Finite-difference Modelling Of Wave Propagation Research Articles

Quantitative identification of pseudofaults underlying igneous rocks through wave-equation-based velocity modeling: A case study of the Shuntuoguole uplift, Tarim Basin, China

Fault identification plays an important role in oil and gas exploration of the Ordovician reservoirs underlying the Permian igneous rocks in the fault-controlled Shuntuoguole uplift, Tarim Basin, China. Faults identified through conventional analysis of seismic coherence attributes, however, usually contain many artifacts or pseudofaults in which velocities of the igneous rocks tend to be selected incorrectly during migration imaging. We have evaluated a quantitative method to identify the pseudofaults by numerical simulation of depth migration on synthetic seismic records generated by finite-difference modeling of wave propagation. Detailed information on the spatial distribution and velocity range of the Permian igneous rocks is used to build a refined velocity model for the wave-equation-based forward modeling, calibrated with core, well log, and seismic data. It is found that the thickness and the migration velocity error used for the igneous rocks in depth migration are important factors affecting the pseudofault throws. There exists a strong quantitative relationship between igneous rock thickness ([Formula: see text]) and pseudofault throw ([Formula: see text]), [Formula: see text], where [Formula: see text], [Formula: see text], and [Formula: see text] are constants for a given migration velocity error. For a maximum migration velocity error of 15% for the dacite bodies in the studied area, [Formula: see text], [Formula: see text], and [Formula: see text] are 0.0002, 0.1864, and [Formula: see text], respectively. Using this relationship, the maximum fault throw ([Formula: see text]) of a pseudofault caused by an arbitrary thickness of any dacite body can be calculated. If the actual fault throw (H) of an apparent fault measured on the migrated seismic profile is greater than the calculated maximum fault throw for the fault, i.e., [Formula: see text], then the apparent fault is a real geologic fault. Otherwise, it is a pseudofault. The method has been successfully applied to produce corrected fault distribution maps for geologic evaluation of the Ordovician reservoirs in the Shuntuoguole region.

Stability analysis of second- and fourth-order finite-difference modelling of wave propagation in orthotropic media

The stability of the finite-difference approximation of elastic wave propagation in orthotropic homogeneous media in the three-dimensional case is discussed. The model applies second- and fourth-order finite-difference approaches with staggered grid and stress-free boundary conditions in the space domain and second-order finite-difference approach in the time domain. The numerical integration of the wave equation by central differences is conditionally stable and the corresponding stability criterion for the time domain discretisation has been deduced as a function of the material properties and the geometrical discretization. The problem is discussed by applying the method of VonNeumann. Solutions and the calculation of the critical time steps is presented for orthotropic material in both the second- and fourth-order case. The criterion is verified for the special case of isotropy and results in the well-known formula from the literature. In the case of orthotropy the method was verified by long time simulations and by calculating the total energy of the system.

Finite-difference modeling of wave propagation on microscale: A snapshot of the work in progress

Digital rock methodology combines modern microscopic imaging with advanced numerical simulations of the physical properties of rocks. Modeling of elastic-wave propagation directly from rock microstructure is integral to this technology. We survey recent development of the rotated staggered grid (RSG) finite-difference (FD) method for pore-scale simulation of elastic wave propagation in digital rock samples, including the dynamic elastic properties of rocks saturated with a viscous fluid. Examination of the accuracy of this algorithm on models with known analytical solutions provide an additional accuracy condition for numerical modeling on the microscale. We use both the elastic and viscoelastic versions of the RSG algorithm to study gas hydrates and to simulate propagation of Biot’s slow wave. We applyRSG method ology to examine the effect of gas hydrate distributions in the pore space of a rock. We compare resulting P-wave velocities with experimentally measured data, as a basis for building an effective-medium model for rocks containing gas hydrates. We then perform numerical simulations of Biot’s slow wave in a realistic 3D digital rock model, fully saturated with a nonviscous fluid (corresponding to the high-frequency limit of poroelasticity), and placed inside a bulk fluid. The model clearly demonstrates Biot’s slow curve when the interface is open between the slab and bulk fluid. We demonstrate slow wave propagation in a porous medium saturated with a viscous fluid by analyzing an idealized 2D porous medium represented alternating solid and viscous fluid layers. Comparison of simulation results with the exact solution for this layered system shows good agreement over a broad frequency range.

Distributed three-dimensional finite-difference modeling of wave propagation in acoustic media

Finite-difference modeling of wave propagation in heterogeneous media is a useful technique in a number of disciplines, including earthquake and oil exploration seismology, laboratory ultrasonics, ocean acoustics, radar imaging, nondestructive evaluation, and others. However, the size of the models that can be treated by finite-difference methods in three spatial dimensions has limited their application to supercomputers. We describe a finite-difference domain-decomposition method for the three-dimensional acoustic wave equation which is well suited to distributed parallelization. We have implemented this algorithm using the PVM message-passing library, and show here benchmarks on two different distributed memory architectures, the IBM SP2 and a network of low-cost PCs running the Linux operating system. We present performance measurements of this algorithm on both the low-bandwidth PC network (10-Mbits/s Ethernet) and the high-bandwidth SP2 cluster (40-Mbits/s switch). These results demonstrate the feasibility of doing distributed finite-difference acoustic modeling on networks of workstations, but point to the substantial efficiencies that can be expected as higher bandwidth networks become available. © 1997 American Institute of Physics.