Seismic modeling plays an important role in geophysics and seismology for estimating the response of seismic sources in a given medium. In this work, we present a MATLAB-based package, FDwave3D, for synthetic wavefield and seismogram modeling in 3D anisotropic media. The seismic simulation is carried out using the finite-difference method over the staggered grid, and it is applicable to both active and passive surveys. The code package allows the incorporation of arbitrary source mechanisms and offers spatial derivative operators of accuracy up to tenth-order along with different types of boundary conditions. First, the methodological aspects of finitedifference method are briefly introduced. Then, the code has been tested and verified against the analytical solutions obtained for the homogeneous model. Further, the numerical examples of layered and overthrust models are presented to demonstrate its reliability.
We have analyzed the angle-dependent reflectivity of microseismic wavefields at a hydraulic fracture, which we modeled as an ideal thin fluid layer embedded in an elastic, isotropic solid rock. We derived full analytical solutions for the reflections of an incident P-wave, the P-P and P-S reflection coefficients, as well as for an incident S-wave, and the S-S and S-P reflection coefficients. The rather complex analytical solutions were then approximated and we found that these zero-thickness limit approximations are in good agreement with the linear slip model, representing a fracture at slip contact. We compared the analytical solutions for the P-P reflections with synthetic data that were derived using finite-difference modeling and found that the modeling confirmed our theoretical results. For typical parameters of microseismic monitoring by hydraulic fracturing, e.g., a layer thickness of [Formula: see text] and frequencies of [Formula: see text], the reflection coefficients depend on the Poisson’s ratio. Furthermore, the reflection coefficients of an incident S-wave are remarkably high. Theoretical results suggested that it is feasible to image hydraulic fractures using microseismic events as a source and to solve the inverse problem, that is, to interpret reflection coefficients extracted from microseismic data in terms of reservoir properties.
Traveltime-based methods depend on the accurate determination of the arrival times of seismic waves. They further benefit from information on the uncertainty with which the arrival times are determined. Among other applications, arrival-time uncertainties are used to weight data in inversion algorithms and to define the resolution of reconstructed velocity models. The most physically meaningful approaches for the estimation of arrival-time uncertainties are based on probabilistic formulations. The two approaches for the assessment of the lower bound of arrival-time uncertainties, the Cramér–Rao Bound (CRB) and the Ziv–Zakai Bound (ZZB), have been reviewed. The CRB determines the minimum-achievable estimation error under the assumption of a high signal-to-noise ratio (S/N) but underestimates said error for small S/N. The ZZB provides a better result for noisy data because it utilizes a priori information. The CRB and ZZB require knowledge of the spectral variance of the signal, which often is hard to determine in seismic experiments. Furthermore, both bounds assume additive white Gaussian noise (AWGN), which does not hold for seismic data. To overcome these problems, alternative expressions have been proposed, which yield comparable estimates as CRB and ZZB but are solely based on the S/N and the dominant period in the data. Moreover, a recipe to correct the S/N and account for the difference between the seismic noise and AWGN has been provided. For a case study of downhole microseismic monitoring, it is determined that the new expressions provide station-dependent arrival-time uncertainties, which are used as weights to improve source location uncertainties.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.