Dynamic Time Warping in Seismic Waveform Inversion

Abstract:

A shape dynamic time warping (shapeDTW) waveform inversion method is applied to explore crustal velocity structure in Tanzania, East Africa. The velocity structure is investigated based on waveform modeling of the Ml 5.9 Lake Rukwa, Tanzania earthquake (18 August 1994) recorded by broadband seismographic stations of the Tanzania Broadband Seismic Experiment. For observed and synthetic waveforms with similar overall shapes but different timing between seismic phases, the dynamic time warping (DTW) method shows high-performance for waveform alignments. Seismic phase arrivals and their shapes are adjusted during the inversion based on travel time differences between aligned data points of observed and synthetic waveforms. This method avoids the inconvenience of manual phase identifications. The cycle-skipping problem is a common issue in waveform inversions derived by minimizing the L-2 norm of amplitude differences when only poor starting models are available. The DTW method can globally correlate data points between waveforms that are significantly separated in time to effectively overcome cycle skipping. As an improved version of DTW, the shapeDTW method takes into account the surrounding data structure characteristics of each data point for producing waveform alignments. This also helps to improve the overfitting problem that the classic DTW method sometimes has. We show that the shapeDTW inversion is a more robust inversion compared to DTW alone and is relatively insensitive to the starting model. The data are modeled over an unusally broadband (0.01 to 1Hz), for regional modeling studies of this type, and show excellent fits to waveform details for a variety of crustal waveguide seismic phases. For local cratonic structure, the calculated velocity models show high-speed features and obvious velocity contrasts between crust and mantle. This inversion approach opens up the possibility of using the full bandwidth of broadband regional waveforms for infering crustal structure and source mechanisms.