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Book Chapter
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.

Journal Article
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.

Denolle, MA, Fan WY, Shearer PM.  2015.  Dynamics of the 2015 M7.8 Nepal earthquake. Geophysical Research Letters. 42:7467-7475.   10.1002/2015gl065336   AbstractWebsite

The 2015 M7.8 Nepal earthquake ruptured part of the Main Himalayan Thrust beneath Kathmandu. To study the dynamics of this event, we compute P wave spectra of the main shock and of two large aftershocks to estimate stress drop and radiated energy. We find that surface reflections (depth phases) of these shallow earthquakes produce interference that severely biases spectral measurements unless corrections are applied. Measures of earthquake dynamics for the main shock are within the range of estimates from global and regional earthquakes. We explore the azimuthal and temporal variations of radiated energy and highlight unique aspects of the M7.8 rupture. The beginning of the earthquake likely experienced a dynamic weakening mechanism immediately followed by an abrupt change in fault geometry. Correlation of backprojection results with frequency-dependent variations in the radiated energy rate and with the suggested geometry of the Main Himalayan Thrust yields new constraints on dynamic ruptures through geometrical barriers.

Allmann, BP, Shearer PM.  2007.  A high-frequency secondary event during the 2004 Parkfield earthquake. Science. 318:1279-1283.   10.1126/science.1146537   AbstractWebsite

By using seismic records of the 2004 magnitude 6.0 Parkfield earthquake, we identified a burst of high-frequency seismic radiation that occurred about 13 kilometers northwest of the hypocenter and 5 seconds after rupture initiation. We imaged this event in three dimensions by using a waveform back-projection method, as well as by timing distinct arrivals visible on many of the seismograms. The high-frequency event is located near the south edge of a large slip patch seen in most seismic and geodetic inversions, indicating that slip may have grown abruptly at this point. The time history obtained from full-waveform back projection suggests a rupture velocity of 2.5 kilometers per second. Energy estimates for the subevent, together with long-period slip inversions, indicate a lower average stress drop for the northern part of the Parkfield earthquake compared with that for the region near its hypocenter, which is in agreement with stress-drop estimates obtained from small-magnitude aftershocks.

Traer, J, Gerstoft P, Bromirski PD, Shearer PM.  2012.  Microseisms and hum from ocean surface gravity waves. Journal of Geophysical Research-Solid Earth. 117   10.1029/2012jb009550   AbstractWebsite

Ocean waves incident on coasts generate seismic surface waves in three frequency bands via three pathways: direct pressure on the seafloor (primary microseisms, PM), standing waves from interaction of incident and reflected waves (double-frequency microseisms, DF), and swell-transformed infragravity wave interactions (the Earth's seismic hum). Beamforming of USArray seismic data shows that the source azimuths of the generation regions of hum, PM and DF microseisms vary seasonally, consistent with hemispheric storm patterns. The correlation of beam power with wave height over all azimuths is highest in near-coastal waters. Seismic signals generated by waves from Hurricane Irene and from a storm in the Southern Ocean have good spatial and temporal correlation with nearshore wave height and peak period for all three wave-induced seismic signals, suggesting that ocean waves in shallow water commonly excite hum (via infragravity waves), PM, and DF microseisms concurrently.

Kaneko, Y, Shearer PM.  2014.  Seismic source spectra and estimated stress drop derived from cohesive-zone models of circular subshear rupture. Geophysical Journal International. 197:1002-1015.   10.1093/gji/ggu030   AbstractWebsite

Earthquake stress drops are often estimated from far-field body wave spectra using measurements of seismic moment, corner frequency and a specific theoretical model of rupture behaviour. The most widely used model is from Madariaga in 1976, who performed finite-difference calculations for a singular crack radially expanding at a constant speed and showed that (f) over bar (c) = k beta/a, where (f) over bar (c) is spherically averaged corner frequency, beta is the shear wave speed, a is the radius of the circular source and k = 0.32 and 0.21 for P and S waves, respectively, assuming the rupture speed V-r = 0.9 beta. Since stress in the Madariaga model is singular at the rupture front, the finite mesh size and smoothing procedures may have affected the resulting corner frequencies. Here, we investigate the behaviour of source spectra derived from dynamic models of a radially expanding rupture on a circular fault with a cohesive zone that prevents a stress singularity at the rupture front. We find that in the small-scale yielding limit where the cohesive-zone size becomes much smaller than the source dimension, P- and S-wave corner frequencies of far-field body wave spectra are systematically larger than those predicted by the Madariaga model. In particular, the model with rupture speed V-r = 0.9 beta shows that k = 0.38 for P waves and k = 0.26 for S waves, which are 19 and 24 per cent larger, respectively, than those of Madariaga. Thus for these ruptures, the application of the Madariaga model overestimates stress drops by a factor of 1.7. In addition, the large dependence of corner frequency on take-off angle relative to the source suggests that measurements from a small number of seismic stations are unlikely to produce unbiased estimates of spherically averaged corner frequency.