Truncated co-seismic geoid and gravity changes in the domain of spherical harmonic degree

Abstract

A concept of truncated geoid and gravity changes is proposed in this study and corresponding truncated expressions are presented for investigating co-seismic deformations. Numerical investigations are carried out to observe whether or not co-seismic geoid and gravity changes are detectable by gravity satellite missions. Results of an individual harmonic degree or a summation to interested degrees are compared with the expected errors of the gravity missions, assuming a seismic source equivalent to the fault size of the Alaska earthquake (1964, mw = 9.2). Corresponding co-seismic deformations indicate that both the gravity and geoid changes are about two orders larger than the precision of GRACE. Based on these results, the minimum magnitudes of earthquakes detectable by GRACE are derived. The conclusion is that co-seismic deformations for an earthquake with a seismic magnitude above m = 7.5 (for the tensile sources) and m = 9.0 (for the shear sources) are expected to be detected by GRACE. Finally, a case study is made on the 2002 Alaska earthquake (m = 7.9). Results show that the co-seismic geoid and gravity changes are at or below the error level of GRACE, and are difficult to detect.