Gravitational changes of the Earth's free oscillation from earthquakes: Theory and feasibility study using GRACE inter‐satellite tracking

GRACE satellites have detected regional‐scale preseismic, coseismic, and postseismic gravity
changes associated with great earthquakes during the GRACE era (2002‐2017). Earthquakes also excite
global‐scale transient gravity changes associated with free oscillations that may be discerned for a few days.
In this study, we examine such global gravity changes due to Earth's free oscillations and quantify how they
affect GRACE measurements. We employ the normal mode formalism to synthesize the global gravity
changes after the 2004 Sumatra earthquake and simulate the (gravitational) free oscillation signals
manifested in the GRACE K‐band ranging (KBR) measurements. Using the Kaula orbit perturbation
theory, we show how GRACE inter‐satellite distances are perturbed through a complex coupling of
eigenfrequencies of the normal modes with the Earth's rotation rate and the GRACE satellites' orbital
frequency. It is found that a few gravest normal modes can generate range‐rate perturbations as large as
0.2 μm/s, which are comparable to actual errors of GRACE KBR ranging and accelerometer instruments.
Wavelet time‐frequency analysis of the GRACE KBR residual data in December 2004 reveals the existence
of a significant transient signal after the 2004 Sumatra earthquake. This transient signal is characterized
by a frequency of ~0.022 mHz that could be potentially associated with the largest excitation due to the
“football” mode of the Earth's free oscillation. However, the results are also affected by low‐frequency noise
of the GRACE accelerometers. Improved space‐borne gravitational instrumentation may open new
opportunities to study the Earth's interior and earthquakes independently from global
seismological analysis.