Coseismic gravitational curvatures changes in a spherical symmetric Earth model

The occurrence of subduction earthquakes usually leads to considerable localized mass migration changes. To improve the detection of earthquake subductions as well as the constraint of fault parameters, we derive expressions that describe changes of the gravitational curvatures (GC), i.e., the third-order derivatives of the Earth's gravitational potential, caused by a point dislocation while adopting a spherical symmetric Earth model. As a 3-D tensor matrix, the GC have twenty-seven components of those seven are independent. First, we investigate the dislocation Love numbers of the Earth's gravitational potential and derive the Green's functions of GC caused by four independent point sources in a spherical inhomogeneous Earth model. We then present the GC changes in a half-space Earth model. Furthermore, we conduct a sensitivity study by using three physical quantities that involve gravitation, gravitational gradients, and GC to compare their abilities in a seismic source depth detection. Our numerical results reveal that changes in the GC are more sensitive to a medium information about the field source compared to gravitation and gravitational gradients. This finding indicates that GC measurements could provide a more detailed information about slip fault parameters when considering a heterogeneous slip. Despite a widespread application of gravity gradients in Earth science, especially after launching the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission, measurements of the third-order derivatives of the gravitational potential have an enormous potential in the study of the solid Earth, although further work is needed in terms of instrument design and development.