A new method for the computation of global viscoelastic post-seismic deformation in a realistic earth model (II)-horizontal displacement

Post-seismic deformation caused by the 2004 Sumatra-Andaman Earthquake ( M = 9.3) has been observed by space geodetic techniques such as the Global Positioning System (GPS) and the Gravity Recovery and Climate Experiment ( GRACE). To estimate such deformation with a spatial scale exceeding 100 km, we can use theories of global post-seismic deformation in which the Earth is treated as a self-gravitating viscoelastic sphere. Previous theories have imposed limitations on employed earth models, such as neglecting compressibility and time variation of self-gravitation or simplifying the radial profile of the viscosity. This is because the normal mode method on which these theories are based cannot evaluate a denumerably infinite set of eigenmodes that will appear when those limitations are removed in the practical computation. To bypass this difficulty, in our previous paper, we showed that the numerical inverse Laplace integration with a rectangular path enabled us to obtain the vertical deformation without using those approximations. In this paper, we apply the same method to the horizontal deformation for a complete set of the fault mechanisms (strike-slip, dip-slip and vertical and horizontal tensile). Next, we reveal error sources in our approach. The largest error arises in different selections of the integration path. This error is less than 1 per cent in the lower-degree deformations (n similar to 10) and 0.1-0.5 per cent in the higher-degree ones (100 < n < 1000), relative to the result obtained with an independent method. Finally, we elucidate differences in far-field deformations obtained for the earth model employed in this study and those used in the previous studies for a large dip-slip event (M-w = 8.3). The result shows that ( 1) differences of 6-50 per cent are seen in the coseismic offset and ( 2) horizontal rate differences of 1- 5 mm yr(-1) ( 5 - 25 per cent of the rates) are observed at the epicentral distance of 100 km during the first thirty years after the event. These differences are detectable with GPS. Therefore, for theory to meet observational accuracy, effects of compressibility and stratification on global post-seismic deformation should be considered.