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EARTHQUAKE LOCATION PROBLEM-SECOND ORDER DERIVATIVES FOR MULTILAYER EARTH AND THEIR IMPLICATIONS

Ashwani Kumar and P.N. Agrawal

Paper No.: 273

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Vol.: 26

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No.: 2

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September, 1989

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pp. 1-48

Abstract

 

Obtainin accurate earthquake hypocenter locations has received considerable attention. Although the problem is non-linear yet the existing algorithms and computer programs primarily make use of linearisation. It is only recently that in some studies the nonlinearity has been Incorporated in the computational schemes with- a view to make improvements in the locations. A study incorporating the second order partial derivatives for half space and a layer over half spece have been reported and in the present study the results have been extended for a multilayer one dimensional earth model. The existing formulation of the nonlinear problem alongwith the details of Geiger method has been included for ready reference as the required background for these derivations.” The expressions developed for second order partial derivatives have been incorporated in an existing program of locations using Geiger metnod. The results from both linear and nonlinear techniques for test earthquake data, synthetic earthquake data and 3 to 6 station real data have been obtained and compared. Numerous aspects require further examination before any generalised conclusions can be drawn. It has, however, been demonstrated that the incorporation of nonlinear terms in computations of hypocenter locations is easily feasible. Based on the results obtained and discussed in the paper, it is concluded that nonlinear inverse seems to provide better control in the estimation of focal depths, improves convergence parti- cularly for events falling outside the array and provides better information of solution statistics.
Keywords: Hypocenter, Nonlinear Inverse, Travel time derivatives, Computer Program, Focal depth, Convergence.

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