Seismic Trace Matching to Well Logs in a Weakly Non-Linear Earth

One of the well established techniques for matching seismic data to well logs is to calculate and apply simple matching filters. When following this approach, one minimizes the residual error between the filtered trace and a nearby reflectivity well log. This is done in the least squares sense by adjusting coefficients of the filter.<br><br>That is, minimize Formula 1,<br><br>where<br><br> F is the filter<br> S is the seismic trace <br> R is the reflectivity log<br> L and M define the span of the filter<br><br>Setting partial derivatives of this functional to zero, leads to an easily solved set of linear equations. After the filter is determined, it will typically be applied to many traces in the vicinity of the well.<br><br>A key physical assumption is that stress is strictly proportional to strain as seismic waves propagate through the earth.<br><br>Proposed in this paper is a method to compensate for non-linear effects and attain a much better match with well logs.<br>