A new approach for traveltime tomography and migration without ray tracing

We present a new method for traveltime tomography. In this method, the traveltime between source and receiver is described by an analytical function, which consists of a series expansion of geometrical coordinates of the source and receiver locations. As the traveltime is derived from the eikonal equation, the analytical function must also satisfy the eikonal equation. This condition imposes a strong constraint on its uniqueness. The coefficients of the series expansion are estimated by minimizing the misfit between the observed and the analytical time function in a least-square sense. Once the coefficients of the series expansion are known, the eikonal equation, which also turns out to be in the form of a series expansion, provides the velocity in the medium. Thus there are two analytical functions, one defining the traveltime and the other defining the slowness, and they can be used for prestack depth migration and velocity model definition. The method can easily be extended to incorporate reflection data and has potential for solving 3-dimensional seismic reflection and global seismology inverse problems.