Shape Dynamic Time Warping for Seismic Waveform Inversion

Abstract

ABSTRACT We illustrate shape dynamic time warping (ShapeDTW) for 1D structure waveform inversion with examples from Tanzania, East Africa, and Northeastern Oklahoma. Seismograms of the Mw 5.9 Lake Rukwa, Tanzania, earthquake (18 August 1994) recorded by regional broadband seismographic stations of the Tanzania Broadband Seismic Experiment are used to demonstrate the method. We also test the inversion through solving for 1D crustal velocity structure of the Cherokee Platform in Oklahoma using seismograms of the 2011 Mw 5.7 Prague, Oklahoma, earthquake recorded by the EarthScope Transportable Array. Dynamic time warping (DTW) bypasses the time expense required for manual identification of seismic phases and shows potential for linking discrete seismic phases between two similar waveforms. ShapeDTW improves inversion performance by characterizing the character of the time series near each amplitude point. Applying Sakoe-Chiba band limits to ShapeDTW and an additional amplitude constraint improves the overfitting problem that occurs with the classic DTW method. We apply ShapeDTW to estimate optimal time shifts between observed and synthetic waveforms with time shifts reduced through inversion. The crustal velocity model of Tanzania found using ShapeDTW is close to that found using “phase time inversion” of numerous regional seismic phases observed in the three-component waveforms in a previous study but avoids the necessity of isolating and interpreting different seismic phases in the waveforms. Reducing the ShapeDTW functional misfits can overcome the cycle-skipping problem that often occurs with direct comparison of amplitudes in waveform inversion. This method may be useful in generating starting models for other 1D and 3D inversion methods.