Derivatives of travel time curves in a horizontally layered medium

1983 ◽  
Vol 27 (3) ◽  
pp. 233-240
Author(s):  
Jaromír Janský ◽  
Oldřich Novotný ◽  
J. Vaněk
Keyword(s):  
Travel Time ◽  
Layered Medium ◽  
Derivatives Of

Nonlinear earthquake location: Theory and examples

1985 ◽  
Vol 75 (3) ◽  
pp. 779-790
Author(s):  
Clifford H. Thurber
Keyword(s):  
Travel Time ◽  
Location Theory ◽  
Nonlinear Behavior ◽  
Second Order ◽  
Earthquake Location ◽  
Source Position ◽  
Realistic Assessment ◽  
Location Algorithm ◽  
Expected Benefits ◽  
Derivatives Of

Abstract A fundamental modification to Geiger's method of earthquake location for local earthquakes is described which incorporates nonlinear behavior of travel time as a function of source position. The use of Newton's method rather than the usual Gauss-Newton method allows the inclusion of second-order partial derivatives of travel time with respect to source coordinates in the location algorithm. These second-order derivatives can be calculated quite easily for half-space and layered crustal models. Expected benefits are improved convergence and stability, as demonstrated in a series of examples, and more realistic assessment of solution uncertainty.

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