The inversion of first‐arrival times of refracted waves in media with laterally varying parameters can be performed using the refraction tomography technique. Tomographic inversion implemented as a linearized, constrained, least‐squares, iterative scheme requires some a priori information on either refractor depth or velocity above the refractor; however, such information may be unavailable. On the other hand, in many cases a reasonable estimate of the average velocity distribution above the refractor can be obtained by a nontomographic technique such as the generalized reciprocal method (GRM). I propose a combined approach to the inversion problem that uses the advantages of both the refraction tomography and GRM techniques and which does not require additional information not contained in first arrival times. The approach is based upon two assumptions (which prove to be true in most situations). The first is that a reasonable local estimate of refractor velocity can be obtained by tomographic inversion independently of other model parameters, and the second is that the derivative of the velocity analysis function as defined by the GRM, gives a good local approximation of the refractor slowness. The proposed combined inversion scheme can be described as a three‐step procedure. In the first step, the laterally varying refractor velocity is estimated by tomographic inversion. In the second step, local estimation of laterally varying average velocity above the refractor is performed by the GRM on the basis of the previously estimated refractor velocity. In the third step, the estimated values of the average velocity are used as the corresponding constrained initial parameters for tomographic inversion.
Sensor-based localization of epidemic sources on human mobility networks
