## Nonlinear hypocentre determination

**Petr Bulant** **&**
**Ludek Klimes**
### Summary

We consider the robust nonlinear approach to hypocentre
determination proposed by Tarantola and Valette, consisting
in direct evaluation of the nonnormalized 3-D marginal
a posteriori density function which describes the relative
probability of the seismic hypocentre. The nonnormalized 3-D
marginal a posteriori density function is discretized at
the gridpoints of a sufficiently dense 3-D spatial grid of points.
This approach takes into account the inaccuracy of the velocity model
and the corresponding influence on the hypocentre determination,
estimates the uncertainty of the hypocentre position, and allows for
testing the model covariance function describing the uncertainty of
the velocity model. The model covariance function is projected onto
the uncertainty of the hypocentral position through the geometrical
covariances of theoretical travel times calculated in the velocity
model.

For the sake of simplicity and rapid numerical implementation,
we consider just the diagonal elements of the geometrical travel-time
covariance matrix in this paper. We discuss the distortion of
the nonnormalized 3-D marginal a posteriori density function caused
by this simplification, and present a numerical example.

### Keywords

Hypocentre determination, velocity model, accuracy of the velocity
model, model covariance function, geometrical travel-time covariance
matrix, marginal a posteriori density function of hypocentral
coordinates, arrival-time residuals, arrival-time misfit.

### Whole paper

The paper is available in
PDF (2088 kB).

*Seismic Waves in Complex 3-D Structures*, **25** (2015), 17-36
(ISSN 2336-3827, online at http://sw3d.cz).