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Determination of seismograph constants from the calibration curve

UNIVERSIDAD NACIONAL DE LA PLATA OBSERVATORIO ASTRONOMICO, 1900, LA PLATA, Argentina

Abstract

The explicit expression of the long-period WWSSN calibration curve can be obtained solving the differential equations of the seismograph system in terms of e^w and identifying the characteristic equation to a product of polynomials of the second degree. The coefficients of these polynomials are the equivalent constants. These and a scale factor can be obtained from the calibration curve. The frequency response of the seismograph system is fully determined by these elements provided that the reduced motor constant and the calibration current are known. The explicit knowledge of the seismograph partial constants is not necessary.

Newton-Raphson's method is generally efficient to obtain the elements from the calibration curve, but it may fail some times. Levenberg's method (slightly modified) and also simple step reduction can be helpful in such cases. The unknowns can be obtained either freely or under the constraint that some of the partial constants have the values assigned to them. The latter may be convenient when the behavior of parts of the system is affected by some trouble.