Timereversal method and crosscorrelation techniques by normal mode theory: a threepoint problem
 Research areas:
 Year:
 2012
 Authors:

 J. P. Montagner
 C. Larmat
 Yann Capdeville
 M. Fink
 H. Phung
 B. Romanowicz
 E. Clevede
 H. Kawakatsu
 Journal:
 GEOPHYSICAL JOURNAL INTERNATIONAL
 Volume:
 191
 Number:
 2
 Pages:
 637652
 Month:
 November
 ISSN:
 0956540X
 BibTex:
 Abstract:
 Since its beginning in acoustics, the TimeReversal method (hereafter referred as TR) has been explored by different studies to locate and characterize seismic sources in elastic media. But few authors have proposed an analytical analysis of the method, especially in the case of an elastic medium and for a finite body such as the Earth. In this paper, we use a normal mode approach (for general 3D case and degenerate modes in 1D reference model) to investigate the convergence properties of the TR method. We first investigate a threepoint problem, with two fixed points which are the source and the receiver and a third one corresponding to a changing observation point. We extend the problem of a single channel TR experiment to a multiple channel and multiple station TR experiment. We show as well how this problem relates to the retrieval of Greens function with a multiple source crosscorrelation and also the differences between TR method and crosscorrelation techniques. Since most of the noise sources are located close to the surface of the Earth, we show that the time derivative of the crosscorrelation of longperiod seismograms with multiple sources at the surface is different from the Greens function. Next, we show the importance of a correct surfacearea weighting of the signal resent by the stations according to a Voronoi tessellation of the Earth surface. We use arguments based on the stationary phase approximation to argue that phaseinformation is more important than amplitude information for getting a good focusing in TR experiment. Finally, by using linear relationships between the timereversed displacement (resp. strain wavefields) and the components of a vector force source (resp. a moment tensor source), we show how to retrieve force (or moment tensor components) of any long period tectonic or environmental sources by time reversal.