Empirical Green's functions (EGFs) are widely applied to correct earthquake spectra for attenuation and other path effects in order to estimate corner frequencies and stress drops, but these source parameter estimates often exhibit poor agreement between different studies. We examine this issue by analyzing a compact cluster of over 3,000 aftershocks of the 1992 Landers earthquake. We apply and compare two different analysis and modeling methods: (1) the spectral decomposition and global EGF fitting approach and (2) a more traditional EGF method of modeling spectral ratios. We find that spectral decomposition yields event terms that are consistent with stacks of spectral ratios for individual events, but source parameter estimates nonetheless vary between the methods. The main source of differences comes from the modeling approach used to estimate the EGF. The global EGF-fitting approach suffers from parameter trade-offs among the absolute stress drop, the stress drop scaling with moment, and the high-frequency falloff rate but has the advantage that the relative spectral shapes and stress drops among the different events in the cluster are well resolved even if their absolute levels are not. The spectral ratio approach solves for a different EGF for each target event without imposing any constraint on the corner frequency, f(c), of the smaller events, and so can produce biased results for target event f(c). Placing constraints on the small-event f(c) improves the performance of the spectral ratio method and enables the two methods to yield very similar results.
We stack a large global data set of 1Hz PKKP waveforms to constrain globally averaged properties of PKKP precursors. We find that the precursor observations are better explained by scattering from core-mantle boundary (CMB) topography than by scattering from the near surface, lower mantle, outer core, or inner core. However, as previously noted, simple models of CMB topography and standard 1-D seismic velocity models fail to model the range dependence of the relative amplitude between PKKPbc and its precursors. We find that this systematic mismatch is due, at least in part, to the assumed velocity gradient in the lowermost 250km of the outer core. Our globally averaged PKKP precursor observations are consistent with random CMB topography with RMS variations of approximate to 390m and a horizontal correlation length of approximate to 7km.
We constrain the heterogeneity spectrum of Earth's upper mantle at scales from a few kilometers to tens of thousands of kilometers using observations from high-frequency scattering, long-period scattering, and tomography. Tomography and high-frequency scattering constraints are drawn from previous studies, but constraints on mantle heterogeneity at intermediate scales (5-500 km) are lacking. To address this, we stack similar to 15,000 long-period P coda envelopes to characterize the globally averaged scattered wavefield at periods from 5 to 60 s and at ranges from 50 to 98 degrees. To fit these observations, we consider models of random mantle heterogeneity and compute the corresponding global wavefield using both a ray theoretical "seismic particle" approach and full spectral element simulations. Von Karman random media distributed throughout the uppermost 600 km of the mantle with a = 2000 km, epsilon = 10%, and kappa = 0.05 provide a good fit to the time, range, and frequency dependence of the stacks, although there is a trade-off between epsilon and the thickness of the assumed scattering layer. This random media model also fits previously published 1 Hz stacks of P coda and agrees with constraints on long-wavelength structure from tomography. Finally, we explore geodynamically plausible scenarios that might be responsible for the RMS and falloff rate of the proposed spectrum, including a self-similar mixture of basalt and harzburgite.
Studies now agree that small-scale (approximate to 10km) weak (approximate to 0.1%) velocity perturbations throughout the lowermost mantle generate the globally averaged amplitudes of 1Hz precursors to the core phase, . The possible frequency dependence and spatial coherence of this scattered phase, however, has been given less attention. Using a large global data set of approximate to 150,000 PKP precursor recordings, we characterize the frequency dependence of PKP precursors at central frequencies ranging from 0.5 to 4Hz. At greater frequencies, we observe more scattered energy (relative to the reference phase PKPdf), particularly at shorter ranges. We model this observation by invoking heterogeneity at length scales from 2 to 30km. Amplitudes at 0.5Hz, in particular, suggest the presence of more heterogeneity at scales >8km than present in previously published models. Using a regional bootstrap approach, we identify large (>20 degrees), spatially coherent regions of anomalously strong scattering beneath the West Pacific, Central/North America, andto a lesser extentEast Africa. Finally, as proof of concept, we use array processing techniques to locate the origin of scattered energy observed in Southern California by the Anza and Southern California Seismic Networks. The energy appears to come primarily from out-of-plane scattering on the receiver side. We suggest that such improvised arrays can increase global coverage and may reveal whether a majority of precursor energy comes from localized heterogeneity in the lowermost mantle.
We present high-resolution compressional wave to shear wave velocity ratios (V-p/V-s) beneath Klauea's summit caldera by applying an in situ estimation method using waveform cross-correlation data for three similar earthquake clusters. We observe high V-p/V-s ratios (1.832 and 1.852) for two event clusters surrounded by the low background V-p/V-s value of 1.412 at similar to 2.1km depth below the surface. These high and low V-p/V-s ratios can be explained by melt- and CO2-filled cracks, respectively, based on a theoretical crack model. The event cluster with the highest V-p/V-s ratio consists of long-period events that followed the 1997 East Rift Zone eruption, indicating their association with fluid and magma movement. The depths of the two clusters with high V-p/V-s ratios are consistent with the magma reservoir location inferred from geodetic observations. Their locations east and north of Halemaumau crater suggest a horizontal extent of a few kilometers for the reservoir.
We present a frequency-independent three-dimensional (3-D) compressional wave attenuation model (indicated by the reciprocal of quality factor Q(p)) for Klauea Volcano in Hawaii. We apply the simul2000 tomographic algorithm to the attenuation operator t(*) values for the inversion of Q(p) perturbations through a recent 3-D seismic velocity model and earthquake location catalog. The t(*) values are measured from amplitude spectra of 26708 P wave arrivals of 1036 events recorded by 61 seismic stations at the Hawaiian Volcanology Observatory. The 3-D Q(p) model has a uniform horizontal grid spacing of 3km, and the vertical node intervals range between 2 and 10km down to 35km depth. In general, the resolved Q(p) values increase with depth, and there is a correlation between seismic activity and low-Q(p) values. The area beneath the summit caldera is dominated by low-Q(p) anomalies throughout the entire resolved depth range. The Southwest Rift Zone and the East Rift Zone exhibit very high Q(p) values at about 9km depth, whereas the shallow depths are characterized with low-Q(p) anomalies comparable with those in the summit area. The seismic zones and fault systems generally display relatively high Q(p) values relative to the summit. The newly developed Q(p) model provides an important complement to the existing velocity models for exploring the magmatic system and evaluating and interpreting intrinsic physical properties of the rocks in the study area.
Theoretical modeling of strike-slip ruptures along a bimaterial interface suggests that earthquakes initiating on the interface will have a preferred rupture direction. We test this model with 450 small earthquakes (2 < M < 5) from Parkfield, California, to look for evidence of consistent rupture directivity along the San Andreas Fault. We analyze azimuthal variations in earthquake source spectra after applying an iterative correction for wave propagation effects. Our approach avoids directly modeling source spectra because these models generally assume symmetric rupture; instead, we look for azimuthal variations in the amplitudes of the source spectra over specified frequency bands. Our overall results show similar proportions of events exhibiting characteristics of rupture directivity toward either the southeast or northwest. However, the proportion of events with southeast rupture directivity increases as we limit the data set to larger magnitudes, with 70% of the 46 events M > 3 exhibiting southeast rupture characteristics. Some spatial and temporal variability in rupture directivity is also apparent. We observe a higher proportion of northwest directivity ruptures following the 2004 M 6 Parkfield earthquake, which ruptured toward the northwest. Our results are generally consistent with the preferred southeast rupture directivity model but suggest that directivity is likely due to several contributing factors. Citation: Kane, D. L., P. M. Shearer, B. P. Goertz-Allmann, and F. L. Vernon (2013), Rupture directivity of small earthquakes at Parkfield, J. Geophys. Res. Solid Earth, 118, 212-221, doi: 10.1029/2012JB009675.
Some studies of coda Q(-1) have found temporal changes that may be associated with earthquake activity, but these analyses are subject to biases due to differences in source locations and other nonstationary behavior in earthquake catalogs. These biases can be greatly reduced by using clusters of repeating earthquakes; studies using this approach have generally found no resolvable changes in coda Q(-1). We examine coda Q(-1) variations across southern California using 22 similar event clusters identified from a recent large-scale waveform cross-correlation project to improve earthquake locations. These clusters are found across the region and span the time period between 1981 and 2005. We apply the method of Beroza et al. (1995) to compute differential coda Q(-1) using waveforms from similar earthquake pairs and analyze the results to constrain any possible temporal variations. Results from individual event pairs show a great deal of scatter in differential coda Q(-1), but exhibit no clear temporal variations or changes associated with large earthquakes. Application of a median filter to smooth the results shows that any persistent large-scale changes in coda Q(-1) during this time period are less than about 30%.
We study earthquakes within California's Salton Trough from 1981 to 2009 from a precisely relocated catalog. We process the seismic waveforms to isolate source spectra, station spectra and travel-time dependent spectra. The results suggest an average P wave Q of 340, agreeing with previous results indicating relatively high attenuation in the Salton Trough. Stress drops estimated from the source spectra using an empirical Green's function (EGF) method reveal large scatter among individual events but a low median stress drop of 0.56 MPa for the region. The distribution of stress drop after applying a spatial-median filter indicates lower stress drops near geothermal sites. We explore the relationships between seismicity, stress drops and geothermal injection activities. Seismicity within the Salton Trough shows strong spatial clustering, with 20 distinct earthquake swarms with at least 50 events. They can be separated into early-M(max) and late-M(max) groups based on the normalized occurrence time of their largest event. These swarms generally have a low skew value of moment release history, ranging from -9 to 3.0. The major temporal difference between the two groups is the excess of seismicity and an inverse power law increase of seismicity before the largest event for the late-Mmax group. All swarms exhibit spatial migration of seismicity at a statistical significance greater than 85%. A weighted L1-norm inversion of linear migration parameters yields migration velocities from 0.008 to 0.8 km/hour. To explore the influence of fluid injection in geothermal sites, we also model the migration behavior with the diffusion equation, and obtain a hydraulic diffusion coefficient of approximately 0.25 m(2)/s for the Salton Sea geothermal site, which is within the range of expected values for a typical geothermal reservoir. The swarms with migration velocities over 0.1 km/hour cannot be explained by the diffusion curve, rather, their velocity is consistent with the propagation velocity of creep and slow slip events. These variations in migration behavior allow us to distinguish among different driving processes.
We study local and regional body-wave arrival times from several seismic networks to better define the active regional fault pattern in the epicentral region of the 3 May 1887 M-w 7.5 Sonora, Mexico (southern Basin and Range Province) earthquake. We determine hypocenter coordinates of earthquakes that originated between 2003 and 2007 from arrival times recorded by the local network RESNES (Red Sismica del Noreste de Sonora) and stations of the Network of Autonomously Recording Seismographs (NARS)-Baja array. For events between April and December 2007, we also incorporated arrival times from USArray stations located within 150 km of the United States-Mexico border. We first obtained preliminary earthquake locations with the Hypoinverse program (Klein, 2002) and then relocated these initial hypocenter coordinates with the source-specific station term (SSST) method (Lin and Shearer, 2005). Most relocated epicenters cluster in the upper crust near the faults that ruptured during the 1887 earthquake and can be interpreted to be part of its long-lasting series of aftershocks. The region of aftershock activity extends, along the same fault zone, 40-50 km south of the documented southern tip of the 1887 rupture and includes faults in the epicentral region of the 17 May 1913 (I-max VIII, M-I 5.0-0.4) and 18 December 1923 (I-max IX, M-I 5.7-0.4) Granados-Huasabas, Sonora, earthquakes, which themselves are likely to be aftershocks of the 1887 event. The long aftershock duration can be explained by the unusually large magnitude of the mainshock and by the low slip rates and long mainshock recurrence times of the faults that ruptured in 1887.
We identify lowered Vp/Vs ratios near earthquake source regions in southern California using observations from a seismic tomography model and high-resolution local Vp/Vs estimates using waveform cross-correlation data from within similar event clusters. The median tomographic Vp/Vs ratio is 1.716 +/- 0.008 at all the relocated crustal earthquake locations, compared to the background median value of 1.729 +/- 0.007 for the tomography model, although the error estimates overlap slightly. The median in situ Vp/Vs ratio of 1.673 +/- 0.022 within the similar event clusters suggests that tomographic studies are overestimating Vp/Vs at source regions. Interpretation of Vp/Vs anomalies is complicated by the scatter in values obtained for individual clusters and in comparisons to absolute Vp and Vs velocities in the tomography model. However, the low Vp/Vs ratios measured for the seismicity clusters are hard to explain with known rocks and suggest the presence of water-filled cracks with several percent porosity in earthquake source regions in southern California, which likely has an effect on faulting and earthquake activity. Citation: Lin, G., and P. M. Shearer (2009), Evidence for water-filled cracks in earthquake source regions, Geophys. Res. Lett., 36, L17315, doi: 10.1029/2009GL039098.
At high frequencies (similar to1 Hz), much of the seismic energy arriving at teleseismic distances is not found in the main phases (e.g. P, PP, S, etc.) but is contained in the extended coda that follows these arrivals. This coda results from scattering off small-scale velocity and density perturbations within the crust and mantle and contains valuable information regarding the depth dependence and strength of this heterogeneity as well as the relative importance of intrinsic versus scattering attenuation. Most analyses of seismic coda to date have concentrated on S-wave coda generated from lithospheric scattering for events recorded at local and regional distances. Here, we examine the globally averaged vertical-component, 1-Hz wavefield (>10degrees range) for earthquakes recorded in the IRIS FARM archive from 1990 to 1999. We apply an envelope-function stacking technique to image the average time-distance behavior of the wavefield for both shallow (less than or equal to50 km) and deep (greater than or equal to500 km) earthquakes. Unlike regional records, our images are dominated by P and P coda owing to the large effect of attenuation on PP and S at high frequencies. Modelling our results is complicated by the need to include a variety of ray paths, the likely contributions of multiple scattering and the possible importance of P-to-S and S-to-P scattering. We adopt a stochastic, particle-based approach in which millions of seismic phonons are randomly sprayed from the source and tracked through the Earth. Each phonon represents an energy packet that travels along the appropriate ray path until it is affected by a discontinuity or a scatterer. Discontinuities are modelled by treating the energy normalized reflection and transmission coefficients as probabilities. Scattering probabilities and scattering angles are computed in a similar fashion, assuming random velocity and density perturbations characterized by an exponential autocorrelation function. Intrinsic attenuation is included by reducing the energy contained in each particle as an appropriate function of traveltime. We find that most scattering occurs in the lithosphere and upper mantle, as previous results have indicated, but that some lower-mantle scattering is likely also required. A model with 3 to 4 per cent rms velocity heterogeneity at 4-km scale length in the upper mantle and 0.5 per cent rms velocity heterogeneity at 8-km scale length in the lower mantle (with intrinsic attenuation of Q(alpha)= 450 above 200 km depth and Q(alpha)= 2500 below 200 km) provides a reasonable fit to both the shallow- and deep-earthquake observations, although many trade-offs exist between the scale length, depth extent and strength of the heterogeneity.
[1] We study the lateral variations in P wave attenuation in the upper mantle at frequencies between 0.16 and 0.86 Hz by analyzing the spectra from >18,000 P and >14,000 PP arrivals. We select seismograms from shallow earthquakes at epicentral distances of 40degrees-80degrees for P waves and 80degrees-160degrees for PP waves. Each spectrum is the product of source, receiver, and propagation response functions as well as local source- and receiver-side effects. We correct each spectrum for average source and attenuation models. Since there are multiple receivers for each source and multiple sources for each receiver, we can approximate the source- and receiver-side terms by stacking the appropriate P log spectra. The resulting source- specific response functions include any remaining source spectrum and near-source Q structure; the receiver stacks include the site response and near-receiver Q structure. We correct the PP log spectra for the appropriate source- and receiver-side stacks. Since attenuation in the lower mantle is small, the residual log spectrum approximates attenuation in the upper mantle near the PP bounce point and is used to estimate delta(t*) over bar. We constrain the anomalies to the top 220 km of the mantle, as suggested by previous Q studies, and translate the delta(t*) over bar measurements to variations in 1000/Q(alpha). The patterns of more and less attenuating regions generally correlate with previously published shear attenuation models and surface tectonics. Continents are usually less attenuating than the global average, whereas oceanic regions tend to be more attenuating. There are interesting exceptions to this tectonic pattern, such as an attenuating region beneath southern Africa.
Using seismograms from globally distributed, shallow earthquakes between 1988 and 1998, we compute spectra for P arrivals from epicentral distances of 40 degrees to 80 degrees and PP arrivals from 80 degrees to 160 degrees. Selecting records with estimated signal-to-noise ratios greater than 2, we find 17,836 P and 14,721 PP spectra. We correct each spectrum for the known instrument response and for an omega (-2) source model that accounts for varying event sizes. Next, we stack the logarithms of the P and PP spectra in bins of similar source-receiver range. The stacked log spectra, denoted as log(D'(P)) and log(D'(PP)), appear stable between about 0.16 and 0.86 Hz, with noise and/or bias affecting the results at higher frequencies. Assuming that source spectral differences are randomly distributed, then for shallow events, when the PP range is twice the P range, the average residual source spectrum may be estimated as 2 log(D'(P))- log(D'(PP)), and the average P wave attenuation spectrum may be Estimated as log(D'(PP)) - log(D'(P)). The residual source spectral estimates exhibit a smooth additional falloff as omega (-0.15+/-0.05) between 0.16 and 0.86 Hz, indicating that omega (-2.15+/-0.05) is an appropriate average source model for shallow events. The attenuation spectra show little distance dependence over this band and have a P wave (t) over bar* value of similar to0.5 s. We use (t) over bar* measurements from individual P and PP spectra to invert for a frequency-independent Q model and find that the upper mantle is nearly 5 times as attenuating as the lower mantle. Frequency dependence in Q, is difficult to resolve directly in these data but, as previous researchers have noted, is required to reconcile these values with long-period Q estimates. Using Q model QL6 [Durek and Ekstrom, 1996] as a long-period constraint, we experiment with fitting our stacked log spectra with an absorption band model. We find that the upper corner frequency f(2) in the absorption band must be depth-dependent to account for the lack of a strong distance dependence in our observed (t) over bar* values. In particular, our results indicate that f(2) is higher in the top 220 km of the mantle than at greater depths; the lower layer is about twice as attenuating at 1 Ha than at 0.1 Hz, whereas the upper mantle attenuation is relatively constant across this band.
Differential waveform analysis provides an excellent tool for studying the attenuation properties of the top of the inner core. We analyse 108 PKP(BC) versus PKP(DF) waveforms from Global Digital Seismograph Network (GDSN) vertical-component seismograms to constrain the frequency and depth dependency of Q(alpha) in this region. We use both frequency- and time-domain techniques. In the time-domain method, the BC phase is mapped onto the DF phase using an attenuation band operator. The mapping operator is parameterized by the upper and lower cut-off frequencies of the absorption band, the time shift required to align these two phases, and t*, the integrated effect of Q(alpha)-1 in the top of the inner core. In the frequency-domain analysis, multitaper spectral estimation is used to compute the complex spectrum of the two phases. The shape of the amplitude spectrum of the spectral ratio between these two phases gives an estimate of Q(alpha). Similar results are obtained from frequency- and time-domain analysis but the Q(alpha) obtained from frequency-domain analysis is approximately 20 per cent greater than the value obtained from time-domain analysis. We prefer the frequency-domain results since they are not affected by the presence of noise at higher frequencies. Apparent Q(alpha) values exhibit considerable scatter with no clear frequency or depth dependence. We find that the average value of Q(alpha) in the top of the inner core is about 360 which is consistent with previous body wave studies but differs by a factor of two from values obtained from studies of the decay of free oscillations.