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

Abstract

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.

Drainage of a deep magma reservoir near Mayotte inferred from seismicity and deformation

“…Important epistemic uncertainties may arise from the assumed local/regional velocity models and the method used for depth estimation. Thus combining different methods and independent datasets is a good strategy to reduce such epistemic uncertainties [18][19][20] .…”

European–Mediterranean Regional Centroid Moment Tensor catalog: Solutions for 2005–2008

“…These two events occurred in areas where seismic activity reaching these magnitudes is rare. The first, the Market Rasen (UK) earthquake, has been the subject of a detailed study (Heyburn and Fox, 2010) to determine source parameters using body and regional surface waves at higher frequencies than those employed in our analysis. The source parameters determined in the two studies are very similar for the location, depth, magnitude and the focal mechanism (Heyburn and Fox, 2010).…”

Optimization Using Genetic Algorithms – Methodology with Examples from Seismic Waveform Inversion

“…This forward modeling operator varies depending upon the flavor of the inversion method. For post-stack or pre-stack amplitude-variation-with-angle (AVA)/elasticimpedance inversion [9,[20][21][22][23][24], gm ðÞ is the convolutional modeling at normal or nonnormal incidence angles [25]. For wave-equation based inversion such as the full waveform inversion (FWI) [26][27][28][29][30][31][32][33][34][35][36][37][38][39], gm ðÞ is the numerical solution of the elastic or acoustic wave equation using finite-difference or finite-element modeling.…”

“…3). Such multi-parameter and multi-objective optimizations have been previously used in geophysics to solve a variety of problems such as estimating anisotropic properties for mantle lithosphere from the splitting parameters of teleseismic S-waves and P-wave residual spheres [18], wave equation migration velocity inversion [19], estimating earthquake focal mechanisms [20], inverting multicomponent seismic and electromagnetic (EM) data [10-12, 14, 17], etc.…”