A combined kinematic-dynamic method for fast computations of the first-arriving waveforms

Michal Kvasnicka & Jiri Zahradnik


Ray and grid travel time methods are powerful for kinematic modelling, i.e. for calculations of the arrival times and rays of seismic body waves. Elastic finite-difference (FD) methods belong to the most powerful tools for computing complete waveforms in complex subsurface structures. However, the FD methods are rather time-consuming, and the physical interpretation of the FD results is difficult, in general.

These facts call for a joint application of the two approaches. The intention of this paper is to show how the two methods, in a combination, improve our understanding of the wave propagation processes in complex subsurface structures.

The most important part of the paper is an extensive investigation of a method allowing an efficient (accurate and fast) calculation of the first-arrival waveforms. The idea is very primitive, and consists of eliminating the unnecessary FD calculations of "zeros" before the true physical arrival of a wave. Such an approach has been already mentioned as "expanding grid" by Boore (1972), and most recently re-introduced in seismology under the name of "speed-up" by Vidale (1988). Although the method is not new, a detailed discussion of its practical aspects is lacking in the literature. Therefore, the main purpose of this paper is to summarize our experience with coding and testing the speed-up method. We describe how our previously developed codes for the ray and FD modelling are technically linked together, and focus on the following issues: free parameters of the speed-up method (the time window around the first arrival), accuracy of the resulting waveforms, and efficiency of the method. By the efficiency we mean the computer-time saving measured with respect to the full FD calculation. The performance of the method is illustrated on model PICROCOL (1994), extended in this paper from the acoustic to elastic case.

Related: Examples.

Whole paper

The paper is available in PDF format (10 635 kB !!!).

In: Seismic Waves in Complex 3-D Structures, Report 4, pp. 251-286, Dep. Geophys., Charles Univ., Prague, 1996.
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