85
V Application of complex trace attributes
{ to re-flection seismic data near
Charleston, South Carolinaw
S bb Sß Steven B. Miller
J. K. Costain, Chairman
Geological Sciences
(ABSTRACT)
Complex trace attribute analysis has been applied to 24-fold
VIBROSEIS reflection data acquired on the Atlantic Coastal Plain near
Charleston, S. C. , to yield an expanded interpretation of a Mesozoic basin
concealed beneath Coastal Plain sediments. Complex trace attributes ex-
press the seismic trace in terms of a complex variable and emphasize
different components of the original seismogram. Attributes derived from
synthetic seismograms of thin beds are used to interpret the patterns
observed on the real data. Complex trace attributes derived from the
original seismic trace complement the interpretation of a Mesozoic basin
originally imaged by conventional data. The combination of single-sweep
recording and use of complex trace attributes is believed to support an
interpretation of a transition from basin border conglomerates into
finer-grained siltstones nearer to the center of the basin.
·Introduction ....... . ...... . . . . ......... 1
Geologie setting ...........„............. 3
complex trace attribute: . . . . . . . . . „ . . . ........
C
9
Application of complex trace attribute: to synthetics ...... 10
Preliminary observations . . . . • . . . . . . . . . . . . . . . . 37
Application to reflection seismic line VT-5 ....g....... 38
conclusions ..... • ........ , ............ 44
Appendix . . . . . . . . . . . . . . . . . . . . . ........ 46
Reference: ............. . . . . . . ......... 47
vita ......... . . . . . . . . . . . . . . . . . . .|. . . 49
Table of Contents iii
Figure 1. Map of field area .................. 4
Figure 2. Interpreted seismic section for VT-5 ......... 5
Figure 3. Single-sweep seismic section for VT-S ........ 6
Figure 4. Line drawing interpretation of single-sweep section forVT-5 . . ....................... 7
Figure 5. Mathematical model for wedge ............. 11
Figure 6. 20 Hz Ricker convolved with noise-free spike synthetic 12
Figure 7. Instantaneous amplitude of noise-free synthetic . . . 13
Figure 8. Instantaneous phase of noise-free synthetic ..... 14
Figure 9. Instantaneous frequency of noise-free synthetic . . . 15
Figure 10. Wedge synthetic seismogram with 1% noise .·...... 17
Figure 11. Instantaneous amplitude with 1% noise . ....... 18
Figure 12. Instantaneous phase with 1% noise. .......... 19
Figure 13. Instantaneous frequency with 1% noise ........ 20
Figure 14. Wedge synthetic seismogram with 10% noise ...... 22
Figure 15. Instantaneous amplitude with 10% noise ........ 23
Figure 16. Instantaneous phase with 10% noise .......... 24
Figure 17. Instantaneous frequency with 10% noise ........ 25
Figure 18. Wedge synthetic with low impedance contrast ..... 27
Figure 19. Instantaneous amplitude of low contrast synthetic . . 28
Figure 20. Instantaneous phase of low contrast synthetic .... 29
Figure 21. Instantaneous frequency of low contrast synthetic . . 30
Figure 22. Mathematical model for a section of VT-5 ....... 32
Figure 23. Synthetic seismogram for model of VT-5 ........ 33
Figure 24. Instantaneous amplitude for model of VT-5 ...... 34
List of Illustrations iv
Figure 25. Instantaneous phase for model of VT-5 ........ 35
Figure 26. Instantaneous frequency for model of VT-5 ...... 36
Figure 27. Section of single-sweep data for VT-5 ........ 40
Figure 28. Instantaneous amplitude for VT-5 ........... 41
Figure 29. Instantaneous phase for VT-5 ............. 42
Figure 30. Instantaneous frequency for VT-5 ........... 43
List of I llustrations v
_
I thank whose dream has brought this reflection seismic community
together. I also thank my committee for their critical reviews of the
manuscript. The student community helped me through the hard times,
especially Tom P introduced me to median filters. In addition Bob
Montgomery, Mildred Memitt, and Alfred Ott of thkept the system up and
graciously put down their work to help me with the VAX. And finally,
this thesis was possible because the Virginia Tech VIBROSEIS crew took
the time to do the job right in the field.
Financial support during the period 6/16/83 to 8/15/83 came from the
Naval Weapons Center under contracts NC 0530·83•M·760Q and N
60530-83-M-589Q to John K. Costain and L. Glover, III.
My family has encouraged me in my education. provided emotional
support. Also, NL Baroid provided me with the desire to strive towards
further education in geophysics.
vi
This study uses complex trace attributes to identify thin beds on
reflection seismograms as part of a continuing program of thin-bed in-
vestigations at the Regional Geophysics Laboratory. The detection and
description of thin beds is an important goal of reflection seismology.
Complex trace attributes transform the data to display components of
standard seismic traces in such a manner as to accentuate thin beds and
potentially refine the understanding of the subsurface. For example,
Sheriff and Geldhart (1983) state that complex trace attributes sometimes
reveal features which are not as obvious otherwise, especially lateral
changes along bedding associated with stratigraphic changes or
hydrocarbon accumulations. While the seismic trace simultaneously dis-
plays the amplitude, phase, and frequency content of the reflections from
the subsurface, the complex trace attributes analyze the trace into its
constituent components of instantaneous amplitude, instantaneous phase,
and instantaneous frequency versus two-way travel time. Instantaneous
amplitude exhibits tuning associated with thin beds (e. g. , Lawrence,
Sengbush, and MacDonal, 1961), as does the instantaneous frequency
(Neidell and Robertson, 1984). The salient feature of these two tuning
phenomena is that they occur at different intrinsic bed thicknesses, so
their use allows different but compatible plots to evaluate thin beds
imaged on conventional seismograms.
1
In order to recognize the tuning patterns of complex trace attri-
butes, numerical modeling with AIMS (trademark of GeoQuest International,
Inc.) is used to generate synthetic seismograms from mathematical modelsl
of thin beds. Complex trace attributes are applied here to synthetics,
and to seismic reflection line VT-5 to explore changes in instantaneous
frequency and tuning from suspected thin beds.
2
.
The current understanding of the geology near Charleston, S.C. , is
summarized in Rankin (1977), Gohn (1983), and Coruh and others (1981).
Regionally, the Atlantic Coastal Plain is a seaward thickening wedge of
Cenozoic and Cretaceous sediments unconformably overlying one of four
rock types: Triassic/Lower Jurassic sedimentary rocks, Mesozoic mafic
igneous rocks, Pre-Mesozoic metasedimentary rocks, or Pre-Mesozoic crys-
talline basement rocks (Dillon, 1983). The stratigraphy has been deter-U
mined by Gohn (1983) from the deepest of three coreholes drilled
approximately 40 km WNW of Charleston, S.C. and shown in Figure 1. In
this location 750 m thickness of Cenozoic and Cretaceous sediments
unconformably overlie a 250 m thickness of _basa1t flows and associated
sedimentary rocks. In turn, the basalt overlies red beds of unmeasured
thickness due to the premature termination of drilling. Gohn's provenance
study (1983) of the recovered core, however, shows that the red beds
contain detrital clasts of felsic·p1utonic rocks, basaltic rocks, and
their cataclastic derivatives, from which it is inferred that the red beds
lie directly on crystalline basement.
In conjunction with the drilling, the Regional Geophysics Laboratory
at Virginia Tech recorded and processed 51 km of 24-fold seismic re-
flection data of which this study re-analyses 2 km of seismic reflection
data from line VT-5.
3
Figure 1. Map of field area: showing location of Virginia Techseismic line VT-5 and U. S. Geological Survey ClubhouseCrossroads Coreholes.
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Figure 4. Line drawing interpretation of single-sweep section forVT-5: from Belcher (1984) showing Mesozoic sedimentaryrocks overlying basement with horizontal exaggeration ap-proximately 2.5 to 1.
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Line VT·5 was chosen for this study because its field parameters and
processing yield the best section for interpretation of the deeper data
which imaged a buried Mesozoic bas:I.n. '1'he processing of Coruh gives the
. final stacked section, shown in Figure 2 which is notable for the re-
flections below approximately 0.6 s compared with the other VT seismic
lines. The interpretation proposed is that of a buried Mesozoic basin
between 1 and 2 s. The results of reprocessing by Belcher (1984) em-
ploying the techniques of VIBROSEIS whitening (Coruh and Costain, 1983)
and single-sweep processing are shown in Figure 3. Be1cher's interpre-
tation in his line drawing (Figure 4) uses the reflector geometry and
velocity analyses to infer either diabase sills or wedging sediments be-
tween 1.2 and 1.8 s. The primary goal of this study is to examine the
Mesozoic basin boundary and interior using complex trace attributes.
8
Taner and others (1977) first applied complex trace attributes to
reflection seismic data using the theoretical work of Gabor (1946).
Displays of complex trace attributes have been used for
lithostratigraphic interpretations (Taner and others; 1977, 1979).
Nogami and Robertson (1984) refined the method using instantaneous fre-
quency to analyze and interpret a sandstone pinchout imbedded in shale.
This application to thin·bed analysis for the interpretation of real
seismograms sparked this research.
Following Taner°s (1979) definitions, the three complex trace at-
tributas under consideration are instantaneous amplitude, instantaneous
phase, and instantaneous frequency. (See Appendix for definitions). The
qualifier "instantaneous" serves to distinguish complex trace attributes
of related but different functions of amplitude, phase, and frequency from
Fourier theory. Uulike Fourier theory where amplitude and phase are
evaluated in the frequency domain, all complex trace attributes are ex-
pressed in the time domain. The term °°instantaneous" refers to the value
of the the function at a particular instant of time.
9
Complex trace attributes are best understood using synthetic
seismograms. Synthetic seismograms produced in this study image the
reflectivity of idealized thin beds. Th:I.n·bed seismograms are modeled
numerically with an approximation of Kirchhoff-Helmholtz diffraction
theory (Trorey, 1970 and 1977) using the Advanced Interpretive Modeling
System, AIMS, from GeoQuest (AIMS and GeoQuest are trademarks of GeoQuest
International, Inc). AIMS takes a particular mathematical model, speci-
fied by compressional wave velocities expressed as functions of depth,
and then synthesizes a common-depth-point stacked seismogram as a func-
tion of two·way travel time.
A simple 3-layer representation of a wedge (Figure S) is used for
the idealization of a thin bed. The wedge geometry is held constant for
the next four models while the reflectivity contrast and noise content
are varied to study the effects on complex trace attributes. For each
model there is a suite of four plots to illustrate the conventional
seismogram, instantaneous amplitude, instantaneous phase, and instanta-
neous frequency.
The first wedge model (Figure 6) derived from Nogami and Robertson
(1984) is a dipole reflectivity sequence convolved with a 20 Hz Ricker
wavelet. The resultant seismogram substantiates the tuning phenomena of
thin beds when decomposed into its complex trace attributes. The in-
stantaneous amplitude (Figure 7) shows the function has its highest am-
10
Figure S. Mathematical model for wedge: where dipole spike seriesof positive and negative unit magnitude define thethinning layer.
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Figure 7. Instautaneous amplitude of noise-free syuthetic: Avariable area display shows the large magnitudes of theinstantaneous amplitude tuning in the presence of a
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Figure 8. Instantaneous phase of noise-free synthetic: The in-
stantaneous phase follows the continuity of the wedge, but
exaggerates the side-lobes of the wavelet.
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Figure 9. Instantaneous frequency of noise-free synthetic: Thecontour plot presents darker shades as larger values ofinstantaneous frequency. The high values of instantaneous
frequency associated with thin beds constitute tuning.
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plitude, or equivalently is tuned (by the definition of Sengbush,
Lawrence, and McDonal, 1961) at around 6000 m and 1.0 s where the layer
thickness is 1/2 the two-way travel time of the dominant period of the
Rieker wavelet. The instantaneous phase (Figure 8) exaggerates the
side-lobes of the Rieker wavelet, but otherwise the display is similar
to the eonventional seismogram. The instantaneous frequency (Figure 9)
has been restricted to the passband of the source wavelet, filtered with
a 2-dimensional 3 X 3 running median filter (Hoaglin and others, 1983),
and contoured. The instantaneous frequency shows the tuning due to the
thin bed; however, the maximum values of instantaneous frequency corre-
spond to two different effects. First, the peak values at 7500 m and 1.0
s are higher frequeneies due to differentiation of the source wavelet by
the thin bed. Where the source wavelet encounters the thinnest part of
the wedge, the wedge differentiates the wavelet. Differentiation in-
creases the frequency content of the source wavelet, and this is observed
in the instantaneous frequency. Second, the high values towards the the
center at 4000 m and 1.05 s correspond to the complete separation of two
reflected wavelets (Crammer and Leadbetter, 1967; Taner, 1979; Nogami and
Robertson, 1984). Only some high values of instantaneous frequency can
be attributed to tuning.
The second wedge model is a synthetic from AIMS with 1% additive
noise. The noise generated with AIMS is white with magnitudes normalized
to a chosen percentage of the maximum value on the entire seismogram.
AIMS calculates a reflectivity series with acoustic wave theory, con-
volves the series with the source wavelet, and then adds noise. The
synthetic data are transferred from AIMS format to DISCO format, resampled
16
Figure 10. Wedge synthetic seismogram with 1% noise: The wedgeis defined by compressional velocities of the layers interms of depth.
17a
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m and 1.0 s, but noise also gives peak values along top
and bottom edges.
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from 0.001 s to 0.004 s, filtered with a low-pass Henning window, and
displayed as a synthesized stacked seismogram. A noise level of 1% has
been added to the seismogram shown in Figure 10. The resultant complex
trace attributes are shown in Figure 11 through Figure 13. A small amount
of noise leaves tuning phenomena undisturbed; however, high values of
instantaneous frequency occur in regions of pure noise in addition to the
two effects for tuning of thin beds and the separation point of thick
beds.
The noise is iucreased to 10% in the third model, but all other pa-
rameters are the same. Similar to previous examples, the standard
seismogram (Figure 14), instantaneous amplitude (Figure 15), and instan-
taneous phase (Figure 16) adequately image the wedge, although the in-
stantaneous frequency (Figure 17) is severly degraded. The noise
displayed in the instantaneous frequency causes numerous high frequency
peaks making it difficult to distinguish thin beds from noise. Amplitude
tuning is more robust than frequency tuning in the presence of noise as
shown by comparing the pair Figure 15 and Figure 17 with the pair
Figure 11 and Figure 13.
The fourth wedge model returns to a low noise condition, but also
changes the velocities to decrease the acoustic impedance contrast in
order to diminish the interference effect between the two reflectors.
The reflection from the top layer on the conventional seismogram
(Figure 23) and on the instantaneous amplitude (Figure 24) masks the
presence of the bottom layer. On the other hand, the instantaneous fre-
quency (Figure 26) has characteristic high values associated with tuning.
21
Figure 14. Wedge synthetic seismogram with 10% noise
° 22a
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Figure 15. Instantaxxeous amplitude with 10% noise: shows tuningof instantaneous amplitude due to wedge.
23a
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Figure 16. Instantaneous phase with 10% noise: images the wedgedespite the noise.
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Figure 17. Instantaneous frequency with 10% noise: Noise degradesthe tuning effect of instantaneous frequency by coalesc·ing the high values due to tuning and due to noise intothe same contour.
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Figure 18. Wedge synthetic with low impedance contrast: Thedeepest region has an impedance much closer to that ofthe wedge compared with previous models which diminishesthe amplitude of the second reflector.
26a
Figure 19. Instautaueous amplitude of low coutrast synthetic: Thetuning shows a slight broadeniug of the top reflector,while the bottom reflector is poorly imaged.
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Figure 20. Iustantaneous phase of low coutrast syuthetic: givesequal weight to both reflectors without regard to theabsolute magnitude of the impedance coutrast.
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Figure 21. Instantaneous frequency of low contrast synthetic: Thehigh values of instantaneous frequency tune between 1/4and 1/2 the dominant wavelet, yet is insensitive to therelative amplitudes between the reflectors.
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In this manner instantaneous frequency is insensitive to the amplitude
response of thin beds. Instantaneous frequency helps to emphasize the
tuning phenomena of thin beds compared with the conventional seismogram.
Before analysis of the real data, a simplified model representing
VT-5 was created using AIMS, and the synthetic was subjected to complexl
trace analysis.
A 10-80 Hz Klauder wavelet used in lieu of the 20 Hz Ricker wavelet
complicates the instantaneous frequency because the side lobes give high
instantaneous frequency values in addition to the main lobe tuning phe-
nomena. The Klauder wavelet is filtered to enhance the interpretability
of the instantaneous frequency by tapering the side lobes at the expense
of broadening the main lobe (Berkout, 1984). The tapered 10-80 Hz Klauder
wavelet represents the source wavelet used. on. VT-5, although the re-
flections near the basin/basement boundary are poor in the higher fre-
quencies with the majority of the energy around 20-40 Hz. The higher
frequencies may have been lost by, for example, attenuation, dispersion,
source and receiver array response, or stacking. The cumulative effect
is that reflections near the basin/basement boundary· contained zux the
final single-sweep section have dominant frequencies around 30 Hz. A
1ow·pass filter is applied to the model synthetic for VT-5 to give the
synthetics presented in Figure 22 through Figure 26.
The mathematical model is an idealization of the angular unconform-
ity between the basin boundary and crystalline basement. The synthetic
seismogram and the instantaneous phase display the changes in polarity
and magnitude along the unconformity as the reflectivity contrast changes
between different layers and the basement. Prominent diffractions occur
30
at the termination of the horizontal layers against basement. The in-
stantaneous amplitude (Figure 24) is high where the acoustic impedance
contrast is large and also where tuning occurs as beds pinch out against
basement.
31
Figure 22. Mathematical model for a section of VT-5: represents
horizontal sedimentary beds in angular unconformity with
basement. The interval velocities are idealized from
Be1cher°s (1984) Velocity functions determined by con-
stant Velocity analyses.
32a
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Figure 23. Synthetic seismogram for model of VT·S: Acoustic wavesolution from AIMS displays reflections from the layersand diffractions from the pinchouts against the basement.
33a
Figure 2h. Instantaneous amplitude for model of VT·5: tuning oc-curs at the pinchouts.
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Figure 26. Instantaneous frequency for model of VT-5: exhibiting
tuning where the beds pinch out against basement.
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36
Instantaneous frequency tunes at less than 1/4 the period of the
source wavelet, and amplitude tuning occurs at 1/2 the period of the
source wavelet (Nogami and Robertson, 1984) for single wedge models. Both
functions are applicable to seismic line VT-5. The real data on VT·5,
however, exhibit variable noise and acoustic impedance contrasts, so the
model of Nogami and Robertson (1984) has been extended to include these
complexities. For example, amplitude tuning is robust in the presence
of noise and if the seismic trace is not too noisy, instantaneous fre-
quency tunes with characteristic peak values where the bed thins, even
if the reflectivity contrast is too small to be easily perceived on the
conventional seismogram. The regions of tuning between instantaneous
amplitude and instantaneous frequency tend to overlap at the scales
plotted for single-sweep data.
37
A segment (Figure 27) of single sweep processed data for VT-5
(Belcher, 1984) has been subjected to complex trace attribute analysis.
The instantaneous amplitude and phase demarcate the curvilinear re-
flections imaged on the conventional seismogram. The variability in re-
flection strength within the rocks makes amplitude tuning ambiguous on
the instantaneous amplitude plot. The instantaneous phase provides a
measure of the character of individual reflections which helps to confirm
continuity of reflections across the section.U
The instantaneous frequency shows peak values in the 40-45 Hz range,
less than the bandwidth expected for a 10-80 Hz Klauder wavelet. In ad-
dition, the instantaneous frequency is noisy, so determining which peak
values are due strictly to tuning is a matter of interpretation. The
largest areas of high instantaneous frequencies occur when several re-
flections merge on the conventional seismogram. For example, Station 97
at 1.55 s, Station 99 at 1.65 s and Station 101 at 1.50 s support the
hypothesis that pinchouts are the cause of tuning on the instantaneous
frequency plot. The character of the instantaneous frequency changes
across the inferred basin/basement contact which is shown, for example,
between the upper left and lower left sections of the display.
A prominent trend in instantaneous frequency occurs around Station
107 and 1.6 s marking a distinct area of low instantaneous frequency even
though the reflections are of large amplitude at this location on the
38
other complex and conventional plots. Instantaneous frequency values
less than 27 Hz are representative of the elliptically-shaped white area.
Several hypotheses may explain this large region of low frequency:
71. The lack of high frequencies is an artifact of processing; however,
neighboring reflections contain higher frequencies.
2. Fracturing of an otherwise homogeneous rock could scatter the
higher frequencies in the returning sigel.
3. A lithology with a low Q value could attenuate the sigel through
intrinsic damping. Coal has a low Q, but rarely forms beds over
3 m thick (Pettijohn, 1975) which makes it difficult to account
for the observed thickness of the low frequency zone.
4. Shale and siltstone may have a sufficiently low Q relative to
conglomerate and sandstone (Waters, 1981) to create the pod shaped
area of low instantaneous frequency seen on VT·5. In eastern
Mesozoic basins, sandstone and siltstone grade into each other,
and border conglomerates are common at basin boundaries
(Pettijohn, 1975). The instantaneous frequency plot may be imag-
ing lithologic changes within the basin sediments. The best in-
terpretation of the low-frequency zone on VT·5 may be a transition
from basin border conglomerates (high Q) into finer-grained
siltstones (low Q) nearer to the center of the basin.
39
Figure 27. Section of sing1e·sweep data for VT-5: expanded por-tion from Belcher (1984) imaging the inferred
basin/basement contact.
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l+3
Instantaneous frequency and instantaneous amplitude tune for simple
thin beds. Adding complexity to the synthetics reveals that instantaneous
frequency is more sensitive to a low reflectivity contrast than is in-
stantaneous amplitude. On the other hand, tuning of instantaneous am-
plitude is more robust in the presence of noise than is instantaneous
frequency. The truism is that any combination of too much noise and too
little reflectivity contrast will degrade any seismogram, whether dis-
played conventionally or with complex trace attributes. or complex.
’l‘un:Lng phenomena depend on the source wavelet as well as the geology.
Taner (1979) and Neidell and Robertson (1984) express tuning in terms
of the Ricker wavelet. This study has been extended to include the
Klauder wavelet, specifically the Klauder 1Q-80 Hz wavelet which is rep-
resentative of the source wavelet used to sound the sub-surface along line
VT-S. Using the Klauder on synthetics, plotting and display character-
istics of tuning in complex trace attributes have been calibrated and then
1:Lne VT-S has been subjected to complex trace attribute analysis.
The results are consistent with the previous interpretation given
by Coruh and others (1981). The complex trace attributes exhibit tuning
patterns consistent with an angular unconformity at depth between base-
ment and basin sediments of heterogeneous red beds. The technique allows
a different perspective with which to view the data. The original inter-
pretation for line VT-5 discovered a buried Mesozoic basin, The applica-
tion of complex trace attributes has explored this basin. Searching for
/+1+
tuning phenomena on VT-5 means looking for large instantaneous amplitudes
(loudness) or large instantaneous frequency (high pitch), but this en-
tails measuring the lows along with the highs. The juxtaposition of the
low instantaneous frequencies next to high instantaneous frequencies in-
itiated a re·examination of the conventional data in a new light. The new
interpretation is the proposal that the data on VT-5 and its complex trace
attributes have imaged a lithologic transition between
conglomerate/sandstone and siltstone/shale within a subsurface Mesozoic
basin.
45I
AEEEEHIK
Let g(t) represent the seismic trace and H[ g(t)] be the HilbertU
transform (Guillemin, 1949) of the seismic trace. Also let D g(t) and D
H[g(t)] be the first derivatives with respect to time of the trace and
Hilbert transform of the trace (Kuo and Kaiser, 1966; Hamming, 1983;
Ziemer, 1983). From Taner and others (1979) or Bracewell (1978):
The instantaneous amplitude, A(t), is
A(1=) = Sqrt{g(t)**2 + (H[s(t)1)**2}-
The instantaneous phase, P(t), is
PU:) = ¤r<=¤=¤¤{H{s(t>l/z(t)}-
The instantaneous frequency, FQ(t), is
FQ(¤) = (D s(¤)*H[s(t)] · s(t)*D H[s(t)]) / A(t)**2-
The use of black and white instead of color displays for complex
trace attributes has necessitated the following modifications to the
functions. The instantaneous amplitude has its mean removed and then
further biased before displaying on a variable area plot. The cosine of
the instantaneous phase is plotted instead of the instantaneous phase
itself. Before contouring, the instantaneous frequency has been re-
stricted to the passband of the source wavelet, and been subjected to at
least one 2-dimensional 9 point (the same as a 3-by-3 box array) runn:|.ng
median filter.
I 46
Belcher, S-W-,1984,RgggggsigggMasters Thesis, Virginia Polytechnic Institute andState University.
Berkcat, A- J-,1984,Eghg__Igghgjggg;* Handbook of Geophysical Exploration, V. 12,Geophysical Press, 228p.
Bracewell, R-N-, 1978, 2nded., McGraw-Hill, New York, chapters 6,12, and 18.
Coruh, C., Costain, J.K., Behrendt, J.C., and Hamilton,R.M., New re-flection seismic evidence for deformation of Mesozoic sedimentsnear* Charleston, South. Carolina, 1981, Annual. meeting of GSA,Cincinnatti, Ohio. Abstracts with Programs, v. 13, no. 7, p. 431.
Cremer H-, and Leadbetter, M- R- ,1967,RggggssgsgJohn Wiley & Sons, New York. _
Dillon, W.P., Klitgord, K.M., Paull, C.K., 1983, Mesozoic development andstructure of the continental margin off South Carolina, in StudiesRelated to the Charleston, South Carolina, Earthquake of 1886-Tectonics and seismicity, G. Gohn ed., USGS PP 1313, Washington,Section N.
Gohn, G., 1983, Geology of the basement rocks near near Charleston, SouthCarolina- Data from detrital rock fragments in lower Mesozoic(?)rocks in Clubhouse Crossroads test hole, #3, in Studies relatedto the Charleston, South Carolina, Earthquake of 1886- Tectonicsand Seismicity, Gohn, G., ed., USGS PP 1313, Washington, SectionE.
Guillemin, E- A- ,1949,;g_;hg_Mg;hgmg§iggl Training of Electrical Engineers, MIT Press,Boston, chapters 6 and 7.
Hoaglin, D.C., Mosteller, F., Tukey, J.W., 1983, §ggg;;;g¤g1gg_;ghg;;LgggJohn Wiley 8 Sans, New Yerk-
Henning, R- W- , 1983, Prentice-Hall, Inc- ,Englewood Cliffs, New Jersey.
Kac, F- F- , and Kaiser, J-F- ,1966,JohnWiley & Sons, New York.
Pettijohn, F, 1975, §ggjmgg;g;y_Rggk;, Third Edition, Harper & Row, NewYork, p. 216.
”47
Phillips, J.D., 1983, Paleomagnetic investigations of Clubhouse Cross-roads basalt in Studies related to the Charleston, South Carolina,Earthquake of 1886-- Tectonics and Seismicity, USGS PP 1313,Washington, Section C.
Rankin. D-W-. 1977.USGS PP 1028.
Washington.
Robertson, J.D., and Nogami,H.H., 1984, Complex seismic trace analysisof thin beds: Geophysics, v. 49, no 4, p. 344-352.
Sengbush, R.L., Lawrence, P.L., and McDonal, F.J., 1963, Interpretationof synthetic Seismograms: Geophysics, v. 26, n. 2, pp. 138-157.
Taner, M.T., Koehler,F., and Sheriff, R.E., 1979, Complex seismic traceanalysis: Geophysics, v. 44, no. 6, p. 1041-1063.
Taner, M.T., and, Sheriff, R.E., 1977, Application of amplitude, fre-quency, and other attributes to stratigraphic and hydrocarbon de-termination, in Seismic Stratigraphy- Applications to hydrocarbonexploration, Am. Assoc. Petr. Geol., Mem., 26, Tulsa, p. 301-327.
Sheriff, R.E., and Geldart,L.P., 1983, Exg1g;g;jgn_sgi5mg1ggy, volume 2:Data-processing and interpretation, Cambridge University Press,Cambridge, p. 73, p. 173.
Waters, K., 1981, Rgf1gg;1gg_§gj5mg1ggg, Second Edition, John Wiley and_ Sons, New York, p.30.
Ziemer, R. E.; Tranter, W. H.; and Fannin, D. R., 1983,Macmillan. 487pp-
48
