Adjustment of relative gravity measurements using weighted and datum-free constraints

Abstract

A program in FORTRAN 90 is developed which can adjust relative gravity measurements and solve for gravimeter parameters using the weighted constraint and datum-free constraint models. The weighted constraint model is chosen when there exist reliable a priori gravity values for use as supplementary data, or when it is required that a gravity network be attached to an existing gravity network of a higher order. The datum-free model uniquely determines relative gravity values among all stations without the need of a fixed gravity value, thus it is suitable for detecting relative gravity change. The optional solve-for gravimeter parameters include drift coefficients, and coefficients of the long wavelength and periodic components of calibration function. The program can also detect outliers in observations using the τ-test method. A set of relative gravity data in Taiwan was used to test this program using five different choices of command-line arguments. The results show that there are no outliers in these data and that the estimated reading accuracy of the LaCoste and Romberg G meter (serial number 838) is about 0.02 mgal and the gravimeter drift rate is 0.9 mgal/month. The coefficients of the long wavelength and periodic components of calibration function are statistically equal to zero. The result from the datum-free solution is used to detect gravity variation due to the 1999 Chi-Chi earthquake, concluding that only one station experiences a significant change.