Calculation of differential seismograms using analytic partial derivatives-II Regional waveforms

Abstract

Solving seismic waveform inverse problem by the linearization approach requires calculating partial derivatives of seismograms (differential seismograms) with respect to velocity model parameters. Herewe extend our previouswork on calculation of differential teleseismic receiver functions using analytic partial derivatives to regional waveforms. We derived analytic partial derivatives of displacement kernels for both P-SV and SH waves generated by a point source in a multilayered half-space. They are expressed explicitly in terms of the analytic partial derivatives of theHaskell propagator matrix and the source vector.Differential seismograms are then computed using the wavenumber-frequency double integration method.We implemented an efficient algorithm to speed up the computation by storing intermediate matrix products. The total computation time for computing differential seismograms with respect to all the layers is only about one extra forward-problem computation time. Numerical tests show that our derivations are correct and the implementation is efficient. Synthetic and real data waveform inversions using more accurate analytic differential seismograms perform better than using finite-difference differential seismograms.