Seismological Versus Geodetic Reference Frames for Seismic Dislocation: Consistency Under Momentum Conservations

xu, changyi ; chao, benjamin f.;

We raise attention to the issue of consistency between the reference frame with respect to which the seismological model calculations of displacement are made on one hand, and that to which the geodetic measurements of crustal deformation refer (e.g.theITRF) on the other. This issue is critical in principle if the seismologically calculated displacement (orgravity change) is to be compared orused in joint inversion with geodetic measurements. A necessary set of conditions tobe satisfied by inertial frames is the conservations oflinear and angular momentums: nonet change in them can be induced by a seismic source indigenous to the Earth. We show that the momentums are embodied in the degree-1 terms of the vector spherical-harmonic expansion of the displacement field. Using three largest recent earthquakes as case examples we find that the algorithms of seismological dislocation modelling in the literature do not conserve the momentums. However, quantitatively this inconsistency amounts to two orders of magnitude smaller than the current precision in the definition of the ITRF, hence insignificant in practice. Some caveats are raised.