Open AccessImaging fault slip using teleseismic waveforms: analysis of a typical incomplete tomography problem
Author(s) -
Menke William
Publication year - 1985
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1985.tb01358.x
Subject(s) - slip (aerodynamics) , tomography , geology , projection (relational algebra) , geophysical imaging , radon transform , seismology , inverse theory , geodesy , geometry , algorithm , mathematics , mathematical analysis , optics , physics , oceanography , deformation (meteorology) , thermodynamics
Summary Several important geophysical imaging problems can be cast in the form of the classic tomography problem, in which a function of two variables is reconstructed from its projection along a set of straight lines. However, geophysical imaging problems tend to be incomplete; some of the straight lines projection paths are missing from the data. A typical example is the problem of imaging the slip rate as a function of position and time along a long, thin fault plane. The far field seismic pulse shape is a projection of the fault's slip rate function. However, a complete suite of far field observations does not span the complete set of possible projection lines. Consequently, the exact slip rate function cannot be recovered from the data. At best, only a filtered version of it can be reconstructed. This filter is not completely determined by the mathematics of the problem, and can therefore be optimized to yield images of the slip rate that have good resolution.