Quadrangle-grid velocity–stress finite difference method for poroelastic wave equations

A quadrangle-grid velocity–stress finite difference method, based on a first-order hyperbolic system that is equivalent to Biot's equations, is developed for the simulation of wave propagation in 2-D heterogeneous porous media. In this method the velocity components of the solid material and of the pore fluid relative to that of the solid, and the stress components of three solid stresses and one fluid pressure are defined at different nodes for a staggered non-rectangular grid. The scheme uses non-orthogonal grids, allowing surface topography and curved interfaces to be easily modelled in the numerical simulation of seismic responses of poroelastic reservoirs. The free-surface conditions of complex geometry are achieved by using integral equilibrium equations on the surface, and the source implementations are simple. The algorithm is an extension of the quadrangle-grid finite difference method used for elastic wave equations.     

Adaptive unstructured grid finite element simulation of two-dimensional magnetotelluric fields for arbitrary surface and seafloor topography

We present an adaptive unstructured triangular grid finite element approach for effectively simulating plane-wave diffusive electromagnetic fields in 2-D conductivity structures.
The most striking advantage of irregular grids is their potential to incorporate arbitrary geometries including surface and seafloor topography. Adaptive mesh refinement strategies using an a posteriori error estimator yield most efficient numerical solutions since meshes are only refined where required.
We demonstrate the robustness of this approach by comparison with analytical solutions and previously published numerical simulations. Maximum errors may systematically be reduced to, for example, 0.8 per cent for the apparent resistivity and 0.2° in the phase.
An additional accuracy study of the thickness of the air layer in E-polarization suggests to keep a minimum thickness depending on lateral conductivity contrasts within the earth.
Furthermore, we point out the new quality and flexibility of our simulation technique by addressing two marine magnetotelluric applications. In the first case, we discuss topographic effects associated with a synthetic sinusoidal sea bottom model and in the second case, we show a close-to-reality scenario using real bathymetry data from the East Pacific Rise at 17°S.     

Traction image method for irregular free surface boundaries in finite difference seismic wave simulation

In this study, we propose a new numerical method, named as Traction Image method, to accurately and efficiently implement the traction-free boundary conditions in finite difference simulation in the presence of surface topography. In this algorithm, the computational domain is discretized by boundary-conforming grids, in which the irregular surface is transformed into a 'flat' surface in computational space. Thus, the artefact of staircase approximation to arbitrarily irregular surface can be avoided. Such boundary-conforming gridding is equivalent to a curvilinear coordinate system, in which the first-order partial differential velocity-stress equations are numerically updated by an optimized high-order non-staggered finite difference scheme, that is, DRP/opt MacCormack scheme. To satisfy the free surface boundary conditions, we extend the Stress Image method for planar surface to Traction Image method for arbitrarily irregular surface by antisymmetrically setting the values of normal traction on the grid points above the free surface. This Traction Image method can be efficiently implemented. To validate this new method, we perform numerical tests to several complex models by comparing our results with those computed by other independent accurate methods. Although some of the testing examples have extremely sloped topography, all tested results show an excellent agreement between our results and those from the reference solutions, confirming the validity of our method for modelling seismic waves in the heterogeneous media with arbitrary shape topography. Numerical tests also demonstrate the efficiency of this method. We find about 10 grid points per shortest wavelength is enough to maintain the global accuracy of the simulation. Although the current study is for 2-D P-SV problem, it can be easily extended to 3-D problem.     

The role of seismicity models in probabilistic seismic hazard estimation: comparison of a zoning and a smoothing approach

Seismic hazard estimations are compared using two approaches based on two different seismicity models: one which models earthquake recurrence by applying the truncated Gutenberg-Richter law and a second one which smoothes the epicentre location of past events according to the fractal distribution of earthquakes in space ( Woo 1996 ). The first method requires the definition of homogeneous source zones and the determination of maximum possible magnitudes whereas the second method requires the definition of a smoothing function. Our results show that the two approaches lead to similar hazard estimates in low seismicity regions. In regions of increased seismic activity, on the other hand, the smoothing approach yields systematically lower estimates than the zoning method. This epicentre-smoothing approach can thus be considered as a lower bound estimator for seismic hazard and can help in decision making in moderate seismicity regions where source zone definition and estimation of maximum possible magnitudes can lead to a wide variety of estimates due to lack of knowledge. The two approaches lead, however, to very different earthquake scenarios. Disaggregation studies at a representative number of sites show that if the distributions of contributions according to source–site distance are comparable between the two approaches, the distributions of contributions according to magnitude differ, reflecting the very different seismicity models used. The epicentre-smoothing method leads to scenarios with predominantly intermediate magnitudes events (5 ≤ M ≤ 5.5) while the zoning method leads to scenarios with magnitudes that increase with the return period from the minimum to the maximum magnitudes considered. These trends demonstrate that the seismicity model used plays a fundamental role in the determination of the controlling scenarios and ways to discriminate between the most appropriate models remains an important issue.