Site-specific strong ground motion prediction using 2.5-D modelling

Abstract

Summary An algorithm was developed using the 2.5‐D elastodynamic wave equation, based on the displacement–stress relation. One of the most significant advantages of the 2.5‐D simulation is that the 3‐D radiation pattern can be generated using double‐couple point shear‐dislocation sources in the 2‐D numerical grid. A parsimonious staggered grid scheme was adopted instead of the standard staggered grid scheme, since this is the only scheme suitable for computing the dislocation. This new 2.5‐D numerical modelling avoids the extensive computational cost of 3‐D modelling. The significance of this exercise is that it makes it possible to simulate the strong ground motion (SGM), taking into account the energy released, 3‐D radiation pattern, path effects and local site conditions at any location around the epicentre. The slowness vector (py) was used in the supersonic region for each layer, so that all the components of the inertia coefficient are positive. The double‐couple point shear‐dislocation source was implemented in the numerical grid using the moment tensor components as the body‐force couples. The moment per unit volume was used in both the 3‐D and 2.5‐D modelling. A good agreement in the 3‐D and 2.5‐D responses for different grid sizes was obtained when the moment per unit volume was further reduced by a factor equal to the finite‐difference grid size in the case of the 2.5‐D modelling. The components of the radiation pattern were computed in the xz‐plane using 3‐D and 2.5‐D algorithms for various focal mechanisms, and the results were in good agreement. A comparative study of the amplitude behaviour of the 3‐D and 2.5‐D wavefronts in a layered medium reveals the spatial and temporal damped nature of the 2.5‐D elastodynamic wave equation. 3‐D and 2.5‐D simulated responses at a site using a different strike direction reveal that strong ground motion (SGM) can be predicted just by rotating the strike of the fault counter‐clockwise by the same amount as the azimuth of the site with respect to the epicentre. This adjustment is necessary since the response is computed keeping the epicentre, focus and the desired site in the same xz‐plane, with the x‐axis pointing in the north direction.

Two and Half Dimensional Simulation of Ridge Effects on the Ground Motion Characteristics

“…An explosive source is of little relevance to earthquake related site effect studies since it cannot explain the observed radiation patterns and is dominated by compressional waves. The successful numerical implementation of a double-couple point source into the computational grid was presented by VIDALE and HELMBERGER (1987), GRAVES (1996), PITARKA (1999) and NARAYAN (2001). NARAYAN (2001) demonstrated that 3-D and 2.5-D radiation pattern, using a double-couple point source based on moment tensor source formulation, corroborates with each other in the xz-plane.…”

“…Moment tensor source formulation was used in implementing the source into the computational grid (PITARKA, 1999 andNARAYAN, 2001). The second derivative of convolution of a polynomial window ½f1 À ðs À 1Þ 2 g 3 and the Gaussian function ½expfÀsðt À t 0 Þ 2 g with a dominant period 't 0 ' was used as an excitation function.…”

“…The second derivative of convolution of a polynomial window ½f1 À ðs À 1Þ 2 g 3 and the Gaussian function ½expfÀsðt À t 0 Þ 2 g with a dominant period 't 0 ' was used as an excitation function. In the present study, vacuum formulation (k, l and q fi 0) above the free surface was adopted (GRAVES, 1996 andNARAYAN, 2001). Vacuum formulation is quite useful in modeling the effects of surface topography, since it can be implemented with the same difference equation as used in the interior of the model.…”

“…An algorithm developed by NARAYAN (2001) was used in the 2.5-D simulations of ridge effects on the strong ground motion characteristics. Algorithm was based on parsimonious staggered grid approximation of 2.5-D elastodynamic wave equations (TAKENAKA and KENNETT, 1996a).…”

“…The configuration for 2.5-D wave simulation is achieved when the medium properties vary only in two dimensions and are assumed constant in the third direction, and the source-receivers are confined in the same plane. The double-couple point shear dislocation source based on moment tensor formulation was implemented into the numerical grid (AKI and RICHARDS, 1980;PITARKA, 1999 andNARAYAN, 2001). Various weathered and non-weathered ridge models were simulated with different slopes and intensity of weathering.…”