Inversion of a normally incident reflection seismogram by the Gopinath–Sondhi integral equation |
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| Authors: | A K M Sarwar Albert J Rudman |
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| Institution: | Department of Geology, Indiana University, Bloomington, Indiana 47405, USA |
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| Abstract: | Summary. The one-dimensional acoustic wave equation has been transformed to two coupled first-order equations whose inverse solution is obtained through application of the Gopinath and Sondhi integral equation. A scattering solution of the Schrödinger wave equation for an explosive source leads us to express the kernel of the Gopinath–Sondhi integral equation in terms of a seismic reflection response. A numerical solution of the integral equation obtained by a trapezoidal rule yields a continuous impedance profile whose derivative has step-like discontinuities. The method is illustrated with computer model studies. |
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