Earthquake Depth Estimation Using the F Trace and Associated Probability

SUMMARY Estimating reliable depths for shallow seismic sources is important in both seismo‐tectonic studies and in seismic discrimination studies. Surface wave excitation is sensitive to source depth, especially at intermediate and short‐periods, owing to the approximate exponential decay of surface wave displacements with depth. A new method is presented here to retrieve earthquake source parameters from regional and teleseismic intermediate period (100–15 s) fundamental‐mode surface wave recordings. This method makes use of advances in mapping global dispersion to allow higher frequency surface wave recordings at regional and teleseismic distances to be used with more confidence than in previous studies and hence improve the resolution of depth estimates. Synthetic amplitude spectra are generated using surface wave theory combined with a great circle path approximation, and a grid of double–couple sources are compared with the data. Source parameters producing the best‐fitting amplitude spectra are identified by minimizing the least‐squares misfit in logarithmic amplitude space. The F‐test is used to search the solution space for statistically acceptable parameters and the ranges of these variables are used to place constraints on the best‐fitting source. Estimates of focal mechanism, depth and scalar seismic moment are determined for 20 small to moderate sized (4.3 ≤Mw≤ 6.4) earthquakes. These earthquakes are situated across a wide range of geographic and tectonic locations and describe a range of faulting styles over the depth range 4–29 km. For the larger earthquakes, comparisons with other studies are favourable, however existing source determination procedures, such as the CMT technique, cannot be performed for the smaller events. By reducing the magnitude threshold at which robust source parameters can be determined, the accuracy, especially at shallow depths, of seismo‐tectonic studies, seismic hazard assessments, and seismic discrimination investigations can be improved by the application of this methodology.

Section: Resultsmentioning

confidence: 99%

Shallow seismic source parameter determination using intermediate-period surface wave amplitude spectra

Fox

Selby²,

Heyburn³

et al. 2012

“…To test these predictions, I18DK array data were analysed using an F ‐Statistic detection scheme (e.g. Blandford 1974; Heyburn & Bowers 2008). Both sets of data were analysed in broad frequency bands associated with the highest signal‐to‐noise ratios (Kasatochi, 0.03–0.3 Hz; STS‐131, 0.06–1 Hz).…”

Section: Application To I18dk Greenlandmentioning

confidence: 99%

“…11, with the signals clearly identified as periods of increased F ‐statistic. For both signals an F ‐Statistic above approximately 20 can be considered significant to identify coherent signal passing across the array with a signal‐to‐noise ratio of 4 with ≥95 per cent confidence (Heyburn & Bowers 2008).…”

Section: Application To I18dk Greenlandmentioning

confidence: 99%

Effect of interarray elevation differences on infrasound beamforming

Edwards¹,

Green

2012

SUMMARY The International Monitoring System infrasound network will, upon completion, contain 60 microbarometer arrays with apertures of between 1 and 4 km. These arrays are located within a variety of terrains, leading to large ratios of interelement elevation differences to array aperture for those arrays situated in areas of significant topography. Systematic errors in beamforming estimates caused by neglecting the vertical extent of the arrays, are quantified for both signal backazimuth and apparent velocity. Of the 43 arrays certified as of 2011 January, I14CL on Juan Fernandez Island has the greatest topography across an array, with a least‐squares fitted plane through the array elements having an 8.1° slope from the horizontal (compared to a network mean of 1.6°). Beamforming errors (both backazimuth and apparent velocity) are a function of the arrival azimuth and become increasingly large for steeply inclined arrivals, such that systematic errors will be significantly larger for signals returned from the thermosphere compared to those from the stratosphere. At several arrays, azimuthal errors due to array topography are comparable in magnitude to deviations often associated with atmospheric propagation. These findings are illustrated using signals recorded in Greenland at I18DK, where differences between results processed using both full 3‐D array geometry and the 2‐D (topography neglected) approximation exhibit good correspondence to theoretical predictions.

“…For P seismograms recorded at seismometer arrays at teleseismic distances, the F statistic and its associated probability theory can be a useful tool for identifying depth phases and hence estimating earthquake depth (Heyburn & Bowers 2008). For an array of N seismometers, the F statistic is the time‐averaged power on the beam divided by N ‐times the time‐averaged variance of the individual channels about the beam (Blandford 1974).…”

Section: Depth Estimationmentioning

confidence: 99%

“…To do this, two recently developed complementary methods of earthquake depth estimation are applied to the observed data. The first method uses the F statistic and its associated probability theory to help identify P and the depth phases pP and sP on teleseismic body‐wave seismograms (Heyburn & Bowers 2008), and the second method involves modelling regional surface wave amplitude spectra (Fox 2007). The study then focuses on finding a focal mechanism that is consistent with both data sets.…”

Section: Introductionmentioning

confidence: 99%

Multi-objective analysis of body and surface waves from the Market Rasen (UK) earthquake

Heyburn¹,

Fox²

2010

Market Rasen (UK) earthquake (m b 4.5) is used to show how earthquake source parameters can be estimated using a multi-objective optimization approach to the joint inversion of teleseismic body wave and regional surface wave observations. To estimate the source depth, short-period teleseismic seismograms are interpreted in terms of P and the depth phases pP and sP using the F-statistic and its associated probability theory. Results of this analysis are inconclusive as two possible source depths are identified. To identify our preferred depth, a method of estimating source depth and mechanism by modelling surface wave amplitude spectra is applied to data recorded at regional distances. A source depth of 22 km is found to be consistent with the observed body and surface waves. Upper and lower amplitude bounds and polarities are then placed on the phases interpreted as P, pP and sP for a source depth of 22 km. The Gaussian relative amplitude method is used to calculate a likelihood for all possible orientations of the double-couple source. A multi-objective optimization approach can then used to compare these likelihoods with calculated misfits between observed and synthetic surface wave amplitude spectra for all orientations of the double-couple source. Our preferred focal mechanism (φ s = 205 • , δ = 50 • and λ = 15 • ) is found by normalizing and summing both misfits to find the focal mechanism with the lowest combined misfit. Synthetic body wave seismograms, surface wave amplitude spectra and seismograms are in good agreement with the observed data for our preferred focal mechanism and depth.