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AuthorAlkhalifah, Tariq Ali (5)Kazei, Vladimir (2)Wu, Zedong (2)Cheng, Jiubing (1)Dunham, Eric M (1)View MoreDepartmentPhysical Sciences and Engineering (PSE) Division (9)Earth Science and Engineering Program (7)Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (1)Extreme Computing Research Center (1)Seismic Wave Analysis Group (1)Journal

Geophysical Journal International (10)

KAUST Grant Number2230 (1)AEA-7000000083 (1)BAS/1/1339-01-01 (1)PublisherOxford University Press (OUP) (9)Oxford University Press (1)SubjectFull waveform inversion (3)Inverse theory (2)Seismic anisotropy (2)3D scattering media (1)Acoustic (1)View MoreType
Article (10)

Year (Issue Date)
2018 (10)

Item AvailabilityOpen Access (10)

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Spectral-infinite-element simulations of gravity anomalies

Gharti, Hom Nath; Tromp, Jeroen; Zampini, Stefano (Geophysical Journal International, Oxford University Press (OUP), 2018-08-07) [Article]

Gravity anomalies induced by density heterogeneities are governed by Poisson's equation. Most existing methods for modelling such anomalies rely on its integral solution. In this approach, for each observation point, an integral over the entire density distribution needs to be carried out, and the computational cost is proportional to the number of observation points. Frequently, such methods are sensitive to high density contrasts due to inaccurate resolution of the volume integral. We introduce a new approach which directly solves a discretized form of the Poisson/Laplace equation. The main challenge in our approach involves the unbounded nature of the problem, because the potential exists in all of space. To circumvent this challenge, we combine a mapped infinite-element approach with a spectral-element method. Spectral elements represent the domain of interest, and a single layer of infinite elements captures outer space. To solve the weak form of the Poisson/Laplace equation, we use Gauss-Legendre- Lobatto (GLL) quadrature in spectral elements inside the domain of interest. Outside the domain, we use Gauss-Radau quadrature in the infinite direction, and GLL quadrature in the other directions. We illustrate the efficiency and accuracy of our method by comparing calculated gravity anomalies for various density heterogeneities with corresponding analytical solutions. Finally, we consider a complex 3-D model of an ore mine, which consists of both positive and negative density anomalies.

Elastic wave-equation-based reflection kernel analysis and traveltime inversion using wave mode decomposition

Wang, Tengfei; Cheng, Jiubing; Guo, Qiang; Wang, Chenlong (Geophysical Journal International, Oxford University Press (OUP), 2018-07-19) [Article]

Elastic reflection waveform inversion (ERWI) utilizes reflections to update the low and intermediate wavenumbers in the deeper part of elastic models and can provide good initial models for elastic full waveform inversion (EFWI). Although ERWI aims to mitigate the nonlinearity of inversion when starting from a poor initial model, it suffers from the cycle-skipping problem due to the objective function of waveform fitting. Building initial P- and S-wave velocity models for EFWI through elastic wave-equation reflection traveltime inversion (ERTI) would be effective and robust since traveltime information relates to the background model more linearly. However, the current implementations of acoustic traveltime inversion is not straightforward in elastic media due to the existence of S-wavefields. Wave mode decomposition, both on the recording surface and in the extrapolated wavefields, is important for ERTI. First, for seismic data with P-wave sources, the P/S separation of multicomponent seismograms isolates the PP and PS reflection events and thus make it possible to extract the event-to-event time-shifts of these isolated reflections through dynamic image warping (DIW). Then, we can use the traveltime residuals of PP and PS reflections to build the objective function for ERTI. Second, based on the investigation of the complicated reflection kernels in an elastic medium, we demonstrate the necessity of wave mode decomposition applied on the extrapolated elastic wavefields, to suppress the artefacts induced by the undesirable cross-correlations of the components in forward and back-propagated wavefields. Therefore, the decomposition of surface recording data and extrapolated wavefields guarantees the dominate contribution of the traveltime is included during the ERTI. Accordingly, we propose a two-stage method to first build the P-wave background velocity using the separated PP reflections and then build the S-wave background velocity using the separated PS reflections based on the well-recovered P-wave velocity model. A numerical example of the Sigsbee2A model shows the effectiveness of the proposed ERTI approach.

Normal modes in orthorhombic media

Ivanov, Yuriy; Stovas, Alexey; Kazei, Vladimir (Geophysical Journal International, Oxford University Press, 2018-12-22) [Article]

Guided waves in a water layer overlaying an elastic half-space are known as normal modes. They are often present in seismic recordings at long offsets in shallow-water environment and generally considered coherent noise. The normal modes, however, carry important information about the near-surface and, as demonstrated by a number of authors, can be used to obtain the shallow velocity model. There is a growing evidence that the latter needs not to be isotropic due to various geological reasons. Motivated by that, we consider the normal-mode propagation in case the elastic half-space exhibits orthorhombic anisotropy. We derive the period equation that describes the normal-mode phase velocity dispersion. To simplify the complicated expression, we present acoustic and ellipsoidal orthorhombic approximations. We also outline the approach towards the group velocity and group azimuth calculation and apply it to the ellipsoidal case to obtain concise and intuitive expressions. Using numerical test, we study the relation between phase and group domains in elastic orthorhombic case. The deviation between velocities and azimuths in these domains is the strongest for low frequencies and it rapidly decreases with increasing frequency. For higher frequencies, the anisotropy effects of the underlaying half-space are barely detectable since the observed signal is composed mainly of the direct acoustic wave, resulting in the two domains being nearly indistinguishable.

Mach wave properties in the presence of source and medium heterogeneity

Vyas, Jagdish Chandra; Mai, Paul Martin; Galis, Martin; Dunham, Eric M; Imperatori, W (Geophysical Journal International, Oxford University Press (OUP), 2018-06-08) [Article]

We investigate Mach wave coherence for kinematic supershear ruptures with spatially heterogeneous source parameters, embedded in 3-D scattering media. We assess Mach wave coherence considering: (1) source heterogeneities in terms of variations in slip, rise time and rupture speed; (2) small-scale heterogeneities in Earth structure, parametrized from combinations of three correlation lengths and two standard deviations (assuming von Karman power spectral density with fixed Hurst exponent); and (3) joint effects of source and medium heterogeneities. Ground-motion simulations are conducted using a generalized finite-difference method, choosing a parametrization such that the highest resolved frequency is ~5 Hz. We discover that Mach wave coherence is slightly diminished at near-fault distances (<10 km) due to spatially variable slip and rise time; beyond this distance the Mach wave coherence is more strongly reduced by wavefield scattering due to small-scale heterogeneities in Earth structure. Based on our numerical simulations and theoretical considerations we demonstrate that the standard deviation of medium heterogeneities controls the wavefield scattering, rather than the correlation length. In addition,we find that peak ground accelerations in the case of combined source and medium heterogeneities are consistent with empirical ground-motion prediction equations for all distances, suggesting that in nature ground-shaking amplitudes for supershear ruptures may not be elevated due to complexities in the rupture process and seismic wave scattering.

Pure Quasi-P-wave calculation in transversely isotropic media using a hybrid method

Wu, Zedong; Liu, Hongwei; Alkhalifah, Tariq Ali (Geophysical Journal International, Oxford University Press (OUP), 2018-04-14) [Article]

The acoustic approximation for anisotropic media is widely used in current industry imaging and inversion algorithms mainly because P-waves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulas tend to be simpler, resulting in more efficient implementations, and depend on fewer medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from shear wave artifacts. Thus, we derive a new acoustic wave equation for wave propagation in transversely isotropic (TI) media, which is based on a partially separable approximation of the dispersion relation for TI media and free of shear wave artifacts. Even though our resulting equation is not a partial differential equation, it is still a linear equation. Thus, we propose to implement this equation efficiently by combining the finite difference approximation with spectral evaluation of the space-independent parts. The resulting algorithm provides solutions without the constrain of ε ≥ δ. Numerical tests demonstrate the effectiveness of the approach.

Micro-seismic imaging using a source function independent full waveform inversion method

Wang, Hanchen; Alkhalifah, Tariq Ali (Geophysical Journal International, Oxford University Press (OUP), 2018-03-26) [Article]

At the heart of micro-seismic event measurements is the task to estimate the location of the source micro-seismic events, as well as their ignition times. The accuracy of locating the sources is highly dependent on the velocity model. On the other hand, the conventional micro-seismic source locating methods require, in many cases manual picking of traveltime arrivals, which do not only lead to manual effort and human interaction, but also prone to errors. Using full waveform inversion (FWI) to locate and image micro-seismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, full waveform inversion of micro-seismic events faces incredible nonlinearity due to the unknown source locations (space) and functions (time). We developed a source function independent full waveform inversion of micro-seismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with these observed and modeled to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for the source wavelet in Z axis is extracted to check the accuracy of the inverted source image and velocity model. Also, angle gathers is calculated to assess the quality of the long wavelength component of the velocity model. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity for synthetic examples used here, like those corresponding to the Marmousi model and the SEG/EAGE overthrust model.

Multiparameter Elastic Full Waveform Inversion with Facies-based Constraints

Zhang, Zhendong; Alkhalifah, Tariq Ali; Naeini, Ehsan Zabihi; Sun, Bingbing (Geophysical Journal International, Oxford University Press (OUP), 2018-03-21) [Article]

Full waveform inversion (FWI) incorporates all the data characteristics to estimate the parameters described by the assumed physics of the subsurface. However, current efforts to utilize full waveform inversion beyond improved acoustic imaging, like in reservoir delineation, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Some anisotropic parameters are insufficiently updated because of their minor contributions to the surface collected data. Adding rock physics constraints to the inversion helps mitigate such limited sensitivity, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a global constraint for the whole area. Since similar rock formations inside the Earth admit consistent elastic properties and relative values of elasticity and anisotropy parameters (this enables us to define them as a seismic facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel approach to use facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such facies using Bayesian theory and update them at each iteration of the inversion using both the inverted models and a prior information. We take the uncertainties of the estimated parameters (approximated by radiation patterns) into consideration and improve the quality of estimated facies maps. Four numerical examples corresponding to different acquisition, physical assumptions and model circumstances are used to verify the effectiveness of the proposed method.

Elastic versus acoustic inversion for marine surveys

Mora, Peter; Wu, Zedong (Geophysical Journal International, Oxford University Press (OUP), 2018-04-25) [Article]

Full Wavefield Inversion (FWI) is a powerful and elegant approach for seismic imaging that is on the way to becoming the method of choice when processing exploration or global seismic data. In the case of processing marine survey data, one may be tempted to assume acoustic FWI is sufficient given that only pressure waves exist in the water layer. In this paper, we pose the question as to whether or not in theory – at least for a hard water bottom case – it should be possible to resolve the shear modulus or S-wave velocity in a marine setting using large offset data. We therefore conduct numerical experiments with idealized marine data calculated with the elastic wave equation. We study two cases, FWI of data due to a diffractor model, and FWI of data due to a fault model. We find that at least in idealized situation, elastic FWI of hard waterbottom data is capable of resolving between the two Lamé parameters λ and μ. Another numerical experiment with a soft waterbottom layer gives the same result. In contrast, acoustic FWI of the synthetic elastic data results in a single image of the first Lamé parameter λ which contains severe artefacts for diffraction data and noticable artefacts for layer reflection data. Based on these results, it would appear that at least, inversions of large offset marine data should be fully elastic rather than acoustic unless it has been demonstrated that for the specific case in question (offsets, model and water depth, practical issues such as soft sediment attenuation of shear waves or computational time), that an acoustic only inversion provides a reasonably good quality of image comparable to that of an elastic inversion. Further research with real data is required to determine the degree to which practical issues such as shear wave attenuation in soft sediments may affect this result.

Waveform inversion for orthorhombic anisotropy with P-waves: feasibility & resolution

Kazei, Vladimir; Alkhalifah, Tariq Ali (Geophysical Journal International, Oxford University Press (OUP), 2018-01-30) [Article]

Various parameterizations have been suggested to simplify inversions of first arrivals, or P −waves, in orthorhombic anisotropic media, but the number and type of retrievable parameters have not been decisively determined. We show that only six parameters can be retrieved from the dynamic linearized inversion of P −waves. These parameters are different from the six parameters needed to describe the kinematics of P −waves. Reflection-based radiation patterns from the P − P scattered waves are remapped into the spectral domain to allow for our resolution analysis based on the effective angle of illumination concept. Singular value decomposition of the spectral sensitivities from various azimuths, offset coverage scenarios, and data bandwidths allows us to quantify the resolution of different parameterizations, taking into account the signal-to-noise ratio in a given experiment. According to our singular value analysis, when the primary goal of inversion is determining the velocity of the P −waves, gradually adding anisotropy of lower orders (isotropic, vertically transversally isotropic, orthorhombic) in hierarchical parameterization is the best choice. Hierarchical parametrization reduces the tradeoff between the parameters and makes gradual introduction of lower anisotropy orders straightforward. When all the anisotropic parameters affecting P −wave propagation need to be retrieved simultaneously, the classic parameterization of orthorhombic medium with elastic stiffness matrix coefficients and density is a better choice for inversion. We provide estimates of the number and set of parameters that can be retrieved from surface seismic data in different acquisition scenarios. To set up an inversion process, the singular values determine the number of parameters that can be inverted and the resolution matrices from the parameterizations can be used to ascertain the set of parameters that can be resolved.

Full waveform inversion using envelope-based global correlation norm

Oh, Juwon; Alkhalifah, Tariq Ali (Geophysical Journal International, Oxford University Press (OUP), 2018-01-30) [Article]
Various parameterizations have been suggested to simplify inversions of first arrivals, or P −waves, in orthorhombic anisotropic media, but the number and type of retrievable parameters have not been decisively determined. We show that only six parameters can be retrieved from the dynamic linearized inversion of P −waves. These parameters are different from the six parameters needed to describe the kinematics of P −waves. Reflection-based radiation patterns from the P − P scattered waves are remapped into the spectral domain to allow for our resolution analysis based on the effective angle of illumination concept. Singular value decomposition of the spectral sensitivities from various azimuths, offset coverage scenarios, and data bandwidths allows us to quantify the resolution of different parameterizations, taking into account the signal-to-noise ratio in a given experiment. According to our singular value analysis, when the primary goal of inversion is determining the velocity of the P −waves, gradually adding anisotropy of lower orders (isotropic, vertically transversally isotropic, orthorhombic) in hierarchical parameterization is the best choice. Hierarchical parametrization reduces the tradeoff between the parameters and makes gradual introduction of lower anisotropy orders straightforward. When all the anisotropic parameters affecting P −wave propagation need to be retrieved simultaneously, the classic parameterization of orthorhombic medium with elastic stiffness matrix coefficients and density is a better choice for inversion. We provide estimates of the number and set of parameters that can be retrieved from surface seismic data in different acquisition scenarios. To set up an inversion process, the singular values determine the number of parameters that can be inverted and the resolution matrices from the parameterizations can be used to ascertain the set of parameters that can be resolved.

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