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Hypothesis Tests on Rayleigh Wave Radiation Pattern Shapes: a Theoretical Assessment of Idealized Source Screening

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Hypothesis Tests on Rayleigh Wave Radiation Pattern Shapes: a Theoretical Assessment of Idealized Source Screening Geophys. J. Int. (2021) 225, 1653–1671 doi: 10.1093/gji/ggab055 Advance Access publication 2021 February 10 GJI Seismology Hypothesis tests on Rayleigh wave radiation pattern shapes: a theoretical assessment of idealized source screening Joshua D. Carmichael Joshua D Carmichael EES-17, Los Alamos National Laboratory, P.O. Box 1663,MSD446, Los Alamos, NM 87545, USA. E-mail: [email protected] Accepted 2021 February 8. Received 2021 January 31; in original form 2020 September 16 Downloaded from https://academic.oup.com/gji/article/225/3/1653/6132273 by guest on 25 September 2021 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. Finally, 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. Key words: Theoretical seismology; Surface waves and free oscillations; Earthquake moni- toring and test-ban treaty verification; Probability distributions. ‘faulting signal’ on the radiation pattern shape is significantly non- 1 INTRODUCTION circular or has a low signal-to-noise ratio (SNR). Smaller yield ex- Seismic sources produce Rayleigh wave radiation patterns that indi- plosions (∼101−103kg) that do not trigger tectonic release may still cate focal mechanism asymmetry (Fig. 1). Teleseismic and regional accompany fracturing events or mechanical sliding on rock joints records of large underground nuclear explosions (∼101−103kT) that output shear energy as bulk damage (Steedman et al. 2016). emplaced in pre-stressed geologies, for example, have historically These bulk effects do not appear to significantly distort surface revealed that tectonic release of strain can superimpose with the wave radiation patterns when they are symmetric about a vertical isotropic explosion source to produce Love and Rayleigh waves axis. In particular, local distance records from a series of conven- with non-circular radiation patterns (Toksoz¨ & Kehrer 1972;Ek- tional explosives conducted through the source physics experiment strom¨ & Richards 1994). These observations contrast with simple (SPE, Snelson et al. 2013) demonstrate that low yield, shallowly models of cylindrically symmetric, shallow sources hosted in verti- buried sources that cause damage are vertical-axis symmetric, and cally stratified geologies that predict azimuthally constant Rayleigh thereby trigger Rayleigh wave radiation patterns that are circular wave amplitudes and absent Love waves. Instead, such observa- within a factor of 1.25 (Larmat et al. 2017). These explosions, tions are partially consistent with models of faulting motion pre- which were emplaced in the granites of Climax stock on the Nevada sented by tectonic release, which produces asymmetric deformation National Security Site (NNSS), also demonstrate that body waves about a vertical axis that excites a Rayleigh-wave field with a non- radiated by the same source in a similar frequency band show ap- circular radiation pattern (Richards & Ekstrom¨ 1995). Observers parent azimuthally asymmetry that is likely sourced by refraction risk misidentifying large, shallow explosions that accompany such effects (Darrh et al. 2019). Experiments with low-yield explosives tectonic release as shallow earthquakes when the imprint of such a emplaced in boreholes within New Hampshire granite demonstrate C The Author(s) 2021. Published by Oxford University Press on behalf of The Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. 1653 1654 J.D. Carmichael Downloaded from https://academic.oup.com/gji/article/225/3/1653/6132273 by guest on 25 September 2021 Figure 1. Surface sensors (triangles) record Rayleigh waves from a shallow explosion that is buried to a depth h in a horizontally-stratified half-space that has moment MI, which creates damage with moment MCLVD that each superimpose with faulting of moment M0. The damage occurs when constructive interference between the incident and reflected waves create a conically shaped zone of failure. (a) An explosion source capable of producing damage that is symmetric about a vertical axis, but that includes no faulting (no tectonic release) radiates a circular radiation pattern REX described at top. (b) A source that includes non-VDS faulting near the explosion point radiates a non-circular radiation pattern REQ described at top. Each radiation pattern shape associates with a deterministic scalar (bottom) that quantifies the power of the hypothesis test between data that record circular versus non-circular radiation patterns (at top). Section 4.1 defines each symbol. more complex effects. Namely, these latter experiments reveal that is therefore more earthquake-like than explosion-like. A discrimi- observationally confirmed radial fracturing in hard rock accom- nant that tests radiation pattern distortion from local to teleseismic panies asymmetric, short period (∼6 Hz), guided Rayleigh waves ranges can therefore benefit both the source physics community (Rg). Body waves sourced by these same New Hampshire explo- and support nuclear test-ban treaty surveillance, if justified on both sions can exhibit even greater azimuthal dependence (Stroujkova theoretical and experimental grounds. 2018). This work determines if a discriminant for shallow source types Both the SPE and New Hampshire experiments cumulatively in- that tests Rayleigh wave radiation pattern shapes is justified on dicate two substantive effects of the seismic source on radiation theoretical grounds. To confront this challenge, we apply binary hy- pattern shape can be observed from local distances. First, verti- pothesis tests to competing data models of noisy radiation patterns cal axis-symmetric damage does not significantly distort Rayleigh and assume several source parameters are unknown. Our models wave radiation pattern shapes from circularity, whereas a struc- also use planar geologies and therefore isotropic propagation of ture at depth can distort body wave patterns. Secondly, signifi- Rayleigh waves; we do not consider Love waves. Under this limited cant radial fracturing and shearing motion at the shallow explo- scope, we derive screening curves from the hypothesis tests that sion source measurably distorts both Rayleigh wave and body bound an observers’s capability to discriminate non-vertical dip- wave radiation patterns. These observations indicate that az- slip (non-VDS) shallow faulting sources from symmetric sources imuthal variability of Rayleigh waves sourced by small yield ex- (like shallow explosions that create damage that is symmetric about plosions indicate faulting or shearing motion at the source, whereas a vertical axis). The screening power of these tests is completely body wave asymmetry appears non-uniquely attributed to source defined by the product of a faulting-signal term, and a term that and path. depends on deployment parameters. Using this test, we illustrate A forthcoming test within the SPE series will provide a unique op- several applications of our theory that include finding deployment portunity to study asymmetry in radiation patterns that are sourced locations for sensors to supplement an existing network and that by explosions and superimposed with historic, tectonic records of maximize our source-type screening probability. We conclude that fault slip. This effort will detonate a conventional explosive in a Rayleigh wave radiation pattern discriminant shows a high proba- tectonic regions and monitor its seismic signatures for compari- bility PrD of success (PrD > 0.9) when a sufficient number of sensors son against earlier earthquake signatures that output radiation that (>12) with a limited azimuthal gap (<90◦) records radiation from shares wavefront paths (Walter et al. 2012). If Rayleigh waves out- sources with moderate strike-slip faulting signals (SNR >20). This put by this explosion remains circular and mismatches historical probability diminishes with more ambiguous focal
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