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

Abstract

SUMMARY The 2008 February 27 Market Rasen (UK) earthquake (mb 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 (φs= 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.