Geophysical data analysis using binary sample functions

Physics – Geophysics

Scientific paper

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Binary Data, Computerized Simulation, Data Processing, Geophysics, Harmonic Functions, Walsh Function, Chebyshev Approximation, Fourier Transformation, Geoids, Run Time (Computers), Spherical Harmonics

Scientific paper

Binary sample functions are shown to allow accurate modeling of geophysical data at a level of detail equivalent to degree 125 in spherical harmonics while using only 1 x 10 to the -6th of the computer time required for the spherical harmonics. The binary sample functions may be transformed by orthogonal transformation to an equivalent set of Walsh functions, whose property of sequency permits the use of these functions for spectral analysis. Two numerical examples are considered: a comparison of the efficiency and accuracy of binary sample functions and spherical harmonic sample functions fitted to a local geoid height surface, and an illustration of the harmonic analysis properties of the Walsh functions for a global distribution of geoid heights.

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