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Park, J, Lindberg CR, Vernon FL.  1987.  Multitaper Spectral-Analysis of High-Frequency Seismograms. Journal of Geophysical Research-Solid Earth and Planets. 92:12675-12684.   10.1029/JB092iB12p12675   Website
Park, J, Vernon FL, Lindberg CR.  1987.  Frequency-Dependent Polarization Analysis of High-Frequency Seismograms. Journal of Geophysical Research-Solid Earth and Planets. 92:12664-12674.   10.1029/JB092iB12p12664   Website
Pavlis, GL, Vernon FL.  1994.  Calibration of Seismometers Using Ground Noise. Bulletin of the Seismological Society of America. 84:1243-1255. AbstractWebsite

We have developed and tested a new technique for calibration of seismometers using continuous recordings of ground noise. The method is founded on analytic techniques recently developed for estimation of transfer functions in magnetotellurics. We find that the technique can produce precise, absolute calibration measurements on sensors that do not have calibration coils. The data used are obtained by placing two sets of sensors close enough together that we can assume they record the same ground motion. It is further assumed that one of the sensors has a known, absolute calibration. One then records ground noise of sufficiently high amplitude to guarantee that one is recording above the amplifier noise floor across the entire frequency band of interest. Data are recorded for a time period that depends upon the lowest frequency that is to be resolved. The data is then divided into a series of N partially overlapping time windows, transfer-function estimates are calculated from each of these N time windows, and finally a robust mean estimation procedure is used to produce transfer-function estimates at a set of discrete frequencies. We applied this technique to produce calibration estimates for four different types of sensors (GS-13, triaxial 4.5-Hz L-28, STS-2, and triaxial L4) in various recording arrangements. We found that the technique worked extremely well in every case at frequencies above the point where the sensor output dropped into the instrument noise floor. Problems were consistently encountered above some high-frequency limit that depended upon the site and sensor being tested, and, as a result, we conclude that obtaining reliable results at higher frequencies requires more care in the experimental procedure. We show results from 4.5- and 1-Hz passive sensors plastered onto the same pier, which show nearly perfect coherence out to 100 Hz, and excellent agreement with theoretical predictions between 0.03 and 20 Hz. However, above 20 Hz, a systematic phase error plagues our results. Other cases were comparable when care was taken in the experimental procedure, but differed in detail. We argue that there are fundamental problems recording ground noise at these higher frequencies as a result of the following three experimental problems that can be difficult to control: (1) coupling of sensors to a common, stable platform, (2) contamination by acoustic and pier resonances in typical recording vaults, and (3) resonances of the sensor-pier-ground system.

Pavlis, GL, Vernon FL.  2010.  Array processing of teleseismic body waves with the USArray. Computers & Geosciences. 36:910-920.   10.1016/j.cageo.2009.10.008   AbstractWebsite

We introduce a novel method of array processing for measuring arrival times and relative amplitudes of teleseismic body waves recorded on large aperture seismic arrays. The algorithm uses a robust stacking algorithm with three features: (1) an initial 'reference' signal is required for initial alignment by crosscorrelation; (2) a robust stacking method is used that penalizes signals that are not well matched to the stack; and (3) an iterative procedure alternates between cross-correlation with the current stack and the robust stacking algorithm. This procedure always converges in a few iterations making it well suited for interactive processing. We describe concepts behind a graphical interface developed to utilize this algorithm for processing body waves. We found it was important to compute several data quality metrics and allow the analyst to sort on these metrics. This is combined with a 'pick cutoff' function that simplifies data editing. Application of the algorithm to data from the USArray show four features of this method. (1) The program can produce superior results to that produced by a skilled analyst in approximately 1/5 of the time required for conventional interactive picking. (2) We show an illustrative example comparing residuals from S and SS for an event from northern Chile. The SS data show a remarkable +/- 10 s residual pattern across the USArray that we argue is caused by propagation approximately parallel to the subduction zones in Central and South America. (3) Quality metrics were found to be useful in identifying data problems. (4) We analyzed 50 events from the Tonga-Fiji region to compare residuals produced by this new algorithm with those measured by interactive picking. Both sets of residuals are approximately normally distributed, but corrupted by about 5% outliers. The scatter of the data estimated by waveform correlation was found to be approximately 1/2 that of the hand picked data. The outlier populations of both data sets are likely produced by cycle skips, but the distribution of hand picked data show a more diffuse departure from a Gaussian error model. (C) 2010 Elsevier Ltd. All rights reserved.

Pavlis, GL, Vernon F, Harvey D, Quinlan D.  2004.  The generalized earthquake-location (GENLOC) package: an earthquake-location library. Computers & Geosciences. 30:1079-1091.   10.1016/j.cageo.2004.06.010   AbstractWebsite

We describe a library and associated set of applications for locating seismic events. The library is called the GENeralized LOCation (GENLOC) library because it is a general library that implements most methods commonly used for single event locations. The library has a flexible implementation of the standard Gauss-Newton method with many options for weighting schemes, inversion methods, and algorithms for choosing an initial location estimate. GENLOC also has a grid-search algorithm that makes no assumptions about the geometry of the grid it is searching returning only the point with a best fit solution for the specified residual norm. GENLOC supports both arrival time and array slowness vector measurements. A unique feature is the strong separation between the travel time/earth model problem and the location estimations. GENLOC can utilize data from any seismic phase for which the user can supply an earth model and method to compute theoretical travel times and/or slowness values. The GENLOC library has been used in five different working applications: (1) a simple command line program, (2) an interactive graphical user interface version used in an analyst information system, (3) a database-driven relocation program, (4) a recent implementation of the progressive multiple event location method, and (5) a real-time location program. We ran a validation test against LOCSAT and found reasonable consistency in estimated locations. We attribute observed differences in the solutions to roundoff errors in different calculators used by the two programs. (C) 2004 Elsevier Ltd. All rights reserved.

Pavlis, GL, Sigloch K, Burdick S, Fouch MJ, Vernon FL.  2012.  Unraveling the geometry of the Farallon plate: Synthesis of three-dimensional imaging results from USArray. Tectonophysics. 532:82-102.   10.1016/j.tecto.2012.02.008   AbstractWebsite

We compare 12 recent three-dimensional (3D) seismic imaging results that made extensive use of data from the Earthscope Transportable Array (TA). Our goal is to sort out what can be said about the geometry of the Farallon plate. Our main approach is 3D visualization using a kinematic plate motion model as a framework. Comparison of results from all 12 image volumes indicates that the results are most consistent with a single, coherent Farallon slab overridden by North American. The Farallon can be tracked from the trench in the Pacific Northwest to its remnants in the lower mantle under eastern North America. From the trench the lithosphere has a low dip to the volcanic arc. Immediately east of the arc the slab steepens sharply before undergoing a decrease in dip above the 410 km discontinuity. The gently dipping section varies along strike. Under Washington the deflection is minor but to the south the slab flattens to become nearly horizontal beneath southern Idaho. There is a strong agreement that the high velocity anomaly associated with the slab vanishes under eastern Oregon. Scattered wave imaging results, however, suggest the top of the anomaly is continuous. These can be reconciled if one assumes the wavespeed anomaly has been neutralized by processes linked to the Yellowstone system. We find that all results are consistent with a 4D kinematic model of the Mendocino slab window under Nevada and Utah. In the eastern US the larger scale models all show a lower mantle anomaly related to the older history of Farallon subduction. The link between the lower mantle and new results in the U.S. Cordillera lies under the High Plains where the required USArray coverage is not yet complete. Image volumes in a unified format are supplied in an electronic supplement. (C) 2012 Elsevier B.V. All rights reserved.

Peach, CL, Collier R, Kelley DS, Thorrold A, Duncan S, Orcutt JA, Vernon FL, Chave AD, Arrott M, Schofield O, Meisinger MJ, Farcas C, Farcas E, Krueger I, Kleinert J, Keen CS.  2010.  Ocean Observatory Educational Infrastructure for 21st Century Learners (Invited). ( Peach CL, Ed.).: American Geophysical Union, 2000 Florida Ave., N.W. Washington DC 20009 USA, [URL:]Website
Prieto, GA, Parker RL, Vernon FL.  2009.  A Fortran 90 library for multitaper spectrum analysis. Computers & Geosciences. 35:1701-1710.   10.1016/j.cageo.2008.06.007   AbstractWebsite

The spectral analysis of geological and geophysical data has been a fundamental tool in understanding Earth's processes. We present a Fortran 90 library for multitaper spectrum estimation, a state-of-the-art method that has been shown to outperform the standard methods. The library goes beyond power spectrum estimation and extracts for the user more information including confidence intervals, diagnostics for single frequency periodicities, and coherence and transfer functions for multivariate problems. In addition, the sine multitaper method can also be implemented. The library presented here provides the tools needed in multiple fields of the Earth sciences for the analysis of data as evident from various examples. (C) 2008 Elsevier Ltd. All rights reserved.

Prieto, GA, Parker RL, Vernon FL, Shearer PM, Thomson DJ.  2006.  Uncertainties in earthquake source spectrum estimation using empirical Green functions. Earthquakes; radiated energy and the physics of faulting. 170( Abercrombie RE, McGarr A, Kanamori H, Di Toro G, Eds.).:69-74., Washington: American Geophysical Union   10.1029/170gm08   Abstract

We analyze the problem of reliably estimating uncertainties of the earthquake source spectrum and related source parameters using Empirical Green Functions (EGF). We take advantage of the large dataset available from 10 seismic stations at hypocentral distances (10 km < d <50 km) to average spectral ratios of the 2001 M5.1 Anza earthquake and 160 nearby aftershocks. We estimate the uncertainty of the average source spectrum of the M5.1 target earthquake by performing propagation of errors, which, due to the large number of EGFs used, is significantly smaller than that obtained using a single EGF. Our approach provides estimates of both the earthquake source spectrum and its uncertainties, plus confidence intervals on related source parameters such as radiated seismic energy or apparent stress, allowing the assessment of statistical significance. This is of paramount importance when comparing different sized earthquakes and analyzing source scaling of the earthquake rupture process. Our best estimate of radiated energy for the target earthquake is 1.24×1011 Joules with 95% confidence intervals (0.73×1011, 2.28×1011). The estimated apparent stress of 0.33 (0.19, 0.59) MPa is relatively low compared to previous estimates from smaller earthquakes (1MPa) in the same region.

Prieto, GA, Parker RL, Thomson DJ, Vernon FL, Graham RL.  2007.  Reducing the bias of multitaper spectrum estimates. Geophysical Journal International. 171:1269-1281.   10.1111/j.1365-246X.2007.03592.x   AbstractWebsite

The power spectral density of geophysical signals provides information about the processes that generated them. We present a new approach to determine power spectra based on Thomson's multitaper analysis method. Our method reduces the bias due to the curvature of the spectrum close to the frequency of interest. Even while maintaining the same resolution bandwidth, bias is reduced in areas where the power spectrum is significantly quadratic. No additional sidelobe leakage is introduced. In addition, our methodology reliably estimates the derivatives (slope and curvature) of the spectrum. The extra information gleaned from the signal is useful for parameter estimation or to compare different signals.

Prieto, GA, Thomson DJ, Vernon FL, Shearer PM, Parker RL.  2007.  Confidence intervals for earthquake source parameters. Geophysical Journal International. 168:1227-1234.   10.1111/j.1365-246X.2006.03257.x   AbstractWebsite

We develop a method to obtain confidence intervals of earthquake source parameters, such as stress drop, seismic moment and corner frequency, from single station measurements. We use the idea of jackknife variance combined with a multitaper spectrum estimation to obtain the confidence regions. The approximately independent spectral estimates provide an ideal case to perform jackknife analysis. Given the particular properties of the problem to solve for source parameters, including high dynamic range, non-negativity, non-linearity, etc., a log transformation is necessary before performing the jackknife analysis. We use a Student's t distribution after transformation to obtain accurate confidence intervals. Even without the distribution assumption, we can generate typical standard deviation confidence regions. We apply this approach to four earthquakes recorded at 1.5 and 2.9 km depth at Cajon Pass, California. It is necessary to propagate the errors from all unknowns to obtain reliable confidence regions. From the example, it is shown that a 50 per cent error in stress drop is not unrealistic, and even higher errors are expected if velocity structure and location errors are present. An extension to multiple station measurement is discussed.

Prieto, GA, Shearer PM, Vernon FL, Kilb D.  2004.  Earthquake source scaling and self-similarity estimation from stacking P and S spectra. Journal of Geophysical Research-Solid Earth. 109   10.1029/2004jb003084   AbstractWebsite

[1] We study the scaling relationships of source parameters and the self-similarity of earthquake spectra by analyzing a cluster of over 400 small earthquakes (M-L = 0.5 to 3.4) recorded by the Anza seismic network in southern California. We compute P, S, and preevent noise spectra from each seismogram using a multitaper technique and approximate source and receiver terms by iteratively stacking the spectra. To estimate scaling relationships, we average the spectra in size bins based on their relative moment. We correct for attenuation by using the smallest moment bin as an empirical Green's function (EGF) for the stacked spectra in the larger moment bins. The shapes of the log spectra agree within their estimated uncertainties after shifting along the omega(-3) line expected for self-similarity of the source spectra. We also estimate corner frequencies and radiated energy from the relative source spectra using a simple source model. The ratio between radiated seismic energy and seismic moment ( proportional to apparent stress) is nearly constant with increasing moment over the magnitude range of our EGF-corrected data (M-L = 1.8 to 3.4). Corner frequencies vary inversely as the cube root of moment, as expected from the observed self- similarity in the spectra. The ratio between P and S corner frequencies is observed to be 1.6 +/- 0.2. We obtain values for absolute moment and energy by calibrating our results to local magnitudes for these earthquakes. This yields a S to P energy ratio of 9 +/- 1.5 and a value of apparent stress of about 1 MPa.