This research demonstrates an innovative numerical technique to simulate seismic wave propagation of a practical point source in complex 2-D geological models, which encompass a free surface topography, an undulating seafloor, and acoustic, elastic isotropic, viscoacoustic and viscoelastic anisotropic rocks. This technique is particularly beneficial in scenarios where 3-D wave modeling is resource-intensive and may efficiently offer the 3-D wavefields from arbitrary 2-D geological models often encountered in practice. Based on the point-source viscoelastic wave equations in a 2-D heterogeneous tilted transversely isotropic (TTI) medium, representative of subsurface igneous and sedimentary rocks, we tailor the wave equations valid for different rocks and the boundary conditions of the free-surface topography and seafloor and adapt the conventional memory variable method and the newly developed Taylor-series recursive convolution method to solve such point-source comprehensive wave equations. To overcome the inherent computational intensity of the methods, we convert the complex domain into a real domain and implement a fully parallelized computing strategy to ensure that the runtime of the numerical simulation remains on par with that of common 2-D wave modeling. Our experimental validations confirm the accuracy of the Taylor-series recursive method to offer the 3-D wavefields in an arbitrary heterogeneous 2-D geological model having a free-surface topography or an undulating seafloor. Moreover, our applications of this technique to two benchmark practical 2-D geological models demonstrate its capability to replicate 3-D wavefields in arbitrary viscoelastic anisotropic media, and greatly help in interpreting offshore and onshore seismic data and generating an accurate image of the subsurface.

Point-source to line-source transformation for seismic data prior to 2-D full waveform inversion is recommended for efficiently producing high-resolution images of the subsurface. The traditional filter of the transformation is derived by comparison of 3-D and 2-D Green’s function inhomogeneous acoustic media, so it doesn’t guarantee accurate transformation in complex heterogeneous viscoelastic anisotropic media. We adhere to a straightforward filter for compensating amplitude, incorporating offsets and phase shifts, and adjusting the stretching factors to rescale amplitude differences across various components. Additionally, we devise new stretching factors to accommodate time-domain transformations. Testing the proposed method with multi-layer and Marmousi models validates better amplitude compensation in both near and far offsets than the traditional hybrid method.

Accurately modeling seismic wave propagation in complex subsurface structures is not only helpful to understanding seismic data and rock properties but also the fundamental part of seismic full waveform inversion to image subsurface geological structure. 3-D seismic wave modeling is often expensive due to the huge consumption of computer resources. Alternatively, an efficient and accurate 2.5-D wave modeling can be employed for obtaining the 3-D wavefield in a 2-D geological model that is often encountered in practice. We present two advanced numerical methods for the 2.5-D viscoelastic anisotropic wave modeling by integrating three innovations. First, we formulate the 2.5-D viscoelastic anisotropic wave equations, particularly for a heterogeneous tilted transversely isotropic (TTI) medium that represents many sedimentary and igneous rocks of the subsurface. Second, we extend the common memory variable method and propose a new generalized recursive convolution (RC) method to the 2.5-D wave modeling. Third, we demonstrate the real-domain fully parallelized computing of the two methods to gain high computational efficiency of wave modeling. Our calibration experiments validate the accuracy of the proposed methods, and our modeling of a benchmark geological model exhibits the capability of the proposed methods to simulate the 3-D wavefield in a complex 2-D heterogeneous viscoelastic anisotropic medium. Such robust numerical simulations may enhance the characterization of seismic wave propagation and high-resolution subsurface imaging through full-waveform inversion, which is applicable for seismic exploration, the seismological study of the earth’s interior, and geohazard detection.

Derivatives of the displacement tensor with respect to the independent model parameters of the subsurface, also called Frechet derivatives (or sensitivity kernels), are a key ingredient for seismic full-waveform inversion (FWI) with a local-search optimization algorithm. They provide a quantitative measure of the expected changes in the seismograms due to perturbations of the subsurface model parameters for a given survey geometry. Because 2.5-D wavefield modelling involves a real point source in a 2-D geological model with 3-D (spherical) wave properties, it yields synthetic data much closer to the actual practical field data than the commonly used 2-D wave simulation does, which uses an unrealistic line-source in which the waves spread cylindrically. Based on our recently developed general 2.5-D wavefield modelling scheme, we apply the perturbation method to obtain explicit analytic expressions for the derivatives of the displacement tensor for 2.5-D/2-D frequency-domain seismic FWI in general viscoelastic anisotropic media. We then demonstrate the numerical calculations of all these derivatives in two common cases: (1) viscoelastic isotropic; and (2) viscoelastic tilted transversely isotropic (TTI) solids. Examples of the differing sensitivity patterns for the various derivatives are investigated and compared for four different homogeneous models involving 2-D and 2.5-D modelling. Moreover, the numerical results are verified against the analytic solutions for homogeneous models. We further validate the numerical derivatives in a 2-D heterogeneous viscoelastic TTI case by conducting a synthetic data experiment of frequency-domain FWI to individually recover the 12 independent model parameters (density, dip angle, 5 elastic moduli and 5 corresponding Q-factors) in a simple model comprising an anomalous square box target embedded in a uniform background. Another 2.5-D multi-target model experiment presenting impacts from four common seismic surveying geometries validates the Frechet derivatives again.

To avoid extensive computation of convolution, common time-domain viscoelastic wave modelling often applies either fractional derivatives or solve many auxiliary partial differential equations of memory variables. Basing on the general Zener model, we found that the memory variables or the convolutions can be directly calculated in a semi-analytic manner, which results in recursive formulas for efficient computations of the convolutions. The formulas show that the computations only require the two wavefields at the time interval, and the accuracies only depend on the time step, and the wavefields at the time interval, nothing related to the time-stepping schemes to solve the partial differential equations of the memory variables. Applying the semi-analytic formulas, new sets of the 1st- and 2nd-order viscoelastic wave equations are established and shown the similar forms to the elastic cases except for the extra ‘body-source’ terms.

PreviousNext No AccessFifth International Conference on Engineering Geophysics, Al Ain, UAE, 21–24 October 2019An alternative to the traditional electrode arrays for 2D electrical resistivity tomography: Enhanced version of the common gradient measurementAuthors: Bing Zhou*Saif UllahMuhammad AsimMoosoo WonSafeya AlkatheeriBing Zhou*Department of Earth Sciences, Khalifa University of Science and Technology, Abu Dhabi, UAESearch for more papers by this author, Saif UllahDepartment of Earth Sciences, Khalifa University of Science and Technology, Abu Dhabi, UAESearch for more papers by this author, Muhammad AsimDepartment of Earth Sciences, Khalifa University of Science and Technology, Abu Dhabi, UAESearch for more papers by this author, Moosoo WonDepartment of Earth Sciences, Khalifa University of Science and Technology, Abu Dhabi, UAESearch for more papers by this author, and Safeya AlkatheeriDepartment of Earth Sciences, Khalifa University of Science and Technology, Abu Dhabi, UAESearch for more papers by this authorhttps://doi.org/10.1190/iceg2019-007.1 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract 2D electrical resistivity tomography (ERT) often employs some traditional electrode arrays in data-acquisition, such as Wenner, dipole-dipole and Schlumberger. These classic arrays are originally developed for obtaining apparent resistivity pseudo-section or sounding curves rather than ERT. The gradient array becomes popular for ERT due to its high data quality, efficient data-acquisition with an automated multi-channel system and good resolution image of subsurface. In this paper, we present an enhanced version of the gradient array for ERT data-acquisition. We conducted numerical simulations and field experiments to investigate the merits and imaging capability of the new version of the gradient measurements and compared it with the traditional dipole-dipole, Schlumberger and gradient arrays. Our results show that the new data-acquisition electrode array inherits all advantages of the gradient array and happily combines sensitivities of the traditional three-electrode arrays: pole-dipole and dipole-pole, so that it offers a better depth coverage of the pseudo-section than the gradient array, and less noise contaminations than traditional dipole-dipole. The enhanced version of the gradient survey may significantly improve the subsurface images and becomes an alternative to the traditional and gradient arrays for ERT. Keywords: resistivity, numerical, aquifer, imaging, arraysPermalink: https://doi.org/10.1190/iceg2019-007.1FiguresReferencesRelatedDetails Fifth International Conference on Engineering Geophysics, Al Ain, UAE, 21–24 October 2019ISSN (online):2159-6832Copyright: 2020 Pages: 315 publication data© 2020 Published in electronic format with permission by the Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished: 03 Apr 2020 CITATION INFORMATION Bing Zhou*, Saif Ullah, Muhammad Asim, Moosoo Won, and Safeya Alkatheeri, (2020), "An alternative to the traditional electrode arrays for 2D electrical resistivity tomography: Enhanced version of the common gradient measurement," SEG Global Meeting Abstracts : 28-31. https://doi.org/10.1190/iceg2019-007.1 Plain-Language Summary KeywordsresistivitynumericalaquiferimagingarraysPDF DownloadLoading ...

SUMMARYIn seismic wave modelling, the boundary reflections caused by the computational grid edges should be reduced to produce accurate simulation results. The perfectly matched layer (PML) method is one of the popular techniques to suppress such artificial reflections, because it can be easily applied to the first-order wave equation in many numerical methods. However, one issue of the PML method is that the stability condition might be violated in complex elastic anisotropic media. In these cases, the PML method will not attenuate the boundary reflections but rather introduce strong artefacts in the simulation results. To tackle this problem, we propose a generalized stiffness reduction method (GSRM) as a substitute for the PML method. We first derive the stability conditions of the PML method and analyse the suitable conditions for their application to time- and frequency-domain seismic wave modelling. Then, we develop a simple and effective numerical implementation of the GSRM to attenuate the boundary reflections and apply it to seismic wave modelling in elastic anisotropic media. We give some numerical experiments to demonstrate the feasibility and advantages of the GSRM compared to the PML method. Numerical examples show the GSRM is conceptually simpler, more computationally efficient and more straightforward in terms of numerical implementation than the PML method for seismic modelling using either first- or second-order time- and frequency-domain wave equations.

PreviousNext No AccessSEG 2019 Workshop: Mathematical Geophysics: Traditional vs Learning, Beijing, China, 5–7 November 2019Limitation of the perfectly matched layer method on numerical seismic wave modellingAuthors: Bing ZhouMoosoo WonBing ZhouEarth Science, Khalifa University of Science and TechnologySearch for more papers by this author and Moosoo WonEarth Science, Khalifa University of Science and TechnologySearch for more papers by this authorhttps://doi.org/10.1190/iwmg2019_12.1 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract In seismic wave modeling, the artificial reflections caused by the computational grid edges should be removed to yield accurate simulation results. The perfectly matched layer (PML) method is one of the popular techniques to attenuate such artificial reflections, because of its direct applicability to the first-order wave equation in many numerical methods. However, the biggest problem of the PML method is that the qSV wave-fronts in complex anisotropic media may violate the stability conditions of the PML and ruin the numerical wavefield solutions. In this paper we show that the PML method loses its role and introduce strong artefacts in the simulation results. We must search for an alternative to the PML. To tackle this problem, we propose a generalized stiffness reduction method (GSRM) as a replacement for the PML method. We show new versions of the stability conditions of the PML method and then demonstrate the PML and GSRM performances in time-and frequency-domain seismic wave modeling in elastic anisotropic media. The numerical examples show the feasibility and advantages of the GSRM compared to the PML method. We show that the GSRM is conceptually simpler, more computationally efficient, and more straightforward in terms of numerical implementation than the PML method. Keywords: isotropic, numerical, polarization, time-domain, wave equationPermalink: https://doi.org/10.1190/iwmg2019_12.1FiguresReferencesRelatedDetails SEG 2019 Workshop: Mathematical Geophysics: Traditional vs Learning, Beijing, China, 5–7 November 2019ISSN (online):2159-6832Copyright: 2020 Pages: 138 publication data© 2020 Published in electronic format with permission by the Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished Online: 17 Jan 2020 CITATION INFORMATION Bing Zhou and Moosoo Won, (2020), "Limitation of the perfectly matched layer method on numerical seismic wave modelling," SEG Global Meeting Abstracts : 48-51. https://doi.org/10.1190/iwmg2019_12.1 Plain-Language Summary Keywordsisotropicnumericalpolarizationtime-domainwave equationPDF DownloadLoading ...