propagation and attenuation of seismic rayleigh waves along single paths in scotland colin d ...

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PROPAGATION AND ATTENUATION OF SEISMIC
RAYLEIGH WAVES ALONG SINGLE PATHS
IN SCOTLAND
COLIN D. MACBETH, B.A. (OXON)
DOCTOR OF PHILOSOPHY
UNIVERSITY OF EDINBURGH
1983
ACKNOWLEDGEMENTS
The research, and the composition of this thesis were executed
while a member of the Global Seismology Unit, I.G.S. Edinburgh and the
Geophysics department of Edinburgh University. For this, I am grateful
to C.W.A. Browitt for allowing me to use the facilities of the unit,
K.M. Creer for accepting me as a student in his department and the
Natural Environment Research Council for providing me with a three
year studentship.
I am extremely grateful to my supervisor P.W. Burton for suggest-
ing the notion of a single-station attenuation measurement, and for his
continual support, encouragement and constructive criticism.
I would like to express my gratitude to G. Neilson and D.C. Booth
who were most obliging in assisting me with a variety of problems.
During the research, I derived great benefit from many illuminating
discussions with the research students in G.S.U., namely J. Singh,
A.J.W. McDonald, G. Roberts and I.G. Main. I must also thank R.W.
McGonigle for providing many useful computer programs and assisting me
with problems in the earlier stages of the research. I am most apprec-
iative of the help received from C.J. Fyfe, who answered a wide variety
of computing problems and made freely available his considerable
software library. A special thanks is extended to J.B. Young and A.
Douglas for providing me with a copy of their synthetic seismogram
program 'BIGE', and for tolerating my questions on its operation. I
also wish to thank R.F. King for providing various information regard-
ing the LISPB experiment.
ABSTRACT
A new technique is developed for measuring the depth distribution
of the shear wave specific attenuation factor (Q ) in the earth, from
the recording of a Rayleigh wave which has travelled along a single
isolated path. This technique is applied to data in the frequency
range 0.7 - 5.5 Hz generated by small underground explosions,
underwater explosions, and an earthquake of magnitude 3.7 (ML),
recorded during the LISPB experiment and on the LOWNET local network
in Scotland. In parallel with this, group velocity characteristics of
the data are analysed to obtain estimates of the distribution of shear
wave velocity () laterally and at depth in the earth.
The single-station techniqueutilizes an expression for the
amplitude spectrum as a series of multiplicative linear functions,
each characterized by a finite set of parameters. The components which
describe each particular source are investigated to obtain the
smallest set of parameters which can accurately represent the
excitation of the waves in the medium. To reduce the number of
parameters specifying the spectrum, group velocity data are inverted
a
to yield single-station and regional depth profiles. Fundamental
mode group velocity data generated by underwater explosions in
Kirkcaldy Bay recorded on LOWNET show a marked correlation with the
surface geological expression,(cid:9) in the top 400m of the single-station
profiles ranging from 1.5 to 2.1 km/sec. First and second higher mode
group velocity data generated by the earthquake yield well resolved
regional profiles down to depths of 17km,(cid:9) increasing from around 3.1
km/sec to 3.7 km/sec. These studies also elucidate some interesting
features of high frequency Rayleigh wave propagation.
The explicit form of each function composing the amplitude
spectrum is used to identify the most important effects. These are
measured by the extent of the fluctuations in the spectrum resulting
from an a priori perturbation (representing a realistic error) in each
parameter. The results of this analysis guide the development of the
single-station methodology for each source. The most influential
parameters pertain to the Q distribution and source strength. The
inverse time constant of the time action and shot depth for
underground and underwater explosions respectively are also important.
The earthquake is the most complex source, having a large number of
important variables. The method consists of correcting for the least
important functions (such as instrument and medium response), and
obtaining estimates for the remaining parameters by mapping the
expected functional form onto this corrected spectrum.
A preliminary survey of the attenuation is attempted using an
approximate formula relating the frequency of the spectral peak to an
average Q value. Applying the single-station method to the
underground and underwater data recorded on the LISPB and LOWNET
arrays respectively, yields well resolved single-station Q-1 values of
between 0.02 - 0.09 in the top 400m of the upper crust for up to 50km
from the source. The values at greater depths are weakly constrained,
but the Q(cid:9) estimates in2pIa decrease to < 0.01 between 400 - 800m
depth, followed by an increase to 0.04 below 800m. The underground
explosion spectra are modelled most accurately by the theory. The
inverse time constant and shot depth are also discerned. There is no
observable correlation between the surface geological expression and
QH
the spatial distribution of single-station measurements. The
fundamental mode and higher mode data generated by the underwater
explosion and earthquake respectively recorded on LISPB, could not be
modelled. However an average of the earthquake source function is
obtained by fitting to the decay of spectral amplitude with distance,
from which a seismic moment of 9.1015 Nm is calculated, in good
agreement with a value obtained using the surface wave magnitude.
More refined techniques to isolate the prominent Rayleigh modes
on high frequency recordings are required before accurate values
Q
and hence the exact mechanism of attenuation can be elucidated.
CONTENTS
Page
1.. . . INTRODUCTION
1 . 1 (cid:9) Preview (cid:9) 1
1.2(cid:9) Theoretical Spectrum of a Rayleigh Wave(cid:9) 3
1.3(cid:9) The Rayleigh Wave Data(cid:9) 11
1.4(cid:9) Techniques for Estimating the Attenuation of Rayleigh Waves(cid:9) 17
1.5(cid:9) Measurement of Lateral Variations(cid:9) 23
1.6(cid:9) Outline of Research Covered(cid:9) S (cid:9) 24
2... .UNDERGROUND AND UNDERWATER EXPLOSION SOURCE FUNCTIONS
2.1 Introduction 26
2.2 Underground Explosions 27
2.2.1 Introduction 27
2.2.2 Physical Interactions of the Source with the Medium 28
0
2.2.3 Rayleigh Wave Medium Response(cid:9) 32
2.2.4 Source Finiteness Effect 32
2.2.5 Spectrum of the Source Time Action 35
2.2.6 The Amplitude of the Source Mechanism and the Explosive 37
Seismic Moment
2.3 Underwater Explosions(cid:9) 39
0
0(cid:9)
2.3.1 Physical Interactions of the Source with the Medium 39
2.3.2 The Amplitude and the Spectrum of the Source Time Action(cid:9) 41
2.3.3 Pressure Function due to the Bubble Oscillations(cid:9) 42
2.3.4 Reverberation Response of Water Layer(cid:9) 45
2.3.5 Rayleigh Wave Medium Response(cid:9) 46
2.4(cid:9) Dispersed Shots(cid:9) 47
2.5 Summary(cid:9) 48
. EARTHQUAKE SOURCE FUNCTIONS
3.1(cid:9) Introduction(cid:9) 50
3.2(cid:9) Earthquakes(cid:9) 50
3.2.1 Introduction(cid:9) 50
3.2.2 Physical Interactions of the Source with the Medium (cid:9) 51
3.2.3 Earthquake Source Mechanism, Seismic Moment, and(cid:9) 53
Medium Response
3.2.4 Derivation of the Source Finiteness Effect(cid:9) 55
'3.2.5 Spectrum of the Source Time Action(cid:9) 59-
3.3 Summary(cid:9) 64
.PROPAGATION OF RAYLEIGH WAVES IN SCOTLAND
4.1 Introduction 66
4.2 Data Processing 67
4.3 Kirkcaldy Bay Data 69
4.3.1 Description of Seismograms 69
4.3.2 Particle Motions 71
4.3.3 Quantitative Explanation of Fundamental Mode Waveform 77
4.3.4 Group Velocities and Single-station Velocity Structure 80
4.3.5 Pure Provincial Velocity Structure 95
4.4 Kyle Earthquake 101
4.4.1 Description of Seismograms 101
4.4.2 Observed Group Velocities 107
4.4.3 Lateral Variation of Velocity 109
4.4.4 Check on Mode Identification 116
4.4.5 Particle Motions 119
4.4.6 Regional Velocity Structure 122
4.5 Summary 132
5... .SINGLE-STATION ATTENUATION METHODS FOR RAYLEIGH WAVES
5.1(cid:9) Introduction(cid:9) S (cid:9) 134
5.2(cid:9) Rough Estimate of Attenuation using the Peak Frequency Method 135
5.3(cid:9) Identification of the Most Important Parameters Shaping the(cid:9) 137
Theoretical Spectrum of a Rayleigh Wave
5.3.1 Introduction(cid:9) 137
5.3.2 Strength of the Source Action(cid:9) 138
5.3.3 Source Spectral Functions(cid:9) 139
5 (cid:9)
5.3.4 Source Finiteness(cid:9) 143
5.3.5 Spectral Response of Medium (cid:9) 147
5.3.6 Attenuation Function(cid:9) 151
5.3.7 Instrument Response(cid:9) 153
5.3.8 Comparison of all Effects(cid:9) 153
5.4(cid:9) Single-station Attenuation Measurements(cid:9) 156
5.4.1 General Methodology for Different Source Types(cid:9) 156
5.4.2 Hedgehog Method(cid:9) 159
5.4.3 Fast Optimization and Boundary Evaluation (FOB)(cid:9) 161
5.4.3a Optimization(cid:9) 161
5.4.3b Bounds on Estimates(cid:9) 163
5.4.4 Uncertainties in the Rayleigh Wave Amplitude Spectrum (cid:9) 164
5.5(cid:9) Summary(cid:9) 166
6... .APPLICATION OF SINGLE-STATION ATTENUATION METHODS TO
0.7 - 5.5 Hz RAYLEIGH WAVES IN SCOTLAND
6.1(cid:9) Introduction(cid:9) 168
6.2(cid:9) Underground and Underwater Explosions Recorded on the LISPB(cid:9) 170
Array
6.2.1 Underground Explosion Source Effects 170
6.2.2 Underwater Explosion Source Effects 173
6.2.3 Description of Observed(cid:9) Rayleigh Wave Spectral Amplitudes 175
6.2.4 Preliminary Study by the Peak Frequency Method 180
6.2.5 Application of Single-station Attenuation Methods 184
6.2.5a Introduction(cid:9) . 184
6.2.5b FOB Inversion of Underground Explosion Spectra 190
6.2.5c FOB Inversion(cid:9) of Underwater Explosion Spectra 200
6.2.5d Hedgehog Inversion of Underground Explosion Data 200
6.2.5e Comparison of Single-station Results with Station-averaged 203
Results
(cid:9)(cid:9)(cid:9)(cid:9)
6.3 Underwater Explosions in Kirkcaldy Bay Recorded on the 205
LOWNET Array
6.3.1 Source Effects 205
6.3.2 Description of Observed Spectral Amplitudes 207
6.3.3 Measurement of the Average Regional Attenuation 212
6.3.4 Preliminary Study by the Peak Frequency Method 214
6.3.5 Application of Single-station Attenuation Methods 217
6.3.5a Introduction 217
6.3.5b FOB Inversion of Underwater Explosion Data 218
6.3.5c Hedgehog Inversion of Underwater Explosion Data 231
6.3.5d Comparisonwith Station-averaged Attenuation Values 234
6.4 KEQ Recorded on the LISPB Array 236
6.4.1 Source Effects 236
6.4.2 Description of Observed Spectral Amplitudes 238
6.4.3 Attempted Measurement of Attenuation by Correcting for 240
the Radiation Pattern
6.5 Summary 247
7.. . .SUMMARY AND CONCLUSIONS
7.1(cid:9) Review and Interpretation of Results(cid:9) 250
7.2(cid:9) Some Implications of the Single-station Results(cid:9) 264
7.3(cid:9) Suggestions for Improvement and Future Work(cid:9) 266
7.4(cid:9) Final Conclusions(cid:9) 268