Abstract

In the 1970s I was employed by GeoQuest International. We formed a Land Wavelet Project to shed some light on the seismic wavelet in land exploration. This project was supported by 35 oil companies. I was the technical leader. Among the various avenues of investigation, I proposed using the numerical Laplace transform in an attempt to establish parameters of the seismic wavelet. I had become familiar with this transform while in graduate school. It was one of the electrical engineer's most powerful tools for designing linear networks for filtering. It was a precursor of this technique that allowed Oliver Heaviside, an English engineer, to determine that the transatlantic cable would fail because of its inability to pass the higher frequencies of key clicks originally proposed for use on this cable. The Laplace transform was not well known in geophysical research circles, and was thus a little far out for the Land Wavelet group. They had all digested the work of the GAG group at MIT who had introduced the concepts of sampled data and the z-transform and its use in polynomial form to do discrete convolution, which was the process of intense interest. It was at this time (the 1960s) that the mathematical model of the seismic trace was being formulated. At that time I was employed at Phillips Petroleum Company in geophysical research and we thought of working with the z-transform, but factoring these long polynomials was considered a virtual impossibility.

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