Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green’s function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data

Optimal fourth-order staggered-grid finite-difference scheme for 3D frequency-domain viscoelastic wave modeling

International audienceWe investigate an optimal fourth-order staggered-grid finite-difference scheme for 3D frequency-domain viscoelastic wave modeling. An anti-lumped mass strategy is incorporated to minimize the numerical dispersion. The optimal finite-difference coefficients and the mass weighting coefficients are obtained by minimizing the misfit between the normalized phase velocities and the unity. An iterative damped least-squares method, the Levenberg–Marquardt algorithm, is utilized for the optimization. Dispersion analysis shows that the optimal fourth-order scheme presents less grid dispersion and anisotropy than the conventional fourth-order scheme with respect to different Poisson's ratios. Moreover, only 3.7 grid-points per minimum shear wavelength are required to keep the error of the group velocities below 1%. The memory cost is then greatly reduced due to a coarser sampling. A parallel iterative method named CARP-CG is used to solve the large ill-conditioned linear system for the frequency-domain modeling. Validations are conducted with respect to both the analytic viscoacoustic and viscoelastic solutions. Compared with the conventional fourth-order scheme, the optimal scheme generates wavefields having smaller error under the same discretization setups. Profiles of the wavefields are presented to confirm better agreement between the optimal results and the analytic solutions

A review of the spectral, pseudo-spectral, finite-difference and finite-element modelling techniques for geophysical imaging

International audienceModelling methods are nowadays at the heart of any geophysical interpretation approach. These are heavily relied upon by imaging techniques in elastodynamics and electromagnetism, where they are crucial for the extraction of subsurface characteristics from ever larger and denser datasets. While high-frequency or one-way approximations are very powerful and efficient, they reach their limits when complex geological settings and solutions of full equations are required at finite frequencies. A review of three important formulations is carried out here: the spectral method, which is very efficient and accurate but generally restricted to simple earth structures and often layered earth structures; the pseudo-spectral, finite-difference and finite-volume methods based on strong formulation of the partial differential equations, which are easy to implement and currently represent a good compromise between accuracy, efficiency and flexibility and the continuous or discontinuous Galerkin finite-element methods that are based on the weak formulation, which lead to more accurate earth representations and therefore to more accurate solutions, although with higher computational costs and more complex use. The choice between these different approaches is still difficult and depends on the applications. Guidelines are given here through discussion of the requirements for imaging/inversion