P-SV multimode summation differential seismograms for layered structures

We present a fast and accurate analytical method for computing differential seismograms with respect to structural model parameters. The method adopts the P-SV-wave multimode summation formalism for laterally homogeneous layered media. The differential seismograms calculated analytically do not suffer from the numerical noise and instability affecting numerical calculations. The frequency range for application of the method spans from regional-scale seismology to seismic engineering. Computationally, the proposed analytical method is equivalent to determining two-mode spectra. In contrast to NS-l (or 2N) mode spectra for a typical 'brute-force' numerical finite difference approach, the method reduces the computations to 2/(N + 1) (if a one-sided perturbation finite difference scheme is used), which corresponds to a 90 per cent saving for 20 (N = 20) layers. The speed and accuracy of the technique make it extremely attractive for structural parameter waveform inversions.