Wave Equation Forward Modeling Research Articles

Simulate the elastic wavefields in media with an irregular surface topography based on staggered grid finite difference

Abstract Wave equation forward modeling is a useful method to study the propagation regulation of seismic wavefields. Finite difference (FD) is one of the most extensively employed numerical approaches for computing wavefields in earthquake and exploration seismology. However, the FD approach relying on regular grids often struggles with calculating wavefields in regions featuring surface topographies. The elastic wave equation can more accurately describe the propagation of seismic wavefields in elastic media compared to the acoustic wave equation. We introduce a new FD scheme to calculate the elastic wavefields in an isotropic model with a surface topography. The novel approach can use a conventional staggered grid FD(SGFD) approach based on regular grids. A new elastic model with a horizontal surface is first obtained from the nearby surface's elastic properties and the undulating terrain elevation. We subsequently employ a topography-related strategy to eliminate the effects of surface topographies on the seismic wavefields in models with irregular surface topographies. The merits of our proposed scheme lie in its ability to stable numerically compute wavefields in models with irregular surface topographies without altering the conventional SGFD relying on regular grids. To validate the effectiveness and practicality of our method, we utilize elastic models featuring complex surface topographies. Numerical experiments demonstrate that our approach efficiently calculates elastic wavefields in isotropic media with irregular topographies based on conventional SGFD.

Seismic modeling using pseudo-impedance derived from physical models

Building accurate numerical models of the earth for simulation is both challenging and time consuming. The subsurface complexity must be captured in sufficient detail for the results to be of practical use for geophysical analysis. Physical models provide an efficient way to add realistic detail to numerical models. Physical models, for example, are scaled simulations of large-scale geologic systems that provide great insight into understanding the interplay between sedimentation, salt tectonics, and faulting. The integration of geophysical workflows with sandbox models has been the subject of previous research, primarily to create synthetic data to compare with observed field data. However, capturing the detail from the physical model is challenging. A novel workflow is presented that uses pixel intensity values from photographic images of the analogue model to create a pseudo-impedance perturbation, mimicking the acoustic impedance contrasts that are encountered in the earth. This solution enables the detailed sedimentary architecture from the sandbox to be transferred to the digital earth model. Acoustic wave equation forward modeling and reverse time migration imaging have been applied using the generated pseudo-impedance model for a Gulf of Mexico-style salt canopy model. The images produced show clear definition of the salt/sediment interface and capture the sedimentary stratigraphy and faulting observed in the original sandbox model.

Acoustic full waveform inversion with elastic wave equation forward modeling

Full-waveform inversion (FWI) is a high-resolution velocity inversion method. Currently, acoustic full waveform inversion (AFWI) has achieved promising results in marine data inversion, but it still faces significant challenges in land data inversion. One of the reasons for the failure of AFWI in land data inversion is that the acoustic wave equation does not account for the elastic effects of seismic waves, such as surface waves and converted waves. This results in errors between the synthesized acoustic waveform and the observed elastic waveform, particularly in the amplitude and phase of the P-wave. To reduce the error caused by the elastic effect, we have improved the inversion process of AFWI. During the forward modeling stage, we replace the original acoustic wave equation with the elastic wave equation to simulate the wavefield. This allows us to obtain synthetic waveforms that incorporate elasticity, thereby reducing the corresponding error. When computing model gradients, we still base on the acoustic wave equation and only update the P-wave velocity model. This approach helps maintain a lower computational cost. We tested the method on the Marmousi model and field land data, and the results demonstrate that the method successfully reduces the error caused by the elastic effect, thereby improving the clarity of the inversion results.

Implicit finite difference wave equation forward modeling based on partial fraction expansion

Implicit finite difference wave equation forward modeling based on partial fraction expansion

Key technologies for complex surface seismic acquisition in the Sichuan Basin and their application effect

The earth surface in the Sichuan Basin and its periphery is geologically complex, which causes low signal-to-noise ratio of seismic data, poor imaging quality of seismic profiles and great difficulty in data acquisition. In order to ensure high-quality operation of the seismic survey project in the complex surface of the Sichuan Basin, researchers have been working continuously to solve the bottleneck problems in the seismic acquisition technology for complex surface in recent years. In addition, the upgrading of acquisition technology and operation capacity is promoted effectively by means of technical innovation, and a series of key technologies for seismic acquisition are developed. And the following application results of this series of technologies are obtained. First, the optimization design technology of the geometry based on wave equation forward modeling and actual data, combined with prestack migration imaging can show the influence of different acquisition schemes on the prestack imaging effect of complex targets more directly, which makes the seismic acquisition scheme more economic and effective. Second, by extracting landform risks and surface obstacle information intelligently, combined with field fine reconnaissance, landform risk identification and hierarchical evaluation and indoors intelligent optimization of well-shot physical point deployment are conducted, and thus the GIS+ intelligent deployment technology of shot point in complex surface is formed, which effectively reduces the risks of operation. Third, the cavity excitation technology which reduces the initial pressure of explosive pulse and extends the explosive action time of explosives can increase the conversion rate of rock excitation energy into effective elastic wave energy and the reflected energy and improve the quality of seismic single shot data. Fourth, combination of the automatic evaluation technology for field seismic data acquired in mountainous regions and the KL-GMLiveQC1.0 software can improve the evaluation efficiency, reduce the evaluation cost and ensure the high-quality acquisition of seismic data in complex surface. In conclusion, this series of key seismic acquisition technologies greatly improve the signal-to-noise ratio and resolution of seismic data, lay a foundation for fine reservoir prediction, and ensure the continuous important breakthrough of three-dimensional natural gas exploration and development in the gas fields of marine carbonate rock, shale gas, volcanic rock and shallow tight sandstone gas in the Sichuan Basin.

Formation Mechanism and Prediction Method for the Permian Fused Breccia Tuff Reservoir, Wuxia Region, Junggar Basin

Fused breccia tuff occurs globally, but its formation mechanism is very controversial. Volcanic reservoirs have developed at the bottom of the Permian Fengcheng Formation in the Wuxia region of the Junggar Basin, and here, the lithology is fused breccia tuff. The reservoir porosity is mainly vesicles, but the development and relative filling of the vesicles vary spatially, resulting in strong reservoir heterogeneity. Through core and thin section observations and structural analysis, and combined with reconstructions of the paleosedimentary environment, we discussed in detail the formation mechanism of the fused breccia tuff reservoir. Our conclusions are as follows. In the high-temperature and high-pressure environment of the deep crust, intermediate acidic lava containing volatile components rapidly rose to the earth’s surface along a fault. The volatile components in the lava foamed strongly and then exploded due to the sharp decline of pressure and temperature. A small part of the volcanic dust and pyroclastic material was erupted into the upper atmosphere. Most of the magma became magmatic pyroclast, vitric pyroclast, rock debris, dust, and other matter. This material was in a semimolten state and overflowed into a nearby low-lying lake. The extremely high-temperature pyroclastic flow quickly vaporized the water into high-pressure water vapor, which was squeezed into the pyroclastic flow and became mixed with other volatiles in the foam. On cooling, the pyroclastic material solidified into rock, and the vesicles were preserved. In a later period, due to strong tectonic movement, faults and fractures developed, surface water penetrated into the vesicles along the faults and fractures, and silica and other substances were deposited, filling the primary vesicles. To quantify the development and relative filling of vesicles, drilling parameters were used to establish different geologic models, and wave equation forward modeling was used to obtain a relationship between the development and filling of vesicles, and the seismic amplitude. The 3D seismic amplitude attributes were then extracted to predict the extent of the reservoir, yielding prediction results consistent with the drilling observations.

二维频率域声波方程正演模拟

二维频率域声波方程正演模拟

Seismic forward and inverse simulation in a tight reservoir model of loess plateau region

Abstract To find out the seismic wave field propagation principles in loess plateau near surface of the Ordos Basin and the seismic response characteristics of tight oil reservoirs, this study established a geological-geophysical model under the real conditions of ground surface of loess plateau, and launched full elastic seismic wave equation forward modeling and pre-stack elastic seismic inversion study. Comparison of modeling and real seismic data shows that, the loose and wavy loess plateau surface is the main reason for causing the problems of seismic static correction and interference wave. Tomographic static correction method with the constraint of traces near shot point can effectively solve the problem of seismic static correction in the loess plateau and enhance seismic imaging accuracy, S-wave impedance obtained from pre-stack seismic inversion can identify sandstone effectively, and Poisson's ratio can identify oil-bearing reservoirs. The seismic forward and inverse simulation and rock physical analysis provide a solid theoretical and experimental basis for the seismic prediction of tight oil reservoir, and have worked well in the oil exploration and development in the loess plateau of the Ordos Basin.

3D Seismic Acquisition Technology and Effect in HX Volcanic Area in Liaohe Depression

Multi-stages volcanic are available in HX area, shielding the seismic waves. Previous seismic acquisitions of large size bin, less fold coverage and narrow azimuth result in indistinct fault images, low S/N ratio and the difficulty of multi-stages volcanic characterization. In reference to the successful experience of domestic and overseas volcanic exploration, the low frequency excitation and receiving, and survey with wide range, high coverage, wide azimuth should be paid more attention, associated with two-dimensional and three-dimensional wave equation forward modeling and real data processing contrast analysis method. The image of underlying strata and fault are remarkably improved in the new method, according to the processing results of new seismic data. The new method will provide technical reference for the similar volcanic development area in the future seismic acquisition design.

Seismic Response and Wave Group Characteristics of Reef Carbonate Formation of Karloff-Oxford Group in Asser Block

In this article, we built a reef complex geological model, which is based on the geological characteristics and electric characteristics on the upper Jurassic Karloff-Oxford Formation of Asser Block at the Right Bank of the Amu River, and studied seismic response of carbonate formation by the wave equation forward modeling. Seismic response characteristics of reef complex in the area are the mound-shaped and lenticular reflections characteristics. Seismic wave in the edges of the reef complex often appear onlap and diffraction seismic reflection phenomenon, and there is upper bend phenomenon on the top of the reflection wave. The reflection wave on the top of the reef complex is trough weak reflection, with weak amplitude and discontinuous wave-front. The internal reflection wave in reef complex are unorganized or weakly, and there is a big difference in continuity between it and that of the surrounding rock on the amplitude, frequency and phase. Moreover, compared with formations of two wings, we found out that the thickness suggested by the reflection waves in the internal reef complex is bigger. The characteristics mentioned above are consistent with seismic section characteristics of reef complex over well. So that, we built a characteristics to recognize pattern of seismic of reef complex by using forward modeling results of a reef complex.

3D elastic wave equation forward modeling based on the precise integration method

The Finite Difference (FD) method is an important method for seismic numerical simulations. It helps us understand regular patterns in seismic wave propagation, analyze seismic attributes, and interpret seismic data. However, because of its discretization, the FD method is only stable under certain conditions. The Arbitrary Difference Precise Integration (ADPI) method is based on the FD method and adopts an integration scheme in the time domain and an arbitrary difference scheme in the space domain. Therefore, the ADPI method is a semi-analytical method. In this paper, we deduce the formula for the ADPI method based on the 3D elastic equation and improve its stability. In forward modeling cases, the ADPI method was implemented in 2D and 3D elastic wave equation forward modeling. Results show that the travel time of the reflected seismic wave is accurate. Compared with the acoustic wave field, the elastic wave field contains more wave types, including PS- and PP- reflected waves, transmitted waves, and diffracted waves, which is important to interpretation of seismic data. The method can be easily applied to elastic wave equation numerical simulations for geological models.

Application of Mixed Boundary Condition to Wave Equation Forward Modeling in 2.5D VTI Medium

A key issue in the wave equation simulation of seismic records is the boundary conditions. Due to computer memory and computation and other restrictions, can only be solved on a limited area, which will cause the introduction of an artificial reflector. So as to simulation of seismic wave propagation in an infinite medium, the boundary conditions must be constructed so that the interface of the reflection as little as possible. In 2.5D VTI media feature analysis absorbing boundary of higher order velocity-stress staggered-grid finite difference method are established. The mixed boundary of the feature analysis absorbing boundary plus damping attenuation condition is used in 2.5 D VTI numerical simulations, simulation results show that this method is an efficient absorption and attenuation boundary conditions.

Frequency domain wave equation forward modeling using gaussian elimination with static pivoting

Frequency domain wave equation forward modeling is a problem of solving large scale linear sparse systems which is often subject to the limits of computational efficiency and memory storage. Conventional Gaussian elimination cannot resolve the parallel computation of huge data. Therefore, we use the Gaussian elimination with static pivoting (GESP) method for sparse matrix decomposition and multi-source finite-difference modeling. The GESP method does not only improve the computational efficiency but also benefit the distributed parallel computation of matrix decomposition within a single frequency point. We test the proposed method using the classic Marmousi model. Both the single-frequency wave field and time domain seismic section show that the proposed method improves the simulation accuracy and computational efficiency and saves and makes full use of memory. This method can lay the basis for waveform inversion.

3-D acoustic wave equation forward modeling with topography

In order to model the seismic wave field with surface topography, we present a method of transforming curved grids into rectangular grids in two different coordinate systems. Then the 3D wave equation in the transformed coordinate system is derived. The wave field is modeled using the finite-difference method in the transformed coordinate system. The model calculation shows that this method is able to model the seismic wave field with fluctuating surface topography and achieve good results. Finally, the energy curves of the direct and reflected waves are analyzed to show that surface topography has a great influence on the seismic wave’s dynamic properties.