Joint tomographic inversion of first‐arrival and reflection traveltimes for recovering 2‐D seismic velocity structure with an irregular free surface

Irregular surface flattening, which is based on a boundary conforming grid and the transformation between curvilinear and Cartesian coordinate systems, is a mathematical method that can elegantly handle irregular surfaces, but has been limited to obtaining first arrivals only. By combining a multistage scheme with the fast-sweeping method (FSM, the method to obtain first-arrival traveltime in curvilinear coordinates), the reflected waves from a crustal interface can be traced in a topographic model, in which the reflected wave-front is obtained by reinitializing traveltimes in the interface for upwind branches. A local triangulation is applied to make a connection between velocity and interface nodes. Then a joint inversion of first-arrival and reflection traveltimes for imaging seismic velocity structures in complex terrains is presented. Numerical examples all perform well with different seismic velocity models. The increasing topographic complexity and even use of a high curvature reflector in these models demonstrate the reliability, accuracy and robustness of the new working scheme; checkerboard testing illustrates the method’s high resolution. Noise tolerance testing indicates the method’s ability to yield practical traveltime tomography. Further development of the multistage scheme will allow other later arrivals to be traced and used in the traveltime inversion.