Multichannel Deconvolution for Earthquake Apparent Source Time Functions

Abstract

Abstract Previous studies of earthquake apparent source time functions (ASTFs) removed propagation effects through seismogram deconvolution with a smaller earthquake known as an empirical Green’s function (EGF). We develop a multichannel deconvolution (MCD) algorithm for recovering ASTFs that does not require an EGF, but instead the availability of two or more earthquakes that share a common Green’s function. Under this condition, ASTFs satisfy U i * S j − U j * S i =0, in which U i and S i are the seismogram and ASTF for a given earthquake. This system can be augmented with a scaling equation and written as Ax = b , in which matrix A comprises the seismograms in a block‐Toeplitz structure and x contains the target ASTFs. We minimize an objective function for this linear system with a Newton‐projection algorithm that honors positivity, causality, and duration constraints. If the earthquakes have a suitable range in magnitude, EGF deconvolution may be used to estimate differences in the duration of the events and to obtain a starting model for the larger ASTF(s). We demonstrate the effectiveness of MCD using synthetic tests and apply it to seven M w ∼5 earthquakes from the Kamaishi sequence, Japan, related to the 2011 Tohoku‐Oki M w 9 event. We demonstrate that MCD is an effective way to recover earthquake ASTFs and that the details of rupture revealed by MCD ASTFs will be useful in furthering our understanding of the earthquake source. Electronic Supplement: Figures of seismograms and multichannel deconvolution (MCD) apparent source time functions (ASTFs) from the Kamaishi earthquake sequence.