Synthetic seismograms are a computer-generated aid in the search for hydrocarbons. Heretofore the solution has been done by z-transforms. This thesis presents a solution based on the method of finite differences. The resulting algorithm is fast and compact. The method is applied to three variations of the problem, all three are reduced to the same approximating equation, which is shown to be optimal, in that grid refinement does not change it. Two types of algorithms are derived from the equation. The number of obvious multiplications, additions and subtractions of each is analyzed. Critical section of each requires one multiplication, two additions and two subtractions. Four sample synthetic seismograms are shown. Implementation of the new algorithm runs twice as fast as previous computer program.

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