Improving modelling and inversion in refraction seismics with a first-order Eikonal solver

A first-order Eikonal solver is applied to modelling and inversion in refraction seismics. The method calculates the traveltime of the fastest wave at any point of a regular grid, including head waves as used in refraction. The efficiency, robustness and flexibility of the method give a very powerful modelling tool to find both traveltimes and raypaths. Comparisons with finite-difference data show the validity of the results. Any arbitrarily complex model can be studied, including the exact topography of the surface, thus avoiding static corrections. Later arrivals are also obtained by applying high-slowness masks over the high-velocity zones. Such an efficient modelling tool may be used interactively to invert for the model, but a better method is to apply the refractor-imaging principle of Hagedoorn to obtain the refractors from the picked traveltime curves. The application of this principle has already been tried successfully by previous authors, but they used a less well-adapted Eikonal solver. Some of their traveltimes were not correct in the presence of strong velocity variations, and the refractor-imaging principle was restricted to receiver lines along a plane surface. With the first-order Eikonal solver chosen, any topography of the receiving surface can be considered and there is no restriction on the velocity contrast. Based on synthetic examples, the Hagedoorn principle appears to be robust even in the case of first arrivals associated with waves diving under the refractor. The velocities below the refractor can also be easily estimated, parallel to the imaging process. In this way, the model can be built up successively layer by layer, the refractor-imaging and velocity-mapping processes being performed for each identified refractor at a time. The inverted model could then be used in tomographic inversions because the calculated traveltimes are very close to the observed traveltimes and the raypaths are available.