Simultaneous P‐ and S‐wave seismic traveltime tomography using physics‐informed neural networks

ABSTRACT Seismic tomography has long been an effective tool for constructing reliable subsurface structures. However, simultaneous inversion of P‐ and S‐wave velocities presents a significant challenge for conventional seismic tomography methods, which depend on numerical algorithms to calculate traveltimes. A physics‐informed neural network—based seismic tomography method (PINNtomo) has been proposed to solve the eikonal equation and construct the velocity model. We propose extending PINNtomo to perform multiparameter inversion of P‐ and S‐wave velocities jointly, which we refer to as PINNPStomo. In PINNPStomo, we employ two neural networks: one for the P‐ and S‐wave traveltimes and another for the P‐ and S‐wave velocities. By optimizing the misfits of P‐ and S‐wave first‐arrival traveltimes calculated from the eikonal equations, we can obtain the predicted P‐ and S‐wave velocities that determine these traveltimes. Recognizing that the original PINNtomo utilizes a multiplicative factored eikonal equation, which depends on background traveltimes corresponding to a homogeneous velocity at the source location, we propose to use an effective‐slowness‐based factored eikonal equation for PINNPStomo to eliminate this dependency. The proposed PINNPStomo, incorporating the effective‐slowness‐based factored eikonal equation, demonstrates superior convergence speed and multiparameter inversion accuracy. We validate these improvements using two‐dimensional Marmousi, two‐dimensional Overthrust and three‐dimensional foothill elastic velocity models across three different seismic data acquisition geometries.