We combine earthquake spectra from multiple studies to investigate whether the increase in stress drop with depth often observed in the crust is real, or an artifact of decreasing attenuation (increasing
 NSFPAR ID:
 10203559
 Date Published:
 Journal Name:
 Geophysical Journal International
 Volume:
 223
 Issue:
 1
 ISSN:
 0956540X
 Page Range / eLocation ID:
 543 to 560
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this

Abstract Q ) with depth. In many studies, empirical path and attenuation corrections are assumed to be independent of the earthquake source depth. We test this assumption by investigating whether a realistic increase inQ with depth (as is widely observed) could remove some of the observed apparent increase in stress drop with depth. We combine event spectra, previously obtained using spectral decomposition methods, for over 50,000 earthquakes (M0 to M5) from 12 studies in California, Nevada, Kansas and Oklahoma. We find that the relative high‐frequency content of the spectra systematically increases with increasing earthquake depth, at all magnitudes. By analyzing spectral ratios between large and small events as a function of source depth, we explore the relative importance of source and attenuation contributions to this observed depth dependence. Without any correction for depth‐dependent attenuation, we find a systematic increase in stress drop, rupture velocity, or both, with depth, as previously observed. When we add an empirical, depth‐dependent attenuation correction, the depth dependence of stress drop systematically decreases, often becoming negligible. The largest corrections are observed in regions with the largest seismic velocity increase with depth. We conclude that source parameter analyses, whether in the frequency or time domains, should not assume path terms are independent of source depth, and should more explicitly consider the effects of depth‐dependent attenuation. 
Let f be a drawing in the Euclidean plane of a graph G, which is understood to be a 1dimensional simplicial complex. We assume that every edge of G is drawn by f as a curve of constant algebraic complexity, and the ratio of the length of the longest simple path to the the length of the shortest edge is poly(n). In the drawing f, a path P of G, or its image in the drawing π = f(P), is βstretch if π is a simple (nonselfintersecting) curve, and for every pair of distinct points p ∈ P and q ∈ P , the length of the subcurve of π connecting f(p) with f(q) is at most β∥f(p) − f(q)∥, where ∥.∥ denotes the Euclidean distance. We introduce and study the βstretch Path Problem (βSP for short), in which we are given a pair of vertices s and t of G, and we are to decide whether in the given drawing of G there exists a βstretch path P connecting s and t. We also output P if it exists. The βSP quantifies a notion of “near straightness” for paths in a graph G, motivated by gerrymandering regions in a map, where edges of G represent natural geographical/political boundaries that may be chosen to bound election districts. The notion of a βstretch path naturally extends to cycles, and the extension gives a measure of how gerrymandered a district is. Furthermore, we show that the extension is closely related to several studied measures of local fatness of geometric shapes. We prove that βSP is strongly NPcomplete. We complement this result by giving a quasipolynomial time algorithm, that for a given ε > 0, β ∈ O(poly(log V (G))), and s, t ∈ V (G), outputs a βstretch path between s and t, if a (1 − ε)βstretch path between s and t exists in the drawing.more » « less

SUMMARY Seismic attenuation (quantified by the quality factor Q) has a significant impact on the seismic waveforms, especially in the fluidsaturated rocks. This dissipative process can be phenomenologically represented by viscoelastic models. Previous seismological studies show that the Q value of Earth media exhibits a nearly frequencyindependent behaviour (often referred to as constantQ in literature) in the seismic frequency range. Such attenuation can be described by the mathematical Kjartansson constantQ model, which lacks of a physical representation in the viscoelastic sense. Inspired by the fractal nature of the pore fluid distribution in patchysaturated rocks, here we propose two fractal mechanical network (FMN) models, that is, a fractal tree model and a quasifractal ladder model, to phenomenologically represent the frequencyindependent Q behaviour. As with the classic viscoelastic models, the FMN models are composed of mechanical elements (spring and dashpots) arranged in different hierarchical patterns. A particular parametrization of each model can produce the same complex modulus as in the Kjartansson model, which leads to the constantQ. Applying the theory to several typical rock samples, we find that the seismic attenuation signature of these rocks can be accurately represented by either one of the FMN models. Besides, we demonstrate that the ladder model in particular exhibits the realistic multiscale fractal structure of the saturated rocks. Therefore, the FMN models as a proxy could provide a new way to estimate the microscopic rock structure property from macroscopic seismic attenuation observation.more » « less

null (Ed.)Abstract Despite multidisciplinary evidence for crustal magma accumulation below Santorini volcano, Greece, the structure and melt content of the shallow magmatic system remain poorly constrained. We use threedimensional (3D) velocity models from tomographic inversions of activesource seismic Pwave travel times to identify a pronounced lowvelocity anomaly (–21%) from 2.8 km to 5 km depth localized below the northern caldera basin. This anomaly is consistent with depth estimates of preeruptive storage and a recent inflation episode, supporting the interpretation of a shallow magma body that causes seismic attenuation and ray bending. A suite of synthetic tests shows that the geometry is well recovered while a range of melt contents (4%–13% to fully molten) are allowable. A thin mush region (2%–7% to 3%–10% melt) extends from the main magma body toward the northeast, observed as low velocities confined by tectonomagmatic lineaments. This anomaly terminates northwest of Kolumbo; little to no melt underlies the seamount from 3 to 5 km depth. These structural constraints suggest that crustal extension and edifice loads control the geometry of magma accumulation and emphasize that the shallow crust remains conducive to melt storage shortly after a calderaforming eruption.more » « less

Abstract The Salton Trough is one of the few regions on Earth where rifting is subaerial instead of submarine. We use the relative attenuation of teleseismic P phases recorded by the Salton Trough Seismic Imaging Project to investigate lithospheric and asthenospheric structures that form during extension. Map‐view analysis reveals stronger attenuation within the Salton Trough than in the adjacent provinces. We then construct tomographic models for variations in seismic attenuation with depth to discriminate between crustal and mantle signals with a damped least squares approach and a Bayesian approach. Synthetic tests show that models from damped least squares significantly underestimate the strength of attenuation and cannot separate crustal and mantle signals even if the tomographic models are allowed to be discontinuous at the lithosphere‐asthenosphere boundary (LAB). We show that a Bayesian approach overcomes these problems when inverting the same synthetic data sets and that shallow and deep signals are more clearly separated when imposing a discontinuity. With greater than 95% confidence, the results reveal first, that attenuation occurs primarily beneath the LAB; second, that the width of the attenuative region is narrower than the rift at 120 km depth; and third, that the strength of attenuation requires that the attenuative feature represents a melting‐column similar to those beneath mid‐ocean ridges. The narrow width of the melting column below the volatile‐free solidus is inconsistent with models for passive upwelling, where flow is driven only by rifting. Instead, we attribute the generation of incipient oceanic crust to mantle upwelling focused by buoyancy into a narrow diapir.