# Acoustic wave-equation-based earthquake location

### Abstract

We present a novel earthquake location method using acoustic wave-equation-based traveltime inversion. The linear relationship between the location perturbation $(δt_0, δx_s)$ and the resulting traveltime residual δt of a particular seismic phase, represented by the traveltime sensitivity kernel $K(t_0, x_s)$ with respect to the earthquake location $(t_0, x_s)$, is theoretically derived based on the adjoint method. Traveltime sensitivity kernel $K(t_0, x_s)$ is formulated as a convolution between the forward and adjoint wavefields, which are calculated by numerically solving two acoustic wave equations. The advantage of this newly derived traveltime kernel is that it not only takes into account the earthquake–receiver geometry but also accurately honours the complexity of the velocity model. The earthquake location is obtained by solving a regularized least-squares problem. In 3-D realistic applications, it is computationally expensive to conduct full wave simulations. Therefore, we propose a 2.5-D approach which assumes the forward and adjoint wave simulations within a 2-D vertical plane passing through the earthquake and receiver. Various synthetic examples show the accuracy of this acoustic wave-equation-based earthquake location method. The accuracy and efficiency of the 2.5-D approach for 3-D earthquake location are further verified by its application to the 2004 Big Bear earthquake in Southern California.

Type
Publication
Geophysical Journal International