Summary. We present a new numerical method to solve the heterogeneous anelastic, seismic wave equations with arbitrary high order accuracy in space and time on

We present a nodal finite-element method that can be used to compute in parallel highly accurate solutions for 3-D controlled-source electromagnetic forward-modelling problems in anisotropic media. Secondary coupled-potential formulation of Maxwell's equations allows to avoid the singularities introduced by the sources, while completely unstructured tetrahedral meshes and mesh refinement support an accurate representation of geological and bathymetric complexity and improve the solution accuracy. Different complex iterative solvers and an efficient pre-conditioner based on the sparse approximate inverse are used for solving the resulting large sparse linear system of equations. Results are compared with the ones of other researchers to check the accuracy of the method. We demonstrate the performance of the code in large problems with tens and even hundreds of millions of degrees of freedom. Scalability tests on massively parallel computers show that our code is highly scalable.

We have developed a new numerical method to solve the heterogeneous poroelastic wave equations in bounded three-dimensional domains. This method is a discontinuous Galerkin method that achieves arbitrary high-order accuracy on unstructured tetrahedral meshes for the low-frequency range and the inviscid case. By using Biot's equations and Darcy's dynamic laws, we have built a scheme that can successfully model wave propagation in fluid-saturated porous media when anisotropy of the pore structure is allowed. Zero-inflow fluxes are used as absorbing boundary conditions. A continuous arbitrary high-order derivatives time integration is used for the high-frequency inviscid case, whereas a space-time discontinuous scheme is applied for the low-frequency case. We conducted a numerical convergence test of the proposed methods. We used a series of examples to quantify the quality of our numerical results, comparing them to analytic solutions as well as numerical solutions obtained by other methodologies. In particular, a large scale 3D reservoir model showed the method's suitability to solve poroelastic wave-propagation problems for complex geometries using unstructured tetrahedral meshes. The resulting method is proved to be high-order accurate in space and time, stable for the low-frequency case, and asymptotically consistent with the diffusion limit.

Summary. We present a new numerical method to solve the heterogeneous elastic anisotropic wave equation with arbitrary high-order accuracy in space and time on

Finite-difference methods for modeling seismic waves are known to be inaccurate when including a realistic topography, due to the large dispersion errors that appear in the modelled surface waves and the scattering introduced by the staircase approximation to the topography. As a consequence, alternatives to finite-difference methods have been proposed to circumvent these issues. We present a new numerical scheme for 3D elastic wave propagation in the presence of strong topography. This finite-difference scheme is based upon a staggered grid of the Lebedev type, or fully staggered grid (FSG). It uses a grid deformation strategy to make a regular Cartesian grid conform to a topographic surface. In addition, the scheme uses a mimetic approach to accurately solve the free-surface condition and hence allows for a less restrictive grid spacing criterion in the computations. The scheme can use high-order operators for the spatial derivatives and obtain low-dispersion results with as few as six points per minimum wavelength. A series of tests in 2D and 3D scenarios, in which our results are compared to analytical and numerical solutions obtained with other numerical approaches, validate the accuracy of our scheme. The resulting FSG mimetic scheme allows for accurate and efficient seismic wave modelling in the presence of very rough topographies with the advantage of using a structured staggered grid.