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Bulletin of the Seismological Society of America; October 1989; v. 79; no. 5; p. 1618-1628
© 1989 Seismological Society of America
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Seismic calibration using the simplex algorithm

LEE STECK and WILLIAM A. PROTHERO, JR.

DEPARTMENT OF GEOLOGICAL SCIENCES UNIVERSITY OF CALIFORNIA, SANTA BARBARA, SANTA BARBARA, CALIFORNIA 93106

Abstract

We have modified the software of Sauter and Dorman (1986) to produce a robust and flexible calibration program that works in the frequency domain for longer and noisy calibration signals, as well as in the time domain when shorter, high signal-to-noise calibration signals may be used. The most important improvement was to replace the least squares fitting of the complex polynomial representation of the response function with the simplex fitting of the pole-zero representation of the response function. The simplex algorithm always converges to a minimum, regardless of starting model, and by fitting the poles and zeroes directly, we minimize the degrees of freedom of the solution. Typical VAX 11/750 CPU requirements are on the order of 2 to 3 minutes for both codes, with average errors less than 1 per cent in amplitude and 1° in phase.




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