RAYLEIGH WAVE SCATTERING
ACROSS STEP DISCONTINUITIES
by
DOUGLAS ROBERT NATHMAN
S.B., Massachusetts Institute
of Technology
(1979)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF
MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
®
September 1980
Massachusetts Institute of Technology 1980
. .. .. ... .. ... .. . . .40.. . . . . . . . . ..
Department of Earth & Planetary Sciences
August 25, 1980
Signature of Author...-.......
Approved by.
Jacques Chamuel
,,---raper Laboratory Supervisor
Certified by...
Accepted by....
.
Nafi Toksoz
fC)
Thesis Supervisor
................................................
Committee
Chairman, Departmental Graduate
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M17LI03ARIES
UIBRARIES
RAYLEIGH WAVE SCATTERING
ACROSS STEP DISCONTINUITIES
by
DOUGLAS ROBERT NATHMAN
Submitted to the Department of Earth and Planetary
Sciences on August 25, 1980 in partial
fulfillment of the requirements for the
Degree of Master of Science in
Earth and Planetary Sciences
ABSTRACT
Propagation of Rayleigh waves across discontinuities
comparable to wavelength was investigated using two-dimensional
ultrasonic models. Specially designed transducers sensitive to
Rayleigh waves were used to generate and detect ultrasonic
waves in nickel sheets through magnetostrictive transduction.
Different discontinuities (steps and mountain-like features)
were cut along the edge of the nickel sheets. Reflection and
transmission coefficients were determined for each discontinuity. Computer plots showing amplitude and phase spectra
are also presented. Wave velocities in the nickel sheets are
2.776 km/sec for the Rayleigh waves and 5.082 km/sec for the
longitudinal body waves.
For the step discontinuities a difference exists between
the scattering of waves incident on an upstep and those incident
on a downstep. A significant amount of energy is scattered as
body waves in both cases, but is more severe for the upsteps.
The reflection and transmission coefficients are dependent on
frequency. Reflected waves from the upsteps show phase shifts
which are fairly constant. The downstep phase shifts change
significantly with frequency. The reflected signals from the
steps were found to be composed of two components: one from the
base of the step and one from the top of the step. The transmitted wave contains both direct surface waves and scattered
body waves which are converted back into surface waves. Due to
scattering and interference from the different components the
amplitude spectra are often irregular shapes. The empirical
relationship h = X/8 + (X/2)n (n=0,1,2...) in conjunction with
the equation c = fX was found to correspond to frequency dips
in the amplitude spectra of ,tbrp-egted waves, in some cases.
The mountain-like shapes "utP4
and rectangular 'mountains.
included ramps, pyramids,
The reflected and transmitted waves from the ramp were
found to be small. The base of the ramp causes large amounts
of conversions from Rayleigh waves to body waves. The ramp's
transmitted wave is also composed of a surface wave component
and a converted body wave component. Reflection from a
pyramid decreases as the pyramid's height is decreased. The
transmitted wave is made up of a body wave component which
travels through the base of the pyramid, and a surface wave
component which travels along the perimeter of the shape. The
converted component is larger than the surface one. Similar
results were found for the rectangular mountains.
Diffracted body waves from a corner are larger in certain
directions; i.e. +30* of the line traveled by the Rayleigh
waves before hitting the corner. These diffracted waves must
be taken into account when studying surface wave propagation.
Thesis Supervisor: M. Nafi Toksbz
Title: Professor of Geophysics
ACKNOWLEDGEMENTS
The author expresses his sincere thanks to all who helped
make this thesis possible: my thesis advisor, Prof. Nafi
Toks6z, for his many hours of help, understanding, and
patience--from the Mojave Desert to the Green Building; my
supervisor at Draper Lab, Jacques Chamuel, for uncountable
hours of guidance and insight; Terry S. Neiman, of M.I.T., for
constantly prodding me onward; Elvis Costello and Joe Strummer
for inspiration while writing many rough drafts; to my good
friends Matt Dolan, Glen Gawarkiewicz, Dave Gould, and Theodore
A. Peck III for their valiant work on the figures; to Ken
Tubman for help with the computer work; to Joseph W. Chapman
for yet another greatly appreciated late night typing job; and
to everyone who wished me luck along the way. A special thanks
goes out to Andy Walton for putting up with everything.
This research was conducted partly at the C. S. Draper
Laboratory, Inc., and partly at M.I.T. in a cooperative effort.
At C. S. Draper the work was supported under contract
F-04704-78-C-0002 with the Ballistic Missile Office of the U.S.
Air Force and CSDL Independent Research and Development project
no. 18325. At M.I.T. the research effort was supported by the
Advanced Research Projects Agency, monitored by the Air Force
Office of Scientific Research, under contract F-44620-75-C-0064.
TABLE OF CONTENTS
Page
Abstract
Acknowledgements
Table of Contents
List of Figures
I.
II.
III.
IV.
INTRODUCTION
ULTRASONIC MODELING APPROACH
RESULTS
3.1
3.2
Steps
Mountain-Like Features
SUMMARY AND CONCLUSION
23
Figures
List of Symbols and Abbreviations
APPENDIX A.
APPENDIX B.
REFERENCES
Amplitude and phase spectra plots shown
with reflection and transmission coefficients
for the steps
65
66
Amplitude and phase spectra plots shown
with reflection and transmission coefficients
111
for the mountain-like features
142
LIST OF FIGURES
Page
Figure 1.
Experimental Set-Up
27
Figure 2.
Picture of a Typical Seismogram
28
Figure 3.
Placement of Transducers for Reflection from a Step
29
Figure 4.
Placement of Transducers for Transmission Through
a Step
30
Figure 5.
Comparison of Infinite Upstep and Infinite Downstep
Reflections
31
Figure 6.
Comparison of Infinite Upstep and Infinite Downstep
Transmitted Waves (scale changed from previous figure)
32
Figure 7.
Amplitude and Phase Spectra for the Infinite Upstep
Model
33
Figure 8.
Reflection and Transmission Coefficients for the
Infinite Upstep Model (Reflection coefficient=
reflected signal/incident signal; Transmission
coefficient=transmitted signal/incident signal.)
34
Figure 9.
Amplitude and Phase Spectra for the Infinite
Downstep Model
35
Figure 10.
Reflection and Transmission Coefficients for the
Infinite Downstep Model
36
Figure 11.
Phase Shift Plots of Reflections from Infinite Step
Model
37
Figure 12.
6 mm Step Seismograms
38
Figure 13.
6 mm Upstep Amplitude and Phase Spectra. (The
amplitude scale is in arbitrary units. The relative
amplitude for the direct, reflected, and transmitted
spectra represent the correct values. Phase spectra
are shown in fractions of a cycle. Frequency is in
MHz.)
39
Figure 14.
6 mm Upstep Reflection and Transmission Coefficients
40
Figure 15.
6 mm Downstep Amplitude and Phase Spectra
41
Figure 16.
6 mm Downstep Reflection and Transmission
Coefficients
42
Figure 17.
Phase Shift Plots of 6 mm Step Reflections
43
Figure 18.
2 mm Step Seismograms
44
Figure 19.
2 mm Upstep Amplitude and Phase Spectra
45
Figure 20.
2 mm Upstep Reflection and Transmission Coefficients
46
Figure 21.
2 mm Downstep Amplitude and Phase Spectra
47
Figure 22.
2 mm Downstep Reflection and Transmission
Coefficients
48
Figure 23.
Phase Shift Plots of 2 mm Step Reflections
49
Figure 24.
Seismograms for the Complete Upstep Case (Step
heights are rounded to the nearest millimeter.)
50
Figure 25.
Seismograms for the Complete Downstep Case
53
Figure 26.
The Two Components of the Reflected Rayleigh Wave
56
Figure 27.
Seismograms of Ramps and Trapezoidal Models
57
Figure 28.
Seismograms of Pyramids
58
Figure 29.
Seismograms of Rectangular Mountains
59
Figure 30.
Paths of the Transmitted Wave Components for the
Ramps
61
Figure 31.
Components of Transmitted Wave Through Pyramids.
(The left column shows the complete transmitted
signal. The right column shows the effect of
damping the top of the pyramid thereby allowing
only the coverted component of the transmitted wave
to pass through.)
62
Figure 32.
Diffracted Body Waves
63
Figure 33.
Summary of Model Shapes and Signal Waveshapes
65
CHAPTER I
INTRODUCTION
The earth is often modeled as a laterally homogeneous
In this simplified
medium comprised of many parallel layers.
view, changes in densities and velocities are functions only
of depth or radius.
While this approximation makes many
theoretical formulations possible, the earth is in actuality
laterally heterogeneous.
Surface topographical features as
well as geologic structure vary laterally.
Surface wave propagation across lateral heterogeneities
is a complex phenomenon.
The aim of this thesis was to study
this problem using two-dimensional scaled ultrasonic models.
The modeling technique is described in detail in the next
section.
Numerous efforts have been made to study surface waves in
the past.
Theoretical, experimental, and in situ methods have
been employed.
Using analytical methods Hudson and Knopoff (1964) used a
Green's function to compute reflection and transmission coefficients of surface Rayleigh waves incident normal to the
corner of a homogeneous elastic wedge.
Mal and Knopoff (1965)
used a similar method to find coefficients for Rayleigh waves
incident on a step change in elevation.
McGarr and Alsop
(1967) employed an approximate variational method to study
Rayleigh waves normally incident on vertical discontinuities
in plane layered structures.
One weak point of this method is
that it accounts for only the Rayleigh waves generated at the
boundary.
Lapwood (1961) used operational methods to ana-
lytically attack the problem of a Rayleigh pulse impinging
onto a corner and found that the transmitted wave was of a
different shape than the incident one.
These results agree
qualitatively with de Bremaecker's (1958) experimental results.
More recently, finite element and finite difference methods
(Munasinghe and Farnell, 1973) have also been used.
Other theoretical studies have examined reflection and
transmission from different shaped boundaries, such as steps
and grooves (Li, 1972; Tuan and Li, 1974; Curtis and Redwood,
1975; Otto, 1977; Parekh and Tuan, 1977), as well as the
general problem of topographic irregularities (Gilbert and
Knopoff, 1960; Hudson and Knopoff, 1967; Thapar, 1970; Bouchon,
1973; Farshad and Ahmadi, 1974; Deresiewicz, 1974; Sills, 1978.)
Because of the complexities imposed by a heterogeneous
media, all of the theoretical analyses involve some form of
approximation or a numerical method.
How accurate these
approximations are and how well the numerical methods converge
is not well known at this time.
Experimental modeling work has been carried out by Oliver
et al. (1954); Knopoff and Gangi (1960), who looked at wedges;
Toks6z and Anderson (1963), who used piezoelectric transducers
on brass sheets; and Pilant et al. (1964),who observed the
behavior of waves incident upon a corner as a function of
angle.
Dally and Lewis (1968) show that reflection and trans-
mission coefficients depend heavily on the angle of the wedge
being observed.
Here and in a later paper (Lewis and Dally,
1970) they used a photoelastic approach to view the waves, yet
it is not easy to separate unwanted wave types and interfering
modes using this method.
Martel et al. (1977) compared
reflection and transmission coefficients and their relation to
step height.
As the coefficients were, for the most part,
fairly small a significant amount of the incident energy is
obviously being scattered into body waves.
All these studies point out the fact that the Rayleigh
waves are quite sensitive to small changes in the shape of the
discontinuity.
Modeling can provide a relatively fast and
easy way of analyzing this phenomenon.
Two-dimensional
modeling is a very useful tool in understanding complicated
aspects of wave propagation and will eventually lead to effective three-dimensional models.
The scope of this thesis was to determine the effect of
different topographical shapes on Rayleigh waves, using the
magnetostrictive seismic ultrasonic modeling approach introduced by Chamuel (1979).
steps was
studied
Scattering across two-dimensional
and reflection and transmission coef-A
12
ficients were obtained to determine the effect of step height.
Then, the experiments were extended to several 'mountain-like'
shapes and, once again, scattering across these topographical
features was analyzed.
CHAPTER II
ULTRASONIC MODELING APPROACH
Two-dimensional models are a useful way to investigate
Rayleigh wave scattering across surface irregularities and
changes in topography.
A thin plate is used to model the
earth and the topographical features being examined are cut
along the edge of the plate.
Elastic waves were generated and detected in a magnetostrictive material (the thin plate) through contactless
magnetostrictive transduction.
Specially designed trans-
ducers (Chamuel, 1977) consisting of electromagnetic coils were
utilized in the experiments.
Reflection, transmission, and
scattering across discontinuities were studied by placing the
source and receiver transducers in different positions.
A 0.02 inch thick sheet of Nickel 200 was chosen as a magnetostrictive material.
The received signal was displayed on an
oscilloscope, where it was photographed and recorded.
When a current is applied to the source transducer a local
stress is produced in the nickel sheet.
This results in a
deformation which travels away from the source.
Magnetostric-
tion is the change in a body's dimensions due to magnetization.
This change in size is associated with domain orientation.
In
14
a ferromagnetic material the magnetization in one small region,
or domain, may be oriented in a different direction from that
of another domain.
In an unmagnetized material the individual
domains, within which the magnetic dipole moments are aligned,
are oriented at random.
As the material is magnetized, by
being placed in an external magnetic field, two things happen.
First, the domains which are favorably oriented with respect to
the field increase in size while the others decrease in size.
Then, the direction of magnetization within each domain rotates
toward the applied field.
Therefore, the section of the nickel
sheet adjacent to the source undergoes a change in dimensions
and the outgoing wave arrives at the receiver at time t=x/c;
where x is the distance between the transducers and c is the
velocity of the wave in the nickel sheet.
As we were concerned with investigating Rayleigh wave
behavior, measurements were made along the edge of the nickel
sheets where the surface waves travel (see Figure 1).
Magneto-
strictive transducers which fit around the edge of the nickel
sheets were used.
These transducers generally have a broader
frequency response than piezoelectric transducers.
The system
response extended over the range 50-400 kHz.
A typical picture of the direct and reflected Rayleigh
waves is shown in Figure 2.
longitudinal body waves;
In this figure [1] represents the
[2] represents the direct Rayleigh wave
traveling from the source to the receiver;
[3] represents the
Rayleigh wave reflected back from the discontinuity.
[4]
represents the reflection from the far edge of the sheet.
In this study when investigating scattering across various
sizes of steps, waves incident on upsteps as well as waves
incident on downsteps have been studied.
Figure 3 shows the
placement of the transducers to observe the direct wave and
the wave reflected from an upstep (top figure) and the direct
wave and the wave reflected from a downstep (lower figure).
Figure 4 shows the transducer arrangement for transmission
through a step.
The goal was to observe the effect of step height on the
reflection and transmission coefficients and to see the differences between the upstep and the downstep cases.
Also the
scattering across several 'mountain-like' shapes was
studied.
CHAPTER III
RESULTS
The experimental results are presented in two sections.
The reflection and transmission coefficients for different
step-like shapes are discussed first, followed by a second
section discussing the effects of mountain-like topographical
features.
3.1
Steps
We found the Rayleigh wave velocity in the nickel sheets
used to be c=2.776 mm/psec and the longitudinal wave velocity
to be cp= 5 .08 2 mm/psec.
(These units scale one-to-one to
km/sec.)
A large cut was made in a nickel sheet approximating an
'infinite' step (many wavelengths long).
The same sheet was
used to study the effects of an infinite upstep and an infinite
downstep on Rayleigh wave propagation.
Figure 5 shows the reflections for both the upstep and
downstep cases.
The upstep reflection is much smaller than
the reflection from the downstep.
The transmitted waves for
both cases are shown in Figure 6.
Once again we see that the
amplitude is slightly greater in the downstep case.
As both
reflection and transmission are smaller for an upstep, more
energy is scattered into body waves in the upstep case.
Figures
7 - 10 show amplitude and phase spectra and reflection and
transmission coefficients for the Infinite Step.
In Figure
11 plots of the phase shift for the reflected waves are presented.
While the phase of the upstep reflection is fairly
constant, the downstep reflection varies greatly with frequency.
Examining the 6 mm step we see similar results.
Both the
reflected and transmitted waves are larger for the downstep
case.
We again see phase reversal for the reflected wave.
The
2 mm step, the smallest one studied, shows high amounts of
transmitted energy, as is expected.
(Figures 12 - 17 show the
data for the 6 mm step and Figures 18 - 23 show the data for the
2 mm step.)
We now turn to the case of the steps in general.
direct, reflected and transmitted wave
The
shapes are shown in
Figures 24 and 25 for upsteps and downsteps, respectively.
(Plots of amplitude and phase spectra, as well as reflection
and transmission coefficients are displayed in Appendix A.)
Looking at the complete picture of wave scattering across
steps we make several observations.
The reflected signal is
consistently larger from a downstep than from an upstep of the
same height.
The transmitted wave, in general, is also larger
in the downstep case.
This confirms our earlier observation
that an upstep causes more scattering of energy than does a
downstep.
Examining the two sets individually, we find that the
reflected upstep signal appears to 'spread out' as the step
height (h) becomes larger.
As the duration of the reflected
signal increases its average amplitude decreases.
The down-
step reflection experiences a similar phenomenon, but, in
this case, when the signal 'spreads out' the first of the two
apparent components stays at approximately the same amplitude
even as h is increased--very unlike the upstep case.
In both
upstep and downstep cases the transmitted signal duration
increases.
When the incident wave 'hits' the base of the step, a
portion of the wave is reflected, another part is converted
into body waves, and a third part is transmitted.
The trans-
mitted wave continues traveling up the side of the step.
At
the top of the step, another boundary is reached causing new
reflections.
Once again, some of the energy continues onward
as the transmitted wave, but some of the energy is reflected
back down the step.
This signal, together with the first
reflection from the base of the step, make up the complete
reflected wave (see Figure 26).
(This holds for upstep and
downstep reflections.)
Therefore, when the incident wave is in the form of a
single pulse, the reflected wave will be composed of two
pulses.
The two reflected wave components can have different
amplitudes and frequency contents.
The time delay of the two
signals is contributing to the interference of the reflected
waves.
As the points of reflection for the two pulses are
separated by the distance h (the step height), the reflected
component from the top will arrive at the receiver at time 2h/c
after the reflection from the base arrives.
When h is not very
large, the two pulses arrive close together in time and conbine
to form one pulse.
As the size of the step is increased the
reflection from the top becomes more delayed and the two Iulses
start to destructively interfere
with one another.
If tie
step height is made large enough, they will be discerned a'
individual pulses.
The reflected and transmitted signals are made up ol
several components causing the spectra of the reflection and
transmission coefficients to be irregular and complex.
Je
amplitude spectra, especially for the upstep case, show lips'
due to the interference at certain frequencies.
It was
observed that the interfering frequencies of the reflecti
signals follow the equation h= X/8 + (X/2)n
where X denotes the wavelength.
(n=0,l,2,3.),
Additional studies areeeded
to verify this empirical relation.
3.2
Mountain-Like Features
We next looked at scattering across several mrtain-like
shapes.
Again,
these shapes were cut along the edg~f nickel
20
sheets.
The wave shapes and the dimensions of the mountain
features are shown in Figures 27 - 29.
(Amplitude and phase
spectra as well as reflection and transmission coefficients
are displayed in Appendix B.)
Reflection and transmission from these mountain-like
features show many interesting characteristics.
In the case
of the ramp, the reflected signal is small as is expected.
Yet, the transmitted signal is small, also.
Instead of the
Rayleigh wave being easily transmitted up the ramp, it is
converted into body waves at the base of the ramp.
Comparing the two ramps, we see that for the lower ramp
the transmitted wave (both up and down the slope) appears to
be a clean pulse.
The higher ramp shows us that the trans-
mitted wave is actually comprised of two parts.
The first
portion has traveled through the interior of the sheet as a
converted body wave, while the later arriving portion of the
transmitted signal is the surface component which follows the
outline of the ramp along the edge of the sheet.
Figure 30
shows the different paths traveled by the two components of
the ramp's transmitted wave.
Perhaps the most intriguing event occurs in the pyramid
case.
The reflected wave decreases slightly as the height of
the pyramid is decreased.
The transmitted wave clearly shows
that it is composed of two distinct components.
By damping
the top of the pyramid to attenuate the waves traveling along
this path, we see that the purely surface component forms the
second part of the transmitted wave.
The leading portion of
the transmitted wave has traveled through the base of the
pyramid as a converted body wave.
Emerging from the base it
becomes converted back into a Rayleigh wave.
This converted
pulse is also larger than the pure surface wave component
traveling along the perimeter of the pyramid.
Figure 31 shows the complete transmitted wave for the
pyramid and then shows the same wave with the top of the
pyramid--and the wave traveling over the top of the pyramid-damped to reveal only the converted transmitted component.
This clearly shows the two distinct components of the transmitted wave.
(Calculation of travel times confirms this, also.)
The reflection and transmission from the rectangular
mountain shapes are not very sensitive to changes in the height
or width of the mountain.
A reflection from a wider mountain
shows ringing from multiple internal reflections.
Comparing the mountains with pyramids of equal height we
unexpectedly (from intuition) find the reflection to be larger
from the pyramid.
Again, the sharp corner at the mountain
base--similar to that in the upstep case--creates a large
amount of scattering into body waves.
Comparing the trapezoid
(a shape half way between the
pyramids and the rectangular mountains) to Pyramid #3 (both
the same height) we find the pyramid's reflection to be larger.
22
The transmitted waves for the two shapes look very different
from one another.
To get an idea of the direction of diffraction of Rayleigh
waves from a corner we placed transducers as shown in Figure
32a.
We found the diffracted body waves are larger in some
directions than in others (Figure 32b).
23
CHAPTER IV
SUMMARY AND CONCLUSION
Ultrasonic modeling is a useful and practical way of
studying surface wave propagation across various shaped discontinuities.
Rayleigh wave scattering from topographical
features is quickly displayed by the modeling technique and
the results often defy intuition (see Figure 33).
In this
study the Rayleigh waves were generated and detected using
contactless magnetostrictive transduction in a nickel sheet.
Two main types of features were studied: steps and mountains.
Reflection and transmission coefficients and amplitude
and phase spectra were calculated for all cases.
Wave
velocities were found to be 2.776 km/sec for the Rayleigh
waves and 5.082 km/sec for the longitudinal body waves.
For the steps, it was found that a significant difference
exists between scattering from an upstep and a downstep.
The
upstep reflection is significantly smaller than the downstep,
as illustrated with the Infinite Step.
The upstep's trans-
mitted wave is also smaller implying that more energy is converted into body waves in the upstep case.
Reflected waves from the steps show phase shifts as is
expected,but the upstep shows a phase shift which is fairly
constant while the downstep phase shift changes significantly
24
with frequency.
The surface waves impinging on the steps are subject to
tremendous amounts of scatter and conversions into body waves.
The reflected signal increases in duration with step height.
This occurs because the reflected signal is composed of two
components: a reflection from the base of the step and a reflection from the wave which continues up the step and is then
reflected back by the top of the step.
These two components
constructively interfere when the step height is small and may
not be detected.
The transmitted wave, also, is made up of
two main components.
One is the surface component
traveling
along the edge of the step, and the other is a diffracted component which is converted to a body wave at the base of the
step.
The body wave travels through the interior of the nickel
sheet and is converted back to a Rayleigh wave as it emerges
onto the edge of the sheet.
This diffracted component travels
at body wave velocities inside the sheet.
Since it also travels
a shorter distance than the surface component, it will arrive
first, followed by the surface component.
Due to the large amounts of scattering and interference
between the different components, the amplitude spectra are
often irregular shapes.
Looking at the reflected amplitude
spectra many dips in amplitude are observed.
The empirical
relation h = A/8 + (A/2)n
(n=0,l,2,3...) in conjunction with
the equation c=fX was found to correspond to the frequency
dips in the amplitude spectra,, in some cases.
The mountain-like shapes studied included ramps, pyramids,
and rectangular mountains.
Like the steps these were cut along
the edge of the nickel sheets.
The wave reflected from the ramp was small in amplitude.
The transmitted wave was small too, however.
Instead of the
Rayleigh waves easily traveling up the ramp they are largely
converted into body waves at the base of the ramp.
Similar to the steps, the ramp's transmitted wave is also
made up of two components.
The diffracted portion and the
surface portion may not be discernable for small ramps.
As the
two path lengths diverge the two components have a larger delay
and are easier to detect.
The reflected wave from the ramp is
smaller than that from a step of the same height.
Reflection from a pyramid decreases as the pyramid's
height is decreased.
The transmitted wave for the pyramid
shows many interesting phenomena.
The transmitted wave con-
tains two distinct signals; a converted portion which travels
through the base of the pyramid; and the surface component
which travels along the perimeter of the shape.
The converted
pulse (Rayleigh wave to body wave and then back to Rayleigh
wave) arrives first and is larger than the surface component.
The difference in the path lengths traveled and the difference
26
in velocities determine the separation in time of the two
pulses.
Small changes in the height and width of the rectangular
mountains do not considerably change the reflected and transmitted waves.
Comparing these mountains to pyramids of the
same height we find the pyramid reflection to be larger.
This
means that--as in the upstep case--the corner of the mountain
is causing heavy conversion of surface waves into body waves.
We also found that the diffracted body waves from a corner
are
larger
in an area +30* of the line traveled by the
Rayleigh waves before hitting the corner.
From these experiments it is clear that Rayleigh wave
propagation across topographical features contains many
interesting facets.
Future studies can shed more light on some
questions raised here.
27
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|I
'
0.20 0.25 0.30 0.35 0.40
0.15
.e
e.00
4.eS
0.1e
STEP
UP
I
0.20
0.25
FREQUENCY
FREQUENCY
INF.
I
e.IS
INF.
Trans.
STEP
UP
Trans.
i.e
e.9
A
P
.8--
m
L0.7
T
U
D
E
0.6
9.
0.5
e.3
0.2
0.1
e.0
e.e5
0.1e
e.IS e.2e e.25
FREQUENCY
0.30
0.35 0.40
e.00
Figure 7.
e.05
0.1e
$.IS 0.20 0.25
FREQUENCY
REF.
(Inf.
00EFF.
Step
UP)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
till
0.0
0.00
0.05
1
0.10
TRANS.
1111111
III
0.20
0.25
0.15
FREQUENCY
COEFF.
(Inf.
0.30
Step
0.35
0.40
UP)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
I
0.0
I
I
I
0.00
I
I
1
0.05
0.10
Figure 8.
0.15
I
I
0.20
0.25
FREQUENCY
I
I
I
0.30
0.35
0.40
35
IMF.
STEP
DOUN
INF.
Dir.
Dir.
DOUN
STEP
1.0
0.9
m
9.8
P
0.7
T
U
E
0.6-
D
to
0.4
8.3-
6.6 620
616 0.1
0.2
0.60
*.S
Imr.
630I
0.39
*.15
9.29
9.25
FREQUENCY
STEP
DOUN
I
.
9.35
6.16
0.40
0.00
0.05
0.15
6.10
0.20
I
0.25
,I
,I
0.30
0.35
0.40
FREQUENCY
INF.
Ref.
Ref.
DOWN
STEP
1.0
6.9
A
0.8
L
0.7-
T
U
E
0.6
0.5
0.4
0.3
0.2
0.1
0.00
S5
0.10
INF. STEP
1
6.15
0.26 6.25
FREQUENCY
DOUN
6.30
0.35
0.40
0.0
6.65
6.10
6.15
0.20
0.25
0.30
0.35
0.40
6.35
0.40
FREQUENCY
INF.
Trans.
Trans.
DOUN
STEP
1.0
0.9
A
P
0.8
1
T
U
0.7
E
0.6
I
0.5
0.4
0.3
0.2
6.1
6.00
0.5
6.16
6.15
6.20
0.25
FREQUENCY
0.30
0.35
0.40
6.6
6.66
I
0.65
0.16
I
'1
6.15
0.20
FREQUENCY
Figure 9.
I
0.25
I'
6.30
36
REF.
COEFF.
(Inf Step
DOWN)
i.7
0.9
0.8
0.7
0.6-
0.50.40.3
0.2
0.1
I
0 .0
0.00
0.05
0.10
TRANS.
*
0.15
0.20
0.25
FREQUENCY
COEFF.
------
II
(Inf. Step
0.30
0.35
0.40
0.35
0.40
DOWN)
1.0
0.9
0.8
0.7
0.6-
0.50.40.3
0.2
0.1
-
0.0
0.00
0.05
0.10
0.15
0.20
0.25
FREQUENCY
Figure 10 .
0.30
1.0i
INF. STEP REFLECT' N
21
A4~ .6
(cycles)
UPSTEr
.2
01
*
21
250
150
50
*
*
*
350.
'
450
Freq.
(MHz.)
.
-. 4
-. 6
-.8
.8
(cycles).4
1
DOWN STEP
.2
0
50 *.
150
.
250
.
350
4.?0
.
-0
-.
Freq.
2
-.4
5
Se
-1.0
Figure 11.
(MHz.)
38
Dir.
Shape
Ref.
6I
'JPSTEP
DOWNST EP
10 psec
Figure 12.
Trans.
39
h-6.859
UP
Dir.
h-6.859
UP
Dir.
1.0
8.9A
m
P
L
0.7
T
U
E
8.6
18
0.5
0.4
0.3
6.2
0.1
0.0
0.65
0.00
6.10
h-6.059
8.15
0.20
FREQUENCY
UP
0.25
0.30
9.35
8.40)
0.00
Ref.
0.05
0.10
h-6.059
$.15 0.20
0.25
FREQUENCY
UP
0.30
0.35
0.40
0.30
0.35
0.40
0.30
0.35
0.40
Ref.
1.0
0.9
A
8.8
L
0.7
T
U
8.6
1
E
0.5
8.4
6.3
-.-
0.2
0.1
16~1
j'I
'
'_
0.88
0.05
6.10
h-6.059
0.15
0.20
FREQUENCY
UP
0.25
0.30
0.35
8.8
0.40
0.08
0.65
0.18
h-6.059
Trans.
0.15
0.20 8.25
FREQUENCY
UP
Trans.
10
1.8
8.9A
8.8P
L
T
U
D
E
0.7
0.6
1
0.5
0.4
0.3
0.2
0.1
0.6
0.0
0.05
0.10
6.15
0.20 0.25
FREQUENCY
0.30
0.35
6.40
0.00
Figure 13.
0.85
0.16
0.15
0.20
0.25
FREQUENCY
REF.
(h-6.059
00EFF.
UP)
1.0
0.9
0.8
0.70.6-
0.50.4
0.3
0.2
0.1
0.00
0.05
0.10
TRANS.
0.15
0.20
0.25
FREQUENCY
(h-6.059
COEFF.
0.30
0.35
0.40
0.35
0.40
UP)
1.0
0.90.80.7
0.6
0.50.4
9.3
0.20.10.
0.00
I
0.05
I
0.10
a
I
a
0.25
0.15
0.20
FREQUENCY
0.30
Figure 14.
Dir.
DOWN
h-6.059
h-6.059
102
Dir.
-
1.
0.g
A
0.8
p
L
0.?
T
U
E
DOWN
6.6
19
8.5
-
6.4-
0.3
0.2
0.1
0.00
0.65
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.0
-
6.0
FREQUENCY
.
0.30
0.40
0.35
Ref.
DOWN
h-6.059
Ref.
DOWN
h-6.059
8.15
0.20 0.25
FREQUENCY
6.16
0.05
1.0
0.9
A
0.8
p
0.7
1
TU
E
.6
1
0.5
0.4
0.3
0.2
0.1
16
0.00
i
I
0.05
I
,
6.10
h-6.059
.
I
,
0.15
I
1
0.20
FREQUENCY
DOWN
0.25
6.8
0.30
0.35
0.40
I1
.
0.00
Trans.
0.05
0.10
h-6.059
16
,
6.15
0.20
FREQUENCY
I
0.25
,
I
0.38
,
I
.
0.35
,
0.40
Trans.
DOWN
1.0
0.9
A
6.8-
p
L
T
U
C
0.7
0.6
I
0.50.4
0.3
0.2
6.00
0.65
6.10
0.15
8.20
0.25
FREQUENCY
0.30
8.35
0.40
6.00
8.65
9.10
0.15
0.20
0.25
FREQUENCY
Figure 15.
0.30
0.35
0.40
42
REF.
COEFF.
(h-6.059
DOWN)
1.0
0.9
0.80.?
0.6
0.5
0.4
0.3
0.2
0.1
I
0.10
0.0
0.00
0.05
TRANS.
'
0.15
0.20
0.25
FREQUENCY
COEFF.
(h-6.059
0.30
'
0.35
0.40
0.35
0.40
DOWN)
1.0
0.9
0.8-
0.7O.S
0.50.4
0.3
0.2
0.1
0.0
'
'
0.00
I
0.05
0.10
Figure 16.
i
I a'
0.15
0.20
0.25
FREQUENCY
0.30
43
6mm. STEP
1.0 T
*A .6
(cycles)
.4
' - LtCT IO'NS
0
*
*
*
*
*
0
*
UPSTEP
.2
0
-. 2
p
J
.
-
50 100 150 200 250 300 350 400 450 500
Freq.
(MHz.)
.8T
(cyc les)
.4
DOWNSTEP
.2
04-2
-.4
.p
i
50 100. 150 200 250 300 350 400 450 500
*
.
Freq.
0
0
-.6
1.0
Figure 17.
(MHz.)
44
Dir.
Ref.
Shape
211
UPSTEP
Dt2
DOWNSTEP
Figure 18.
Trans.
45
h1.880
UP
h1.980
Dir.
UP
Dir.
102
1.6
-
0.9
A
P
p
L
0.8
T
U
D
E
6.6-
6.7
19
6.5.1
6.46.3-
6.1-
0.65
.0
0.16
$.15
0.20
FREQUENCY
0.25
6.35
6.30
6.40
6.66
0.05
6.16
0.25
6.15
6.20
FREQUENCY
0.36
0.35
0.30
0.35
0.40
0.30
0.35
6.40
6.40
1
h-1.889
Ref.
UP
he1.886
UP
Ref.
1.6
0.9
A
R
P
L
0.8
T
U
D
E
0.6
6.7
6.56.46.36.26.10-1 v
I
0.00
I
6.65
,
I
0.16
ha1.880
.
I
,
I
0.20
I
6.15
0.25
FREQUENCY
UP
,
I
0.30
,
I
6.35
,
\l
0.40
-00
0.05
0.10
0.15
0.20
0.25
FREQUENCY
h"1.880
Trans.
UP
Trans.
1.6
6.9
A
m
P
L
T
U
E7
E
6.8-
9.7
0.6
0
-6
6.5
6.4
0.3
0.2
6.1
6.00
6.65
6.16
6.15
6.20
0.25
FREQUENCY
0.30
0.35
0.40
0.00
6.65
Figure 19.
0.10
6.15
0.20 0.25
FREQUENCY
46
REF.
1.0
COEFF.
(h-1.880
UP)
-
0.90.80.7
0.6
0.5
0.4
0.3
0.2
0.1
I '
0.0
0.00
0.05
I
0.10
I
'
0.15
0.20
I
I
0.25
0.30
'
I
'
0.35
0.40
0.35
0.40
FREQUENCY
TRANS.
i.e
COEFF.
(h-1.880
UP)
--
0.90.80.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-
0.00
0.05
0.10
0.15
0.20
FREQUENCY
Figure 20.
0.25
0.30
h-1.880
DOWN
h-1.880
Dir.
DOWN
Dir.
162
1.6
-
6.96.8P
0.7
T
U
E
E
0.6
16
6.5-
0.4
6.3
0.2
0.1
1
0.00
S.65
0.10
0.9
0.15
0.20
6.25
0.30
0.35
0.00
0.40
0.05
0.10
FREQUENCY
h=1.880
DOWN
Ref.
Do&
0.15
0.20
FREQUENCY
0.25
0.30
0.35
0.40
0.36
0.35
6.46
Ref
DOW"N
1.0
0.9
0.8
0.7
6.6
0.5
0.4
0.3
6.2-
I I I I
9.00
0.05
0.10
hel.880
., . . . , ,,I
0.15
6.20
6.25
FREQUENCY
DOWN
0.30
6.1
9.0
0.35
0.00
0.65
0.10
0.15
0.26
6.25
FREQUENCY
Trans.
h-1.880
102
DOWN
Trans.
1.0
0.9A
e.g-
P
L
0.7
T
U
E
0.6
16
6.5
0.4
0.3
0.2
0.1
6.6
6.00
0.05
-
0.10
0.15
0.20
0.25
0.30
6.35
6.40
0.0
FREQUENCY
Figure 21.
0.05
0.10
0.15
6.25
6.26
FREQUENCY
6.36
0.35
6.40
48
REF.
1.0
COEFF.
(h-1.880
DOUN)
-
0.80.7
0.6
0.5
0.4
0.3
0.2
0.10.0
0.00
III
Ill
-
-
0.05
0.10
TRANS.
0.15
0.20
0.25
FREQUEHCY
COEFF.
(ho1.880
I
0.30
I
J
I
0.35
0.40
0.35
0.40
DOUN)
1.0
0.9
0.80.70.60.50.4
0.3
0.2
0.1
0.0
'
0.00
0.05
0.10
0.15
0.20
FREQUENCY
Figure 22.
0.25
0.30
49
2mm.
1.0
(Cyclcs
STEP RE LECTltN
.4[
UPSTEP
50
,50..
0
250
150
450
350
Freq.
-. 2
(MHz.)
-. 4
0
-. 6
-.8
-1.0
.ar
A( s .6
DOWNSTEP
(cycleGs)4
50
250
150
*
350
450
- -
-. 2
Freq.
-
-. 4
-. 8
1.Ot
0.0
Figure 23.
(MHz.
Dir.
Trans.
Ref .
UPSTEPS
4
61
8$11
Figure 24a.
Dir
Shape
Ref .
10l
12
1
14
Figure 24b.
Trans.
Dir
Ref .
Shape
16
Figure 24c.
18
{
20
{
Trans.
Dir.
Trans.
Ref .
DOWNSTEPS
12
114,
16
I18
Figure 25a.
Dir.
Ref -.
Shape
10
112
Figure 25b.
Trans.
Dir.
Ref .
Shape
~13
Figure 25c.
Trans.
56
I->
1 direct wave
2 reflected wave
from 'base' of
step
S
R
3 reflected wave
from 'top' of
step
Figure 26
Dir.
Ref.
Trans.
Shape
(up)
19.5
Ramp #1
8
Ramp #2
41
Trapezoid
Figure 27.
(down)
58
Dir.
Ref.
Shape
41
Pyr #3
Figure 28.
Trans.
59
Dir.
Ref .
Shape
Trans.
Mt #2
10
Mt #3
.
20
20
Mt #4
720
20
Fig.
29a
60
Dir .
Tr ans .
Shape
Re f.
#5
#5
41.5
15
41.5
Fig.
29b
surface component
diffracted component
Figure 30
62
complete transmitted wave
converted component
path of
converted
component
path of
surface
component
Figure 31.
1
~r~Th
64
R
n
a0
Distance
(mm)
450
165
900
205
1350
237
1500
243
162.50
247
180*
249
2070
245
2370
230
V.v
Yll
Iim
n
YWULULUU
R6
Figure 32b.
65a
Dir.
Trans.
Shape
ReF.
...2
10 Psec
10 Isec
I
7
19.5
28
19
41
U10
Figure 33.
65b
LIST OF SYMBOLS AND ABBREVIATIONS
c
Rayleigh wave velocity
cp
longitudinal body wave velocity
h
step height
f
frequency
A
wavelength
R
reflection coefficient
T
transmission coefficient
Dir.
direct (incident wave)
Ref.
reflected wave
Trans.
transmitted wave
Pyr
pyramid feature
Mt
rectangular mountain feature
Trap.
trapezoid feature
APPENDIX A
This appendix contains the amplitude and phase spectra
plots as well as the reflection and transmission coefficient
curves for all of the step discontinuities.
(The amplitude
spectra are displayed in the left column and the phase spectra
are in the right column.)
The seismograms were digitized and
then the plots were generated by computer.
scale is in arbitrary units.
The Amplitude
The relative amplitude for each
set (direct, reflected, and transmitted) represents the correct
values.
The phase spectra are shown in fractions of a cycle.
The units on the frequency axis are MHz.
he1.980
Dir.
UP
h-1.880
Dir.
UP
A
S0.8
-
P
0.7
U
E
0.6
1
0.5
0.4
0.3
0.2
0.1
SII
0.00
0.05
,
,I
0.10
I
1
,I
6.15
0.20
0.25
FREQUENCY
h=1.880
1.
1
0.30
1
1
0.35
1
.0
0.00
0.40
Ref.
UP
0.05
0.10
h-1.880
6.15
0.20 0.25
FREQUENCY
UP
0.30
0.35
6.40
Ref.
10
1.6
0.9
M
-0.8
P
-
0.7
T
U
0.6
E1
-
0.5
0.4
0.3
0.2
0.1
_-1
_________.___________
0.00
0.05
6.16
h-1.880
102
0.25
6.15
0.20
FREQUENCY
0.30
I
.
._________
0.35
0.00
0.40
0.16
he1.880
Trans.
UP
0.05
.,
0.15
0.25
0.20
FREQUENCY
UP
I
I
0.30
0.35
8.30
0.35
0.46
Trans.
1.0
0.9
0.8
P0.7
T
U
0.6
10
0.4
0.3
0.2
0.1
0.00
0.05
0.16
0.15
0.20
0.25
FREQUENCY
0.30
0.35
0.40
S.00
0.05
0.16
0.15
0.25
0.20
FREQUENCY
6.40
68
REF.
COEFF.
(h-1.880
UP)
1.0
0.90.8
0.7
9.6-
0.5
0.4
0.3
0.2
0.1
I
8.0
0.00
0.05
I
0.10
TRANS.
I
0.15
0.20
FREQUENCY
COEFF.
0.25
(h-1.880
0.30
0.35
0.40
0.35
0.40
UP)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.00
0.05
0.10
0.25
0.15
0.20
FREQUENCY
0.30
69
h-3.939
102
h-3.939
Dir.
UP
Dir.
UP
1.0
0.9
A
0.8
-
M
P
L
10.7
T
-
U
D
E
0.6
i
-
0.5
0.4
0.3
0.2
0.1
e.ee
e.10
0.05
0.15 0.20
0.25 0.30 0.35 0.40
0.00 0.05
0.10
FREQUENCY
1e
h-3.939
9.35
0.40
FREQUENCY
h*3.939
Ref.
UP
0.20 0.25 0.30
0.15
Ref.
UP
1.0
0.9Aea
0.8-
m
p
P
L
0.7
T
0.6
U
D
E
i
0.5
0.4
0.3
0.2
e.00
G.A5
e.10
e.15
0e. 0.20 0.25 0.30 0.35 0.40 0.00 0.5
9.1
2
h-3.939
10
UP
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FREQUENCY
FREQUENCY
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(h-3.939
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FREQUENCY
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FREQUENCY
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(h-6.059
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FREQUENCY
TRANS.
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(h-6.059
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Ref.
h-8.050
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Dir.
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Ref.
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(h-11.843
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FREQUENCY
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(h-11.843
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FREQUENCY
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Trans.
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0.90.80.7
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h"16.091
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Dir.
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FREQUENCY
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REF.
COEFF.
(h-16.001
UP)
1.e
0.9
0.80.70.60.5
0.4
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FREQUENCY
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0.10
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0.20
0.25
FREQUENCY
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83
Dir.
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h-18.014
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UP
Dir.
i.e
6.9A
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84
TRANS.
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FREQUENCY
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(h-18.014
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h-19.997
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Dir.
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0.9A
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10.7
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0.10
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0.30
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FREQUENCY
Ref.
h-19.997
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Ref.
11
1.e
0.9
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m
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FREQUENCY
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Trans.
UP
0.15
0.20
FREQUENCY
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0.25
0.30
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0.30
0.35
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Trans.
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REF.
COEFF.
(h-19.997
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1.0
0.9
0.8
0.7
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0.15
0.20
0.25
FREQUENCY
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0.30
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INF.
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Dir.
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Dir.
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m
0.8-
L
P
T
0.7
p
0.6
U
0
E
0.5
1
CI
0.4
-
0.3
0.2
0.1
0.0
1.-I
0.00
0.05
0.10
0.25
0.15
0.20
FREQUENCY
0.30
0.00
0.35
0.40
0.05
0.10
0.15
0.20
FREQUENCY
0.25
0.30
0.35
0.40
104
REF.
COEFF.
DOWN)
(h-16.001
1.0
0.9
0.7
0.4
0.3
0.2
iI
lI
0.0
0.00
0.05
I1
0.10
TRANS.
I
1I
I
1I
0.15
0.20 0.25
FREQUENCY
COEFF.
(h-16.001
0.30
0.35
0.40
0.35
0.40
DOWN)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.1
0.0
0.00
0.05
0.10
0.25
0.15 0.20
FREQUENCY
0.30
105
h-18.014
DOUN
Dir.
h-18.014
1.2
DOUN
Dir.
1.0
A
R
p
L
I
U
0
E
0.9
0.6
10
0.5
0.4
0.3
0.2
0.1
.00
0.05
0.10
0.15
0.20
0.25'
FREQUENCY
0.35
0.40
0.00
Ref.
DOUN
h-i8.014
0.30
0.05
0.10
h=8.014
0.15
0.20
0.25
FREQUENCY
DOUN
0.30
0.35
0.40
0.30
0.35
0.40
Ref.
1
1.0
0.9
A
0.8
0.?
T
0.6
E
0.50.40.3
0.2
0.1
p
L 4-1
I
I
00
I
I
0.05
I
0.10
I
0.15
I
I
0.20
0.25
0.0
0.30
0.35
0.40
0.00
0.05
0.10
FREQUENCY
h-18.014
DOUN
h-18.014
Trans.
0.15
0.20
0.25
FREQUENCY
DOUN
Trans.
1.0
0.9
0.8
0.?
T
U
D
E
10.
0.6
1
0.5
0.4
0.3
0.2
6.1
0.00
0.05
0.10
0.15
0.20
0.25
FREQUENCY
0.30
0.35
0.40
0.0
0.00
0.05
0.10
0.15
0.20
FREQUENCY
0.25
0.30
0.35
0.40
106
REF.
COEFF.
(h-18.014
DOWN)
0.15
0.20 0.25
FREQUENCY
0.30
i.e
0.90.80.7
0.6
0.5
0.4
0.3
9.2
0.1-
9.0
0.00
0.05
0.10
TRANS.
COEFF.
(h=18.014
0.35
0.40
0.35
0.40
DOWN)
1.0
0.90.80.7
0.6
0.5
0.4
0.3
9.2
0.1
-
0.00
0.05
0.10
0.25
0.20
0.15
FREQUENCY
0.30
107
he19.997
DOWN
Dir.
h-19.997
DOWN
Dir.
1.0
.9
-
A
p
L
1
T
U
D
E
0.8
Ii
-
0.7
0.6
10
0.5
6.4
0.3
0.2
0.1
I
.0I
1
0.00
6.05
0.10
h-19.997
0.30
0.25
0.26
FEUNY0.00
FREQUENCY
0.15
0.35
0.40
0.0
0.05
DOUN
h-19.997
Ref.
DOWN
0.25
0.20
0.15
FREQUENCY
6.10
0.30
6.40
0.35
Ref.
10
1.0
e.9
A
0.8
P
L
0.7
T
U
D
E
0.6
I
0.5
0.4
0.3
0.2
0.1
0.0
0.06
6.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.00
0.05
0.10
FREQUENCY
h-19.997
0.30
0.40
0.35
Trans.
DOWN
h*19.997
Trans.
DOUN
0.15
0.20
0.25
FREQUENCY
10
1.0
e.9
A
m
p
L
T
U
D
E
0.8
e.7
0.6
1
-0.5
0.4
0.3
0.2
0.1
10-1
0.00
_____________'
0.05
0.10
___'
I.
_______'___'
0.25
0.20
0.15
FREQUENCY
0.30
0.35
0.40
0.00
0.05
6.10
.
I
'
0.20 0.25
0.15
FREQUENCY
i'i
0.30
'
0.35
0.40
108
REF.
(h-19.997
COEFF.
DOWN)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
I
I
0.0
0.00
0.05
0.10
TRANS.
0.20
0.25
0.15
FREQUENCY
COEFF.
(h-19.997
0.30
0.35
0.40
0.35
0.40
DOWN)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
-
0.2
0.1
0.0
0.00
0.05
0.10
0.15
0.20
0.25
FREQUENCY
0.30
109
INF.
102
Dir.
DOUN
STEP
INF.
STEP
0.65
0.10
Dir.
DOWN
1.0
A
N
P
L
0.8
T
U
E
-
0.7
0.6
10
9.S
0.4
0.3
0.2
0.1
0.05
0.00
INF.
0.20
6.15
FREQUENCY
6.16
DOWN
STEP
0.30
0.25
6.35
0.40
0.00
Ref.
INF.
STEP
6.05
6.16
0.25
0.26
6.15
FREQUENCY
0.30
0.35
6.40
0.30
0.35
6.40
Ref.
DOWN
10
1.6
6.9
A
0.8
-
P
0.7
1
T
U
0.6
E
0.5
0.4
0.3
0.2
6.1106'
6.05
INF.
0.10
STEP
0.15
6.25
0.20
FREQUENCY
0.0
'
'
'
'
0.00
0.30
6.35
0.40
6.06
INF.
Trans.
DOWN
6.25
6.20
6.15
FREQUENCY
STEP
Trans.
DOWN
10
-
1.6
e.9
A
N
P
-0.8
0.7
1
T
U
E
0.6
1
0.5
0.4
6.3
0.2
6.1
.
-1~
0.60
6.65
6.10
6.26
6.15
FREQUENCY
l a
0.25
I
6.30
.
I,
6.35
I
I
6.6
,
0.40
6.66
0.65
6.16
0.15
0.20
FREQUENCY
I
0.25
I
0.30
I
8.3S
6.40
110
REF.
COEFF.
(Inf Step
DOWN)
0.15
0.20
0.25
FREQUENCY
0.30
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
TRANS.
COEFF.
(Inf.
Step
0.35
0.40
0.35
0.40
DOWN)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
|
I
|I
0.25
0.20
0.15
FREQUENCY
0.30
111
APPENDIX B
This appendix contains the amplitude and phase spectra
plots as well as the reflection and transmission coefficient
curves for all of the mountain-like features.
The dimensions
of the features are shown with the figures displaying their
seismograms.
(The amplitude spectra are displayed in the
left column and the phase spectra are in the right column.)
The seismograms were digitized and then the plots were
generated by computer.
units.
The amplitude scale is in arbitrary
The relative amplitude for each set (direct, reflected,
and transmitted) represents the correct values.
spectra are shown in fractions of a cycle.
frequency axis are in MHz.
The phase
The units on the
112
Dir.
RAMP S1
Dir.
RAMP t1
192
1.0
0.9
A
0.8
P
L
0.7
0.6
D
E
10
0.5
0.4
0.3
0.2
0.1
,.
0.00
0.05
0.10
I
0.15
0.25
6.20
FREQUENCY
1
,
0.30
I
0.35
1
0.40
0-0
0.00
0.05
RAMP
Ref.
RAMP S1
0.15
0.25
0.20
FREQUENCY
0.10
0.30
0.35
0.40
Ref.
$1
1.0
0.9
A
0.8
P
L
0.7
T
D -1
E 10
0.6
0.5
0.4
0.3
0.1
0.2
0.00
0.05
0.10
0.15
0.20
FREQUENCY
0.25
0.30
_
0.0
_____________________________
0.35
0.40
0.00
0.05
0.10
0.15
0.20
FREQUENCY
0.25
0.30
0.35
6.40
113
Trans.
RAMP 01
(up slope)
Trans.
RAMP $1
(up slope)
10
1.0
e.9
A
M
P
L
0.8
0.7
T
U
D
E
0.6
I0.5
0.4
0.3
0.2
0.1-
0.00
0.05
1010.00
0.29
0.15
0.10
FREQUENCY
RAMP
18
0.25
Trans.
$1
0.306.35
*.ee
0.40
.5
8.05
01
RAMP
(down slope)
-
02
.5
03
.5
6.30
0.25
6.20
.15
FREQUENCY
0.10
Trans.
31
.5
0.35
04
.40
(down slope)
1.0
0.9
A
M
P
0.8
0.7
1
T
D
D
E
0.6
1
0.5
0.4
0.3
0.2
0.1
'___
_'___'___
10
0.00
0.05
0.10
0.15
0.25
0.20
FREQUENCY
0.30
0.0
'____
0.35
0.40
0.00
0.05
0.10
0.15
0.25
0.20
FREQUENCY
0.30
0.35
0.40
114
COEFF.
TRANS.
(RAMP
(up slope)
I1)
1.0
0.8
0.7
0.6
0.5
0.40.3
-
0.2
-
0.1
0.0
0.00
0.05
0.25
0.15
0 .20
FREOU ENCY
0.10
REF.
(RAMP
COEFF.
0.30
0.35
6.40
1)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
0.25
0.20
FREQUENCY
0.15
0.30
0.35
0.40
115
TRANS.
COEFF.
(down slope)
(RAMP
31)
1.0
0.90.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
0.15
0.20
0.25
FREQUENCY
0.30
0.35
9.40
116
RAMP
102
Dir.
RAMP *2
Dir.
62
1.6
0.9
0.8
A
P-
L
-0.7
T
U
0.6
D
16
E
0.5
0.4
0.3
0.2
6.1-
0.0
0.05
6.10
RAMP S2
0.26 6.25
FREQUENCY
0.15
0.30
0.35
0.00
6.40
0.20 6.25
0.15
FREQUENCY
6.10
6.05
RAMP 62
Ref.
6.30
0.35
0.40
Ref.
1.0
0.9A
M
P
0.8
0.7
L
T
U
0.6
D
E 10~
0.5
0.4
0.3
6.2
0.1
I
6.6
10-2
6.66
6.65
0.10
6.15
0.26 0.25
FREQUENCY
0.36
6.35
0.46
0.00
.5
,
I
0.10
,
0.15
I
0.26
|
0.25
FREQUENCY
6.30
0.35
,
0.40
117
RAMP $2
Trans.
RAMP $2
(up slope)
Trans.
(up slope)
16
1.6
A
P
L
0.7
T
U
0.6
E
0.5
0.4
0.3
0.2
6.1
16
-I
0.00
0.05
RAMP
10
0.20
6.15
FREQUENCY
0.10
$2
0.25
Trans.
0.30
0.35
0.40
0.00
6.05
6.16
RAMP 62
(down slope)
0.30
6.15
6.20
6.25
FREQUENCY
Trans.
6.35
6.40
(down slope)
A
P
L
I
T
U
D
E
I
0.00
6.65
6.16
6.15
0.20
FREQUENCY
0.25
6.30
0.35
0.40
0.00
0.05
0.10
0.20 0.25
6.15
FREQUENCY
0.30
0.35
0.40
118
REF.
COEFF.
(RAMP
#2)
1.0
0.9
0.8
0.7
0.60.50.40.3
0.2
0.1
0.0
0.00
0.05
0.10
TRANS.
0.25
0.15
0.20
FREQUENCY
COEFF.
(up slope)
0.30
(RAMP
0.35
0.40
S2)
1.0
0.9
0.8
-
0.7
-
0.
-
0.5
0.40.30.20.1
0.0
0.00
0.05
0.10
0.25
0.20
0.15
FREQUENCY
0.30
0.35
0.40
119
TRANS.
COEFF.
(down slope)
(RAMP
#2)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
0.15
0.20
0.25
FREQUENCY
0.30
0.35
*.4S
120
Dir.
Trap.
Dir.
Trap.
1.0
6.9
A
6.8
P
L
.0.7
6.6
U
.
6.4
0.3
0.2
6.1-
0.05
6.66
9.16
6.15
0.20 6.25
FREQUENCY
6.30
6.35
0.40
0.00
6.10
6.15
6.26
FREQUENCY
0.25
0.30
6.35
0.40
Ref.
Trap.
Ref.
Trap.
6.05
1.0
6.9
A6.8
m
L.
0.7
T
U
0.6
.5
E l1
6.4
6.3
0.2
6.1
e
10-
0.60
6.05
0.10
6.25
0.26
6.15
FREQUENCY
0.30
0.35
0.5
6.0
0.40
0.35
0.30
0.40
Trans.
Trap.
Trans.
Trap.
0.20 6.25
6.15
FREQUENCY
6.10
1.0
0.9
A
N
8
-.
P
1
0.7
T
0.6
U
E
1
6.5
-
6.4
0.3
6.2
0.1
-61
,
6.66
i
6.05
.
(
0.16
,
I
0.15
0.20
FREQUENCY
-
6.6
'
0.25
0.30
0.35
0.46
,
0.0
6.65
I
0.10
,
,
I
,
I
6.15
6.26
6.25
FREQUENCY
,
,
0.30
I
0.35
,
0.40
121
REF.
COEFF.
(Trap.)
i.e
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
'
0.05
*'
'
'
0.10
0.15
0.20
0.25
FREQUENCY
TRANS.
0.30
0.35
0.40
0.30
0.35
0.40
(Trap
COEFF.
1.0
0.9
0.80.7
0.6
0.5
0.4
0.3
0.2
0.1
0 .0
0.00
I
0.05
I
0.10
i
I
,
I
i
0.15
0.20
0.25
FREQUENCY
122
PYR t*
PYR *1
16
1.7
0.9
A
0.8
p
0.7
T
U
E
0.3
0.5
0.1
0.6
0.00
0.05
0.10
PYR
0.25
0.20
0.15
FREQUENCY
0.35
6.30
6.46
0.00
Ref.
Si
0.16
6.65
PYR
0.15
0.20 6.25
FREQUENCY
#I
6.30
6.35
0.40
0.30
6.35
0.40
Ref.
A
P
L
T
U
D
E1
I
IL
1
10
.00
0.05
6.10
a
I
0.15
0.2e
I
I
0.25
I
%
0.30
I
~
0.35
6.46
0.00
0.05
PYR
0.25
FREQUENCY
PYR
Trans.
*I
0.20
0.15
0.10
FREQUENCY
Trans.
$I
16
1.6
6.9
A
6.8-
P
L
0.7
T
U
D
0.6
I
E
6.5
0.4
0.3
6.2
6.1
1
-I
I I
6.00
I
0.05
I
I
0.10
I
0.15
6.0
0.26
FREQUENCY
0.25
0.30
0.35
6.40
0.00
0.05
0.10
0.15
6.20
FREQUENCY
0.25
0.30
0.35
0.40
123
REF.
COEFF.
(PYR
31)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
TRANS.
0.25
0.20
0.15
FREQUENCY
COEFF.
(PYR
0.30
0.35
0.40
0.30
0.35
0.40
$1)
1.0
0.90.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
0.25
0.20
0.15
FREQUENCY
124
PYR $2
PYR 82
10
A
fI
p
L
T
U
D
I
E
6
-
0.00
6. I
6.1
9.05
0.10
0.15
0.20
0.30
6.25
0.35
0.46
0.15
FREQUENCY
0.20
6.25
0.30
0.35
6.40
0.25
0.30
0.35
0.46
0.30
0.35
0.40
FREQUENCY
PYR $2
PYR $2
I.e
0.9
6.8
p
L
T
U
D
E
0.7
0.6
1
0.5
0.4
6.3
6.2
6.1
6.65
0.00
0.10
0.15
0.25
6.20
0.30
0.40
6.35
6.6
0.00
0.05
0.10
FREQUENCY
PYR S2
Trans.
PYR
$2
0.15
6.20
FREQUENCY
Trans.
16
I 0
1.6
0.9
A
0.8
P
0.7
T
U
D
0.6
1
E
0.5
0.4
0.3
-
0.2
6.1
1
-I I
0.00
i
f
0.05
I
0.16
I
I
'
I
0.15
0.20
FREQUENCY
,
I
0.25
,
I
0.30
,
I
0.35
,
j
0.40
0.0
0.00
0.05
0.10
6.15
0.20
FREQUENCY
0.25
125
REF.
COEFF.
(PYR
#2)
i.e
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
I
0.00
0.05
I
0.10
TRANS.
I
I
i
I1 1
0.15
0.20 0.25 0.30
FREQUENCY
COEFF.
(PYR
1
0.35
0.40
0.35
0.40
S2)
1.e
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
0.15
0.20
0.25
FREQUENCY
0.30
126
Dir.
PYR 23
Dir'
$3
PYR
12
1.0
0.9-
A
p
0.8-
1
9.7
L
T
U
D
E
0.6
10
0.5-
0.4-
-
0.30.2-
1
0.00
I
0.05
0.10
0.15
0.20
0.25
9.30
0.35
0.00
4.49
FREQUENCY
PYR
1o
I
0.05
I
I
0.15
0.29
I
, I
0.25 0.38 0.35
,
9.40
-FREQUENCY
Ref.
$3
PYR
Re(.
S3
I
0.10
1.0
0.9-
A
p
0.8-
1
0.7
L
T
U
D
E
0.6
-
0.5-
0.4-
-
0.3-
0.10.0
0.2-
I,
-1lei
0.00
9.10
0.05
I :
0.15
0.20
0.25
0.30
0.35
0.40
0.00
0.05
0.10
FREQUENCY
PYR
PYR
0.35
0.40
t3
0.20 9.25
O.15
FREQUENCY
0.39
0.35
9.40
Trans.
0.9-
~
M
0.30
0.20
FREQUENCY
Trans.
*3
0.25
O.15
-
0-8
-
0.7-
T
U
-
0.60.5-
E
0.30.2-
0.00
0.05
9.10
0.29
$.I5
FREQUENCY
0.25
e.30
9.35
8.4e
0.00
G.05
G.10
127
1.0
(PYR
COEFF.
REF.
#3)
--
0.9
0.8
0.7
0.60.50.4
0.3
0.2
0.1
0.0
-
0.00
I
I
0.05
i
I
0.10
TRANS.
,
I
t
i
I
0.25
0.20
0.15
FREQUENCY
COEFF.
(PYR
I
0.30
0.35
e.40
0.30
0.35
0.40
$3)
1.0
0.9
0.8
0.7
0.60.5-
0.40.30.2
0.1
0.00
0.05
0.10
0.25
0.20
0.15
FREQUENCY
128
Dir.
MT *I
Dir.
MT *1
1.0
0.9
A
M
0.8
L
0.7
T
0.6-
U
E
10
-
0.4
0.3
0.2
0.1
1.t6
0.00
0.15
0.10
0.05
MT
0.25
0.20
FREQUENCY
0.30
0.40
6.35
MT
Ref.
$1
0.10
6.65
0.00
$I
I
0.15
I
I
.
6.20
0.25
FREQUENCY
6.30
0.35
0.46
Ref.
10
1.0
0.9
A
m
P
L
0.8
0.7-
1
T
U
D
E
0.6
1
0.5
0.4
0.3
0.2
0.1
-
0.6
101
6.66
MT
2
0.26
0.15
FREQUENCY
0.16
0.65
0.25
0.35
0.30
0.00
0.40
0.05
MT
Trans.
*1
0.10
31
6.26
0.15
FREQUENCY
0.25
0.30
0.35
6.40
Trans.
1.e
0.9
A
0.8
M
P
L
T
0.6
U
D
E
-
0.7
10
6.56.4
0.3
0.2
0.1
1
0.60
,
6.05
0.10
I
,
0.15
I
,
0.20
FREQUENCY
:
0.25
6.30
I
0.35
.
0.40
6.6
6.06
6.65
0.10
0.25
0.20
0.15
FREQUENCY
0.30
0.35
0.40
129
REF.
(MT
COEFF.
#1)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
I
|
0.00
0.10
0.05
TRANS.
I
|
I
iVV
0.25
0.20
0.15
FREQUENCY
COEFF.
(MT
|
0.30
0.35
0.40
0.35
0.40
*1)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
-
0.2
-
0.1
I
I|
0.0
0.00
0.05
0.10
I
0.20 0.25
0.15
FREQUENCY
*|I |
0.30
130
MT
Dir.
82
MT
82
Dir.
18
i.e
A
P
L
T6.
U
D
E
M
0.8-
1
0.78.6
1
0.5
0.4
0.3
0.2
0.1
0.00
6.65
0.10
MT
6.15
0.20 0.25
FREQUENCY
0.30
8.35
0.40
0.00
8.85
MT
Ref.
82
0.10
82
8.15
0.20 0.25
FREQUENCY
0.30
0.35
0.40
Ref.
1.1
0.9
A
0.8
-
PL
0.7
.
T
U
D
E
0.6
0.50.4
0.3
0.2
8.1
16~~~1
0.00
0.85
8.16
MT
~0.8
.
0.26 0.25
6.15
FREQUENCY
6.30
0.35
0.40
0.00
MT
Trans.
82
0.10
.5
82
1.
0.25
6.20
8.15
FREQUENCY
0.30
0.35
6.40
0.30
8.35
0.40
Trans.
1.6
0.9
A
e.8
M
P
L
0.7
T
U
D
E
0.6
1
8.5
0.4
0.3
8.2
0.1
-61
8.88
8.85
6.18
6.15
6.28
8.25
FREQUENCY
0.38
0.35
0.40
6 .0
0.00
8.85
0.10
0.20 0.25
8.15
FREQUENCY
131
REF.
COEFF.
(MT
82)
1.0
0.80.7
0.6
0.5
0.4
0.3
0.2
0.10.0
0.00
0.05
0.10
TRANS.
0.20
0.25
0.15
FREQUENCY
COEFF.
(MT
0.30
0.35
0.40
0.30
0.35
.40
$2)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.00
0.05
0.10
0.25
0.20
0.15
FREQUENCY
132
MT 33
Dir.
33
MT
102
Dir.
1.0
A
m
P
L
0.8
-
0.7
T
U
D
E
0.6
10
0.5
0.4
0.3
0.2
0.1
1
0.65
0.00
a
I
0.10
MT
0.0
0.15
0.20
FREQUENCY
33
0.25
6.30
0.35
0.40
0.00
0.05
Ret.
0.16
MT
0.15
6.20
0.25
FREQUENCY
33
6.30
0.35
6.46
0.30
6.35
6.40
Ref.
10
1.0
0.9
A
M
P
6.8
6.7
1
T
U
D
E
0.6
-
6.5
0.4
0.3
0.2
0.1
0.0
16-1
0.00
0.05
6.16
0.35
0.40
0.00
0.10
0.05
@.15
0.20
FREQUENCY
0.25
Trans.
MT 33
Trans.
MT 33
102
0.30
6.15
0.20
6.25
FREGUENCY
1.0
0.9
A
M
P
1
T
U
D
E
0.8
0.7
0.6
10
0.5
0.4
0.36.26.1I1
0.00
0.65
,
0.10
0.15
0.20
FREQUENCY
0.25
I e
6.36
0.6.
6.35
0.40
0.00
,
0.05
i i
0.10
I
.
0.15
I
.
I
6.25
6.20
FREQUENCY
I
0.30
I.
0.35
0.40
133
REF.
COEFF.
(MT
#3)
1.0
0.9-
0.8
-
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
TRANS.
0.15
0.20
0.25
FREQUENCY
COEFF.
(MT
0.30
0.35
0.40
0.30
0.35
0.40
#3)
1.0
0.9
0.8
0.7
0.60.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
0.15
0.20
0.25
FREQUENCY
134
MT
Dir.
$4
MT t4
Dir.
16
1.6
0.9
A
M
P
L
".8
0.7
T
U
0.6
E
1
0.5
6.4
0.3
0.2
6.1
16-
0.05
0.00
I
I
0.10
6.15
6.26
6.25
FREQUENCY
MT
34
I
I
,
0.36
6.35
.,
,
0.46
I
6.00
0.05
,
,
,
0.10
0.15
I ,
I., !
0.26 0.25 6.30
I
,
6.35
0.40
0.35
0.40
FREQUENCY
Ref.
MT
34
Ref.
I
1.6
0.9
A
M
P
L
0.8
0.7
T
U
D
0.6
0.5
0.4
6.3
0.2
0.1
0.0
18-
6.0
6.65
6.10
6.35
0.40
0.00
0.5
0.10
0.15
0.20
0.25
0.30
FREQUENCY
Trans.
MT $4
Tran.
MT 34
2
0.36
6.15
6.26
6.25
FREQUENCY
1.0
0.9
A
M
P
L
T
U
D
E
0.8
-
0.7
0.6
10
6.5
0.4
0.3
6.26.11
0.00
,
0.05
6.10
6.15
I
,
0.20
FREQUENCY
I
0.25
6 .6
,
0.30
0.35
6.46
6.66
0.05
0.10
0.15
0.20
FREQUENCY
6.25
0.30
6.35
6.40
135
REF.
(MT
COEFF.
*4)
1.e
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.10.00
0.05
0.10
TRANS.
0.25
0.20
0.15
FREQUENCY
COEFF.
(MT
0.30
0.35
1.40
0.30
0.35
1,49
#4)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0I
0.00
0.05
I
0.10
I
0.15
I
0.20
FREQUENCY
0.25
136
35
MT
35
MT
16
1.7
0.
-
A
m
P
L
0.8
T
U
D
,E
6.6
0.7
6.56.4-
0.3
0.2
0.1
1 .1.
1 L1
1
19-1
0.05
0.00
0.0
1
0.10
6.15
0.20
FREQUENCY
0.25
0.30
0.35
0.40
0.66
0.15
0.20
0.25
0.30
0.35
3.40
0.25
6.30
6.35
0.40
FREQUENCY
35
MT
0.10
6.65
MT 85
16
1.6
A
m
P
6.7
T
U
0.6
E
£
0.5
0.4
0.3
0.2
6.1
I
I
0.05
0.16
e-I, I
0.00
MT
I
,
0.15
1-
0.35
0.30
6.20
0.25
FREQUENCY
35
IV A
,
,lJ I
.
6.0
0.40
0.00
0.05
6.16
0.15
0.26
FREQUENCY
MT
Trans.
35
Trans.
16
A
P
L
T
U
D
E1
i -I, I I
6.0
0.05
,
I
0.10
,
I
,
0.15
I
I
0.20
0.25
FREQUENCY
,
I
0.30
,
I IIN "j
0.35
0.46
0.00
0.05
0.10
0.15
0.20
FREQUENCY
6.25
0.30
6.35
6.40
137
REF.
COEFF.
(MT
35)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
9.0
0.00
'
0.05
0.10
TRANS.
0.15
0.20
0.25
FREQUENCY
COEFF.
(MT
0.30
0.35
0.40
0.30
0.35
0.40
35)
1.0
0.8-
0.7
0.6
0.5
0.4
6.3
0.2
0.1
9.0t
0.00
0.05
0.10
0.15
0.20
0.25
FREQUENCY
138
MT
36
MT
36
1.0
0.9A
0.8
P
L
-
e.7-
T
U
D
E
0.6
0.5
0.4
0.30.2
0.1
.L
,
I9-1
0.10
0.05
0.00
-
'
9.0
0.15
0.25
0.20
FREQUENCY
MT 36
0.30
0.35
0.40
0.00
LLL
0.10
0.05
0.15
0.20
0.25
0.30
0.35
0.40
FREQUENCY
Ref.
MT 36
10
A
P
T
U
D
E
I
S10
0.00
0.05
0.15
0.10
0.20
0.25
0.30
0.35
0.40
0.00
0.05
0.10
FREQUENCY
MT
36
Trans.
MT
*6
6.15
6.20
0.25
FREQUENCY
6.30
0.35
0.40
0.30
0.35
0.40
Trans.
10
A
m
P
L
T
U
D
E
19-1
1
0.00
,
I
0.05
,
I
0.10
,
I
I
I
0.25
0.20
0.15
FREQUENCY
I
0.36
I F
\I
0.35
9.40
0.00
0.05
0.10
0.15
0.20
0.25
FREQUENCY
139
REF.
COEFF.
(MT
36)
i.e
0.9
0.8
0.70.60.50.4
0.3
0.2
0.1
.0
'
.
0.10
TRANS.
e.9
0.20 0.25
0.15
FREQUENCY
(MT
36)
0.20
0.15
FREQUENCY
0.25
COEFF.
0.30
0.35
0.40
0.30
0.35
0.40
-
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
140
MT *7
Dir.
MT 17
10
A
p
P
L
T
U
D
E
1
101
0.00
0.05
0.10
0.20
0.15
0.25
0.30
0.35
0.40
FREQUENCY
0.20
0.25
FREQUENCY
0.30
0.35
0.40
0.25
0.20
0.15
FREQUENCY
0.30
0.35
0.40
0.35
0.40
MT 17
Ref.
17
MT
0.15
10
1.0
-
0.9
A
0.8-
P
L
T
U
D
E
1
I
0.5
0.4
0.3
0.2
0.1
o 1 I
0.00
I
I
0.05
0.10
I
0.15
0.05
0.10
I
0.20
I
I
0.25
FREQUENCY
I
0.30
, II x
0.35
_j
0.40
0.0
0.00
0.05
0.15
0.25
0.20
FREQUENCY
0.10
MT $7
Trans.
MT S7
0.00
,
0.30
0.35
0.40
0.00
0.05
0.10
Trans.
0.15
0.20
0.25
FREQUENCY
0.30
141
REF.
COEFF.
(MT
*7)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
TRANS.
0.25
0.20
0.15
FREQUENCY
COEFF.
(MT
0.30
0.35
0.40
7)
1.0
0.9
0.8
0.7
0.60.5
0.4
0.3
0.2
0.1
0.0
0.00
0.05
0.10
0.20 0.25
0.15
FREQUENCY
0.30
0.35
*.40
142
REFERENCES
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Reflection and Transmission of Inhomogeneous Waves
With Particular Application to Rayleigh Waves,
Bull. Seism. Soc. Am., 64,
1635 -
1652, 1974.
Bjerkan, L., J.O. Fossum, K. Fossheim.
The Surface Barrier Rayleigh Wave Transducer,
J. Appl. Phys., 50,
5307 -
5321, 1979.
Bolt, B.A., and W.D. Smith.
Finite-Element Computation of Seismic Anomalies For
Bodies of Arbitrary Shape,
Geophysics, 41,
145 -
150, 1976.
Bouchon, M.
Effect of Topography On Surface Motion,
Bull. Seism. Soc. Am., 63,
615 -
632,
1973.
Chamuel, J.R.
Magnetostrictive Position Sensing Readouts For Commercial
and Military Applications,
C.S. Draper Lab, Report C - 4607,
1976.
143
Chamuel, J.R.
Position Sensing Readout, U.S. Patent 4,035,762,
12 July 1977.
Chamuel, J.R.
Seismic Ultrasonic Modeling,
Presentation to Air Force, C.S. Draper Lab,
Report No. 15L-79-081,
18 May 1979.
Chamuel, J.R., and M.N. Toksoz.
Seismic Ultrasonic Modeling Program Final Report,
C.S. Draper Lab,
Report R-1385, 1980.
Chen, R.C., and L.E. Alsop.
Reflection and Transmission of Obliquely Incident
Rayleigh Waves at a Vertical Discontinuity Between
Two Welded Quarter-Spaces,
Bull. Seism. Soc. Am.,
69,
1409 - 1423, 1979.
Curtis, R.G., and M. Redwood.
Approximate Analysis of the Reflection of Surface
Acoustic Waves by Steps,
J. Appl. Phys., 46.
4627 -
4630, 1975.
Dally, J.W., and D. Lewis III.
A Photoelastic Analysis of Propagation of Rayleigh
Waves Past a Step Change in Elevation,
Bull. Seism. Soc. Am., 58,
539 -
563, 1968.
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de Bremaecker, J.Cl.
Transmission and Reflection of Rayleigh Waves at Corners,
Geophysics, 23,
253 -
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