scholarly journals Hypothesis Tests on Rayleigh Wave Radiation Pattern Shapes: A Theoretical Assessment of Idealized Source Screening

2021 ◽  
Author(s):  
Joshua D Carmichael
Keyword(s):  
Rayleigh Wave ◽  
Ground Motion ◽  
Wave Radiation ◽  
Underground Explosion ◽  
Radiation Patterns ◽  
Hypothesis Tests ◽  
Unknown Parameters ◽  
Discrimination Power ◽  
Explosion Monitoring ◽  
Sensor Locations

Summary Shallow seismic sources excite Rayleigh wave ground motion with azimuthally dependent radiation patterns. We place binary hypothesis tests on theoretical models of such radiation patterns to screen cylindrically symmetric sources (like explosions) from non-symmetric sources (like non-vertical dip-slip, or non-VDS faults). These models for data include sources with several unknown parameters, contaminated by Gaussian noise and embedded in a layered half-space. The generalized maximum likelihood ratio tests that we derive from these data models produce screening statistics and decision rules that depend on measured, noisy ground motion at discrete sensor locations. We explicitly quantify how the screening power of these statistics increase with the size of any dip-slip and strike-slip components of the source, relative to noise (faulting signal strength), and how they vary with network geometry. As applications of our theory, we apply these tests to (1) find optimal sensor locations that maximize the probability of screening non-circular radiation patterns, and (2) invert for the largest non-VDS faulting signal that could be mistakenly attributed to an explosion with damage, at a particular attribution probability. Lastly, we quantify how certain errors that are sourced by opening cracks increase screening rate errors. While such theoretical solutions are ideal and require future validation, they remain important in underground explosion monitoring scenarios because they provide fundamental physical limits on the discrimination power of tests that screen explosive from non-VDS faulting sources.

Use of reciprocity theorem for obtaining Rayleigh wave radiation patterns

1966 ◽  
Vol 56 (4) ◽  
pp. 925-936 ◽  
Author(s):  
I. N. Gupta
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Three Dimensional ◽  
Reciprocity Theorem ◽  
Point Sources ◽  
Dimensional Case ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
Homogeneous Half Space ◽  
Double Couple

abstract The reciprocity theorem is used to obtain Rayleigh wave radiation patterns from sources on the surface of or within an elastic semi-infinite medium. Nine elementary line sources first considered are: horizontal and vertical forces, horizontal and vertical double forces without moment, horizontal and vertical single couples, center of dilatation (two dimensional case), center of rotation, and double couple without moment. The results are extended to the three dimensional case of similar point sources in a homogeneous half space. Haskell's results for the radiation patterns of Rayleigh waves from a fault of arbitrary dip and direction of motion are reproduced in a much simpler manner. Numerical results on the effect of the depth of these sources on the Rayleigh wave amplitudes are shown for a solid having Poisson's ratio of 0.25.

Single-force representation of shallow landslide sources

1993 ◽  
Vol 83 (1) ◽  
pp. 130-143
Author(s):  
F. A. Dahlen
Keyword(s):  
Rayleigh Wave ◽  
Moment Tensor ◽  
Shear Velocity ◽  
Vertical Surface ◽  
Shallow Landslide ◽  
Point Force ◽  
Wave Radiation ◽  
Underground Explosion ◽  
Surface Point ◽  
Slide Mass

Abstract A horizontal thrust fault situated at the Earth's surface does not excite any seismic radiation. Because of this and because it provides a satisfactory fit to the data, Kanamori and his co-workers have used a point force rather than a conventional moment tensor to represent the long-period Love- and Rayleigh-wave radiation from a number of shallow landslide sources. The force is supposed by Newton's third law to be ω2MD, where ω is the angular frequency, M is the slide mass, and D is the displacement. Day and McLaughlin (1991) have recently shown that the spall accompanying an underground explosion can be represented either by a shallow horizontal tension crack or by a vertical surface point force ω2MD, where M is the spall mass and D is the crack separation. Using their method, we show that a landslide can be represented in the JWKB approximation either by a shallow double couple or by a horizontal surface point force; for a Love wave the force is FL = ω2MD(1 − β20/c20), whereas for a Rayleigh wave it is FR = ω2MD(1 − 8β20/3c20), where β0 is the shear-wave velocity within the slide mass and c0 is the phase velocity of the surface wave in the vicinity of the source. The sliding block appears to be mechanically decoupled from the rest of the Earth, so that FL ≈ FR ≈ ω2MD, because of the reduced shear velocity β0 within the brecciated rockmass.

Seismoacoustic analysis of underground explosions using the Rayleigh integral

2020 ◽  
Vol 223 (2) ◽  
pp. 1069-1085 ◽  
Author(s):  
Philip Blom ◽  
Alex Iezzi ◽  
Garrett Euler
Keyword(s):  
Ground Motion ◽  
Acoustic Signal ◽  
Low Frequency ◽  
Free Fall ◽  
Acoustic Signals ◽  
Frequency Component ◽  
Underground Explosion ◽  
Ground Zero ◽  
Surface Motion ◽  
Explosion Monitoring

SUMMARY A coupled seismoacoustic model is developed for the analysis of acoustic signals produced by underground explosive events with an aim to develop a means of improving estimated depth and yield for explosion monitoring. A ground spall model is used to predict surface motion characteristics produced by an underground explosion and the Rayleigh integral is applied to relate the surface motion to the acoustic signal some distance from surface ground zero. The low-frequency component of the ground motion associated with the prolonged free fall of lofted material during spall is found to dominate the acoustic signal propagating away from surface ground zero at shallow angles. The model is applied to observed ground motion and acoustic signals recorded during the Source Physics Experiment (SPE) with promising results. In addition to accurately predicting characteristics of the observed acoustic signals from several of the SPE events, the model provides a means of explaining the lack of signals observed during several events in the SPE due to the directionality of the higher frequency acoustic signals associated with the uplift and closure components as well as the lack of a spatially localized, longer duration dwell.

Polar radiation patterns of P and SV waves in a multi-layered medium

1973 ◽  
Vol 63 (2) ◽  
pp. 529-547
Author(s):  
Tien-Chang Lee ◽  
Ta-Liang Teng
Keyword(s):  
Displacement Field ◽  
Layered Medium ◽  
Focal Depth ◽  
Focal Mechanisms ◽  
P Wave ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
Double Couple ◽  
Spatial Coordinates ◽  
P And Sv Waves

abstract The displacement field in a multi-layered medium due to incident plane P or SV waves is formulated in terms of Haskell's layer matrices. Based on the reciprocity theorem, the far-field polar radiation patterns of single force, double force, single couple, double couple, and dilatation in a multi-layered medium can be obtained from the displacement field and its first derivatives with respect to the spatial coordinates. Numerical results for models of one layer overlying a half-space indicate that (1) the radiation patterns are sensitive to the variation of focal depth, (2) the layering has a more pronounced effect on SV-wave radiation patterns than on P-wave radiation patterns, (3) the radiation patterns become simpler as the wavelength increases, (4) polarity may reverse abruptly somewhere beyond the critical angle in SV-wave radiation patterns, (5) radiation may be discontinuous across interfaces for some assumed focal mechanisms applied slightly above and below the interfaces, and (6) no clearcut distinction among the various radiation patterns can be used to single out one type of the assumed focal mechanisms from the rest.

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