same

    manner as first events with the convolution process. Both the addition of the

    traveltimes and the multiplication of amplitudes take place. However, there is an

    additional feature in which cross-convolution artifacts are also generated. These

    artifacts occur as relatively steeply dipping events in the RCS and therefore, they

    can be removed by dip filtering. The filtered RCS shows better continuity of

    events than is the case with the unfiltered section.

    For events which have traveled through the surface layer, the filtered RCS shows

    a series of events which occur at a time which is a function of the distance

    between the two shot points and the wavespeed in the surface layer. The time of

    this event can be used to improve the estimates of the wavespeed in the surface

    layer.

    8.8 - References

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

    66, 1582-1589.

    Sheriff, R. E., and Geldart, L. P., 1995, Exploration Seismology, 2ndedition:

    Cambridge University Press.