William R. Walter

Moment, energy, stress drop, and source spectra of western United States earthquakes from regional coda envelopes

We present a new method to estimate stable seismic source parameters, such as energy, moment, and Orowan stress drop, using regional coda envelopes from as few as one broadband station. We use the method to compute path- and site-corrected seismic moment-rate spectra for 117 recent western United States earthquakes. Empirical Greens function corrections were applied to our surface- and body-wave coda envelope measurements to generate S-wave source spectra. These source spectra provide stable, single-station estimates of radiated seismic energy Es and seismic moment Mo that for common events are in excellent agreement with network-averaged estimates obtained using local and regional data. Teleseismic moment estimates are compatible with our regional results, but teleseismic energy estimates appear to be nearly an order of magnitude low. We estimated the seismic moment of events ranging between Mw 2.2 and 7.3, and energy estimates for which we had measured at least 70% of the total energy, generally events above Mw 3.3. We use these estimates to examine the behavior of derived parameters such as the Orowan stress drop (Δσ = 2μEs/Mo). While the earthquakes we studied have a small range in Orowan stress drop, generally between 0.1 and 20 MPa, they show a strong tendency for Orowan stress drop to increase with moment, approximately as Mo0.25. We believe this is a source effect and is not due to inadequate bandwidth or attenuation correction, and note that this trend appears to continue for microearthquakes as described in a recent deep borehole study in southern California. Many of the large high stress drop earthquakes show complexity in their moment-rate spectra near the corner frequency and cannot be fit by a simple ω-square model. Instead, above the first corner frequency, the spectral decay ranges between f−1.0 and f−1.5. This leads to larger estimates of radiated energy than predicted with a simple ω-square model and has implications for seismic hazard estimation. Coda envelopes have three main advantages over direct arrivals for estimating seismic moment and energy: (1) Coda amplitudes vary little with geology and source-radiation anisotropy and allow accurate single-station applications; (2) path-corrected coda amplitude measurements can be applied to very large regions, allowing a comparison of source parameters throughout the western United States using a common methodology and stations; (3) because long-period coda can last for hours for large local and regional events, it allows the analysis of seismograms with clipped early arrivals.

Upper mantle velocity structure beneath the Tibetan Plateau from Pn travel time tomography

We inverted 1510 P arrival times from regional distances (333–1600 km), in and around the Tibetan Plateau to map the lateral velocity variation within the uppermost mantle. Previous studies have placed first-order constraints on upper mantle velocities but relied on data recorded almost exclusively at stations outside of the plateau. We improve resolution by using 40 events recorded at stations within the Tibetan Plateau. We combine these data with observations obtained from the International Seismological Centre (ISC) to extend our coverage by including Pn arrivals from 85 additional plateau events, relocated in previous studies, and recorded at stations in and around the Tibetan Plateau. We use synthetic travel time data to evaluate the resolution of our data set. The observations provide good resolution to about 1° over most of the plateau and surrounding regions. Our results show average Pn velocities that are about 3% lower in the northern plateau relative to the southern plateau. These variations correlate well with major tectonic features and previous geophysical observations. In the Qiangtang terrane of the northern plateau, an area known to be inefficient for Sn propagation, Pn is slow relative to both the plateau south of the Banggong-Nujiang suture and the tectonically stable Tarim basin north of the plateau. This is strong evidence for the existence of partial melt within the uppermost mantle beneath the northern Tibetan Plateau. However, when laboratory estimates of relationships between temperature, velocity, and attenuation are applied, a relatively small temperature variation (240° to 370°C) is required to explain our Pn velocity observations. When combined with geochemical constraints from volcanics in the northern plateau, our results strongly suggest that the mantle lid is intact beneath the northern plateau. This result would preclude tectonic models involving wholesale delamination of the mantle lithosphere in the northern Tibetan Plateau.

Observations of regional phase propagation across the Tibetan Plateau

We present observations of regional phase velocity and propagation characteristics using data recorded during a 1-year deployment of broadband digital seismic stations across the central Tibetan Plateau along the Qinghai-Tibet highway from Golmud to Lhasa. Previous seismological studies within this region have had to rely on earthquakes recorded almost exclusively at stations outside of the plateau. We have the opportunity to study numerous source-receiver paths confined entirely within the Tibetan Plateau. Our analysis concentrates on travel time, amplitude, and frequency content measurements of the Pg, Pn and Sn phases. Pn can be clearly picked for all observed paths and propagates at an average velocity of 8.16±0.07 km/s within the Tibetan Plateau. Sn, however, shows dramatic variations in propagation efficiency across the Tibetan Plateau that is strongly dependent on frequency. We observe that Sn rapidly decreases in frequency and amplitude as it passes through the northern portion of the plateau. We show that in general, Sn propagation efficiency decreases with increasing frequency content. We use 122 events from outside of the plateau and 61 from within to refine the boundaries of a region of inefficient high-frequency Sn propagation. Specifically, we show that a larger portion of the northern Tibetan Plateau attenuates Sn energy than was previously suggested. In the southern plateau, where high-frequency Sn is observed, we computed an average velocity of 4.59±0.18 km/s. We also observed that the Pn velocity within this region of inefficient high-frequency Sn propagation is nearly 4% slower than the Pn velocity computed for paths restricted to the southern plateau and that the crust is about 10 km thinner than in the south. The coincident locations of inefficient Sn propagation and slow Pn velocity is commonly observed in regions of active tectonics. Our results add constraints to the velocity structure of the lithosphere beneath the Tibetan Plateau and require first-order lateral variations in the uppermost mantle structure, despite the relatively uniform topography of the plateau.

Stable and Transportable Regional Magnitudes Based on Coda-Derived Moment-Rate Spectra

We describe an empirical calibration method for obtaining stable seismic source moment-rate spectra derived from regional coda envelopes using broadband stations. The results of applying this method yield source spectra that are more stable than any other direct-phase measure to date. The procedure accounts for all propagation, site, and S -to-coda transfer function effects. The resultant coda-derived moment-rate spectra are then used to provide traditional band-limited magnitudes (e.g., M L , m b ), as well as an unbiased, unsaturated magnitude (moment magnitude, M w ) that is tied to a physical measure of earthquake size (i.e., seismic moment). We validate our results by comparing our coda-derived moment estimates with those obtained from long-period waveform modeling. Most importantly, we demonstrate that the interstation magnitude scatter is significantly reduced when using long-window-length coda (i.e., M w (coda) and m b (coda)). However, when we use short-window coda measurements of 5 sec in length taken after twice the direct-wave travel time, the scatter remains large, comparable to direct waves. Once calibrated, the coda-derived source spectra provide stable, unbiased magnitude estimates for events that are too small either to be reliably waveform modeled or to be seen at far-regional and teleseismic distances. This property is ideal for sparse local or regional networks. We found that our source amplitude estimates were nearly insensitive to the expected source radiation pattern and exhibited roughly a factor of 3-5 less interstation scatter when compared against coda duration and conventional direct-phase measurements (e.g., P g , L g ). We also found that the coda stability, as measured by the interstation scatter for common events, reached a minimum value beyond a certain critical measurement window length. For example, at 6-8 Hz, the interstation standard deviation was less than 0.08 provided the coda measurement was at least ∼80 sec in duration, whereas at 1.5-2.0 Hz, the critical window length was ∼100 sec. For all frequency bands, as the coda window becomes shorter, the standard deviation increases, asymptotically approaching the direct-wave scatter. In this article we describe in detail the calibration methodology and address concerns related to choosing optimal measurement window lengths, estimating error, testing empirical path corrections, and tying coda amplitudes to an absolute scale. In order to demonstrate the usefulness and transportability of our method, we chose the Dead Sea Rift as our study area.

Spectra of seismic radiation from a tensile crack

A model for the average far-field P and S wave amplitude spectra from a circular crack failing in tension is presented. The model explicitly avoids specifying the details of the rupture process; instead, the spectral amplitude is determined by applying physically realistic constraints to an idealized spectral shape for each wave type. The idealized spectral form is given by Ω0 /(1 + (ω/ωc,)2)ψ/2, where ωc is a parameter representing the corner frequency, Ω0 determines the overall scaling of the spectra, and ψ determines the falloff at high frequencies. For fixed ψ, the complete specification of the body wave spectra, P and S waves, requires the determination of four unknowns: Ω0P, Ω0S, ωcP, and ωcS. The P and S spectral models are constrained by fixing the low-frequency level of each to be equivalent to a point source. They are further constrained by equating the total radiated energy with the available elastic energy through a seismic efficiency parameter η. A final constraint between the corner frequencies of the P and S spectra is needed to determine the four free parameters. For the type of model considered here: an equidimensional fault with greatest displacement in the center, we expect the P to S corner frequency ratio to range between 1 and 1.73 depending on the details of the rupture. For ψ = 2, this model gives an average S/P spectral amplitude ratio of about 2.1 at very low frequencies and between 2.1 and 0.7 at very high frequencies, depending on the P to S corner frequency ratio. Applying the same criteria to a circular shear crack gives an average S/P spectral amplitude of about 7.1 at very low frequencies and between 7.1 and 2.4 at very high frequencies, again depending on the P to S corner frequency ratio. The tensional crack thus has lower average S/P spectral amplitudes than the shear crack, and such low S/P spectral amplitudes may be an identifying characteristic of tensile or tensile equivalent rupture. Using the shear and tensional models, we construct composite spectra that have significantly smaller S/P spectral amplitude ratios than the shear cracks alone, even when the tensional events radiate just a fraction of the total seismic energy. The tensile crack average spectral model may be useful as a first approximation for modeling seismic sources with a volumetric component in them, such as slip on a nonplanar fault, or magma injection.

Amplitude corrections for regional seismic discriminants

Abstract — A fundamental problem associated with event identification lies in deriving corrections that remove path and earthquake source effects on regional phase amplitudes used to construct discriminants. Our goal is to derive a set of physically based corrections that are independent of magnitude and distance, and amenable to multivariate discrimination by extending the technique described in Taylor and Hartse (1998). For a given station and source region, a number of well-recorded earthquakes is used to estimate source and path corrections. The source model assumes a simple Brune (1970) earthquake source that has been extended to handle non-constant stress drop. The discrimination power in using corrected amplitudes lies in the assumption that the earthquake model will provide a poor fit to the signals from an explosion. The propagation model consists of a frequency-independent geometrical spreading and frequency-dependent power law Q. A grid search is performed simultaneously at each station for all recorded regional phases over stress-drop, geometrical spreading, and frequency-dependent Q to find a suite of good-fitting models that remove the dependence on mb and distance. Seismic moments can either be set to pre-determined values or estimated through inversion and are tied to mb through two additional coefficients. We also solve for frequency-dependent site/phase excitation terms. Once a set of corrections is derived, effects of source scaling and distance as a function of frequency are applied to amplitudes from new events prior to forming discrimination ratios. Thus, all the corrections are tied to just mb (or M0) and distance and can be applied very rapidly in an operational setting. Moreover, phase amplitude residuals as a function of frequency can be spatially interpolated (e.g., using kriging) and used to construct a correction surface for each phase and frequency. The spatial corrections from the correction surfaces can then be applied to the corrected amplitudes based only on the event location. The correction parameters and correction surfaces can be developed offline and entered into an online database for pipeline processing providing multivariate-normal corrected amplitudes for event identification. Examples are shown using events from western China recorded at the station MAKZ.

The Scaling of Seismic Energy With Moment: Simple Models Compared With Observations

The scaling between small and large earthquakes remains an unresolved issue in seismology. The predominant hypothesis is the rupture process is self-similar, leading to predictions that source parameters such as apparent stress are the same for all earthquakes. As digital broadband data has become widely available, a number of published empirical studies have challenged self-similarity, though the evidence remains mixed. Using simple point source models in the time and frequency domains, we review the predicted scaling behavior of earthquake energy and other source parameters, under self- and non-self-similar assumptions. The models show self-similar scaling leads to some testable hypotheses, including the constancy of apparent stress and the invariance of spectral shape under a particular frequency transformation, regardless of the true (and perhaps unknown) source time function. We also review the problems posed by measurement errors in determining seismic energy and the limited magnitude ranges of events within given studies to answering the scaling question. To address these problems we apply multiple techniques to the 1999 Hector Mine California earthquake sequence. For two regional wave types, direct Lg and scattered coda waves, we examine spectral scaling using both seismic energy, and source shape invariance. The results show the Hector Mine sequence exhibits non-self-similar scaling with apparent stress increasing with moment approximately as M o 0.14 . Finally we briefly present four general scaling models, one self-similar with high variance, the others non-self-similar, which appear to be consistent with the earthquake apparent stress behavior that has been observed to date.

Upper mantle structure beneath central Eurasia using a source array of nuclear explosions and waveforms at regional distances

We have observed very consistent broadband, regional, three-component P waveforms from a set of 11 explosions that occurred at the former Soviet test site in Kazakhstan during 1988 and 1989 and have modeled most of the prominent features in these waveforms to determine upper mantle structure beneath central Eurasia. Using a subset of events as a source array, we have identified four consistent arrivals during the first 15 s of P waves recorded at the Soviet/Incorporated Research Institutions for Seismology (IRIS) stations Arti (ARU) (d ≈1500 km) and Garm (GAR) (d ≈1380 km). These arrivals show consistent variations in frequency content, relative timing, and amplitudes from event to event despite a range in source magnitude (mb) between 4.9 and 6.1. We have also identified consistent features in P waveforms of these events recorded at Obninsk (OBN) (d ≈2880 km). We argue that most of the prominent features in these waveforms can be explained by reflections at or refractions near discontinuities or large velocity gradients in the upper mantle. We show that a model with discontinuities of approximately 3.0% and 6.5% near 200 km and 400 km, respectively, produces a better fit to the broadband data at ARU and GAR than previous models for this region. This model also produces a good match to waveforms recorded at OBN and NORESS, however, this model is not unique. For example, we show that it is also possible to produce similar waveforms by replacing the 200 km discontinuity with a large, notch shaped, low velocity zone between approximately 100 and 140 km. Based on reflectivity synthetics, we suggest that additional data, especially from distances less than 1000 km, should indicate which of these models is more accurate. Although our models are not unique, our observations do constrain the following features. (1) There must be reflectors between about 140 and 200 km and near 400 km depth in the upper mantle to explain the large secondary arrivals at both ARU and GAR. (2) Based on the relative size of some of the secondary arrivals at ARU and GAR, the discontinuity near 400 km must be large. However, it cannot be much greater than about 6.5% because there is no evidence, in our data, of a reflection from 400 km at OBN. (3) The relatively small amplitude of the first arrivals at both ARU and GAR suggests that either the gradient in the uppermost mantle is very small or that a shallow low velocity zone is present. Comparison of our results with other upper mantle studies shows that the central Eurasian upper mantle is similar to the upper mantle of the central and eastern United States.

2‐D or not 2‐D, that is the question: A northern California test

[1] Reliable estimates of the seismic source spectrum are necessary for accurate magnitude and energy estimation. In particular, how seismic radiated energy scales with increasing earthquake size has been the focus of recent debate within the community and has direct implications on earthquake source physics studies as well as hazard mitigation. The 1-D coda methodology of Mayeda et al. [2003] has provided the lowest variance estimate of the source spectrum when compared against traditional approaches that use direct S-waves, thus making it ideal for networks that have sparse station distribution. The 1-D coda methodology has been mostly confined to regions of approximately uniform complexity. For larger, more geophysically complicated regions, 2-D path corrections may be required. The complicated tectonics of the northern California region coupled with high quality broadband seismic data provides for an ideal ‘‘apples-to-apples’’ test of 1-D and 2-D path assumptions on direct waves and their coda. Using the same station and event distribution, we compared 1-D and 2-D path corrections and observed the following results: (1) 1-D coda results reduced the amplitude variance relative to direct S-waves by roughly a factor of 8 (800%); (2) Applying a 2-D correction to the coda resulted in up to 40% variance reduction from the 1-D coda results; (3) 2-D direct S-wave results, though better than 1-D direct waves, were significantly worse than the 1D coda. We found that coda-based moment-rate source spectra derived from the 2-D approach were essentially identical to those from the 1-D approach for frequencies less than � 0.7-Hz, however for the high frequencies (0.7 � f � 8.0-Hz), the 2-D approach resulted in inter-station scatter that was generally 10–30% smaller. For complex regions where data are plentiful, a 2-D approach can significantly improve upon the simple 1-D assumption. In regions where only 1-D coda correction is available it is still preferable over 2-D direct wave-based measures. Citation: Mayeda, K., L. Malagnini, W. S. Phillips, W. R. Walter, and D. Dreger (2005), 2-D or not 2-D, that is the question: A northern California test, Geophys. Res. Lett., 32, L12301, doi:10.1029/2005GL022882.

Mapping Crustal Heterogeneity Using Lg Propagation Efficiency Throughout the Middle East, Mediterranean, Southern Europe and Northern Africa

Abstract — In this paper we describe a technique for mapping the lateral variation of Lg characteristics such as Lg blockage, efficient Lg propagation, and regions of very high attenuation in the Middle East, North Africa, Europe and the Mediterranean regions. Lg is used in a variety of seismological applications from magnitude estimation to identification of nuclear explosions for monitoring compliance with the Comprehensive Nuclear-Test-Ban Treaty (CTBT). These applications can give significantly biased results if the Lg phase is reduced or blocked by discontinuous structure or thin crust. Mapping these structures using quantitative techniques for determining Lg amplitude attenuation can break down when the phase is below background noise. In such cases Lg blockage and inefficient propagation zones are often mapped out by hand. With our approach, we attempt to visually simplify this information by imaging crustal structure anomalies that significantly diminish the amplitude of Lg. The visualization of such anomalies is achieved by defining a grid of cells that covers the entire region of interest. We trace Lg rays for each event/station pair, which is simply the great circle path, and attribute to each cell a value equal to the maximum value of the Lg/P-coda amplitude ratio for all paths traversing that particular cell. The resulting map, from this empirical approach, is easily interpreted in terms of crustal structure and can successfully image small blockage features often missed by analysis of raypaths alone. This map can then be used to screen out events with blocked Lg prior to performing Q tomography, and to avoid using Lg-based methods of event identification for the CTBT in regions where they cannot work.¶For this study we applied our technique to one of the most tectonically complex regions on the earth. Nearly 9000 earthquake/station raypaths, traversing the vast region comprised of the Middle East, Mediterranean, Southern Europe and Northern Africa, have been analyzed. We measured the amplitude of Lg relative to the P-coda and mapped the lateral variation of Lg propagation efficiency. With the relatively dense coverage provided by the numerous crossing paths we are able to map out the pattern of crustal heterogeneity that gives rise to the observed character of Lg propagation. We observe that the propagation characteristics of Lg within the region of interest are very complicated but are readily correlated with the different tectonic environments within the region. For example, clear strong Lg arrivals are observed for paths crossing the stable continental interiors of Northern Africa and the Arabian Shield. In contrast, weakened to absent Lg is observed for paths crossing much of the Middle East, and Lg is absent for paths traversing the Mediterranean. Regions that block Lg transmission within the Middle East are very localized and include the Caspian Sea, the Iranian Plateau and the Red Sea. Resolution is variable throughout the region and strongly depends on the distribution of seismicity and recording stations. Lg propagation is best resolved within the Middle East where regions of crustal heterogeneity on the order of 100 km are imaged (e.g., South Caspian Sea and Red Sea). Crustal heterogeneity is resolvable but is poorest in seismically quiescent Northern Africa.