Viscoelastic true-amplitude prestack reverse-time depth migration

Geophysics ◽  
2008 ◽  
Vol 73 (4) ◽  
pp. S143-S155 ◽  
Author(s):  
Feng Deng ◽  
George A. McMechan
Keyword(s):  
Synthetic Data ◽  
Wave Impedance ◽  
P Wave ◽  
Reverse Time ◽  
Recursive Procedure ◽  
Depth Migration ◽  
Transmission Coefficients ◽  
Intrinsic Attenuation ◽  
Anelastic Attenuation ◽  
Attenuation Models

A new true-amplitude prestack elastic depth-migration algorithm includes compensation for transmission and anelastic attenuation losses in an isotropic medium. Geometric spreading and its compensation are incorporated by extrapolating up- and downgoing waves using a full two-way wave equation. Intrinsic attenuation is simulated and compensated for using composite memory variables derived from standard linear solid relaxation mechanisms. Zoeppritz equations and their approximations are used to compute and analyze the angle-dependent reflection/transmission coefficients; converted energy is included at each interface. Transmission losses for compressional waves are compensated, based on estimation of angle-dependent elastic reflectivity using a two-pass recursive procedure. The image condition is the ratio of the compressional receiver/source wavefield amplitudes. Application to synthetic data from a dipping-layer model and a salt model accurately extracts P-velocity, S-velocity, density, and P-wave impedance beneath the target reflector, even under a salt overhang. Factors not explicitly considered include building of the smooth background velocity and attenuation models, estimates of the source time function, directivity and coupling, multipathing arrivals, and effects of attenuation and anisotropy on the reflection/transmission coefficients.

3-D elastic prestack, reverse‐time depth migration

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 597-609 ◽  
Author(s):  
Wen‐Fong Chang ◽  
George A. McMechan
Keyword(s):  
Finite Differences ◽  
Synthetic Data ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
Depth Migration ◽  
Full Wave ◽  
Source Data ◽  
Recorded Data ◽  
Time Extrapolation

By combining and extending previous algorithms for 2-D prestack elastic migration and 3-D prestack acoustic migration, a full 3-D elastic prestack depth migration algorithm is developed. Reverse‐time extrapolation of the recorded data is by 3-D elastic finite differences; computation of the image time for each point in the 3-D volume is by 3-D acoustic finite differences. The algorithm operates on three‐component, vector‐wavefield common‐source data and produces three‐component vector reflectivity distributions. Converted P‐to‐S reflections are automatically imaged with the primary P‐wave reflections. There are no dip restrictions as the full wave equation is used. The algorithm is illustrated by application to synthetic data from three models; a flat reflector, a dipping truncated wedge overlying a flat reflector, and the classical French double dome and fault model.

3-D prestack migration in anisotropic media

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 79-90 ◽  
Author(s):  
Zhengxin Dong ◽  
George A. McMechan
Keyword(s):  
A Priori ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Anisotropic Media ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Prestack Migration ◽  
Time Migration

A three‐dimensional (3-D) prestack reverse‐time migration algorithm for common‐source P‐wave data from anisotropic media is developed and illustrated by application to synthetic data. Both extrapolation of the data and computation of the excitation‐time imaging condition are implemented using a second‐order finite‐ difference solution of the 3-D anisotropic scalar‐wave equation. Poorly focused, distorted images are obtained if data from anisotropic media are migrated using isotropic extrapolation; well focused, clear images are obtained using anisotropic extrapolation. A priori estimation of the 3-D anisotropic velocity distribution is required. Zones of anomalous, directionally dependent reflectivity associated with anisotropic fracture zones are detectable in both the 3-D common‐ source data and the corresponding migrated images.

True-amplitude prestack depth migration

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. S155-S166 ◽  
Author(s):  
Feng Deng ◽  
George A. McMechan
Keyword(s):  
Velocity Ratio ◽  
Synthetic Data ◽  
Transmission Losses ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Prestack Migration ◽  
Time Migration ◽  
Geometric Spreading

Most current true-amplitude migrations correct only for geometric spreading. We present a new prestack depth-migration method that uses the framework of reverse-time migration to compensate for geometric spreading, intrinsic [Formula: see text] losses, and transmission losses. Geometric spreading is implicitly compensated by full two-way wave propagation. Intrinsic [Formula: see text] losses are handled by including a [Formula: see text]-dependent term in the wave equation. Transmission losses are compensated based on an estimation of angle-dependent reflectivity using a two-pass recursive reverse-time prestack migration. The image condition used is the ratio of receiver/source wavefield amplitudes. Two-dimensional tests using synthetic data for a dipping-layer model and a salt model show that loss-compensating prestack depth migration can produce reliable angle-dependent reflection coefficients at the target. The reflection coefficient curves are fitted to give least-squares estimates of the velocity ratio at the target. The main new result is a procedure for transmission compensation when extrapolating the receiver wavefield. There are still a number of limitations (e.g., we use only scalar extrapolation for illustration), but these limitations are now better defined.

Anisotropic parsimonious prestack depth migration

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. S25-S36 ◽  
Author(s):  
Ernesto V. Oropeza ◽  
George A. McMechan
Keyword(s):  
Model Building ◽  
Computing Time ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Velocity Model ◽  
P Wave ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Tti Media ◽  
Map Migration

An efficient Kirchhoff-style prestack depth migration, called “parsimonious” migration, was developed a decade ago for isotropic 2D and 3D media by using measured slownesses to reduce the amount of ray tracing by orders of magnitude. It is conceptually similar to “map” migration, but its implementation has some differences. We have extended this approach to 2D tilted transversely isotropic (TTI) media and illustrated it with synthetic P-wave data. Although the framework of isotropic parsimonious may be retained, the extension to TTI media requires redevelopment of each of the numerical components, calculation of the phase and group velocity for TTI media, development of a new two-point anisotropic ray tracer, and substitution of an initial-angle isotropic shooting ray-trace algorithm for an anisotropic one. The model parameterization consists of Thomsen’s parameters ([Formula: see text], [Formula: see text], [Formula: see text]) and the tilt angle of the symmetry axis of the TI medium. The parsimonious anisotropic migration algorithm is successfully applied to synthetic data from a TTI version of the Marmousi2 model. The quality of the image improves by weighting the impulse response by the calculation of the anisotropic Fresnel radius. The accuracy and speed of this migration makes it useful for anisotropic velocity model building. The elapsed computing time for 101 shots for the Marmousi2 TTI model is 35 s per shot (each with 501 traces) in 32 Opteron cores.

Elastic least-squares reverse time migration with hybrid l1/l2 misfit function

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S271-S291 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Peng Yang ◽  
Wencai Xu ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Adjoint Equations ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Wave Image

We have developed the theory and synthetic tests of elastic least-squares reverse time migration (ELSRTM). In this method, a least-squares reverse time migration algorithm is used to image multicomponent seismic data based on the first-order elastic velocity-stress wave equation, in which the linearized elastic modeling equations are used for forward modeling and its adjoint equations are derived based on the adjoint-state method for back propagating the data residuals. Also, we have developed another ELSRTM scheme based on the wavefield separation technique, in which the P-wave image is obtained using P-wave forward and adjoint wavefields and the S-wave image is obtained using P-wave forward and S-wave adjoint wavefields. In this way, the crosstalk artifacts can be minimized to a significant extent. In general, seismic data inevitably contain noise. We apply the hybrid [Formula: see text] misfit function to the ELSRTM algorithm to improve the robustness of our ELSRTM to noise. Numerical tests on synthetic data reveal that our ELSRTM, when compared with elastic reverse time migration, can produce images with higher spatial resolution, more-balanced amplitudes, and fewer artifacts. Moreover, the hybrid [Formula: see text] misfit function makes the ELSRTM more robust than the [Formula: see text] misfit function in the presence of noise.

Polarization-based wave-equation migration velocity analysis in acoustic media

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. U77-U88 ◽  
Author(s):  
Qunshan Zhang ◽  
George A. McMechan
Keyword(s):  
Wave Equation ◽  
Velocity Ratio ◽  
Empirical Relation ◽  
Synthetic Data ◽  
P Wave ◽  
Reverse Time ◽  
Seismic Reflection Data ◽  
Prestack Migration ◽  
Time Migration ◽  
Acoustic Media

The source extrapolation step in wave-equation prestack reverse-time migration gives wavefield polarization information, which can be used to generate angle-domain common-image gathers (ADCIGs) from seismic reflection data from acoustic media. Concatenation of P-wave polarization segments gives wavefield propagation paths (“wavepaths”), which are similar to the raypaths in ray-based velocity tomography. The ADCIGs provide residual depth moveout (RMO) information, from which a system of linear equations is constructed for tomography to solve for the velocity ratio used for velocity updating. An empirical relation between the RMO data and the velocity ratio updates reduces the amount of computation, and is stabilized by the feedback provided by the iterative loop through prestack migration, to RMO, to velocity update, to prestack migration. Correcting the RMOs to flatten the ADGIGs is the convergence condition. Synthetic data for a layered model with a fault successfully illustrates the method.

A wavefield-separation-based elastic least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S279-S297 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Numerical Tests ◽  
Time Migration

Elastic least-squares reverse time migration (ELSRTM) has the potential to provide improved subsurface reflectivity estimation. Compared with elastic RTM (ERTM), ELSRTM can produce images with higher spatial resolution, more balanced amplitudes, and fewer artifacts. However, the crosstalk between P- and S-waves can significantly degrade the imaging quality of ELSRTM. We have developed an ELSRTM method to suppress the crosstalk artifacts. This method includes three crucial points. The first is that the forward and backward wavefields are extrapolated based on the separated elastic velocity-stress equation of P- and S-waves. The second is that the separated vector P- and S-wave residuals are migrated to form reflectivity images of Lamé constants [Formula: see text] and [Formula: see text] independently. The third is that the reflectivity images of [Formula: see text] and [Formula: see text] are obtained by the vector P-wave wavefields achieved in the backward extrapolation of the separated vector P-wave residuals and the vector S-wave wavefields achieved in the backward extrapolation of the separated vector S-wave residuals, respectively. Numerical tests with synthetic data demonstrate that our ELSRTM method can produce images free of crosstalk artifacts. Compared with ELSRTM based on the coupled wavefields, our ELSRTM method has better convergence and higher accuracy.

3D coupled acoustic-elastic migration with topography and bathymetry based on spectral-element and adjoint methods

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. S193-S202 ◽  
Author(s):  
Yang Luo ◽  
Jeroen Tromp ◽  
Bertrand Denel ◽  
Henri Calandra
Keyword(s):  
Surface Topography ◽  
Large Scale ◽  
Mass Density ◽  
Spectral Element ◽  
Wave Impedance ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wave Speeds ◽  
Time Migration

In the context of the adjoint method, we considered 3D coupled acoustic-elastic migration in the presence of surface topography and/or bathymetry. Isotropic elastic imaging involves three primary kernels, related to mass density and shear and bulk moduli, and various secondary kernels, for example, related to P-wave impedance and compressional and shear-wave speeds. Similar to reverse-time migration, these kernels reflect the constructive interference between a forward wavefield generated by active sources and an adjoint wavefield triggered by simultaneously back propagating recorded reflections from all receivers. Forward and adjoint wavefields were simulated using a spectral-element method, which, due to its weak nature, captures free-surface topography in land surveys and bathymetry in marine acquisition. To avoid storing the entire 3D forward wavefield, required for calculating its interaction with the adjoint wavefield, we only saved information on domain boundaries and reconstructed the forward wavefield while simulating the adjoint wavefield. Their interactions were calculated and integrated on the fly, thereby eliminating storage issues but doubling memory and CPU requirements. Our 3D images confirmed a previous conclusion based on 2D simulations, namely, that the impedance kernel best highlights reflectors, whereas wave-speed kernels constrain large-scale structures, i.e., the background model.

scholarly journals Machine Learning as a Seismic Prior Velocity Model Building Method for Full-Waveform Inversion: A Case Study from Colombia

2021 ◽  
Vol 178 (2) ◽  
pp. 423-448
Author(s):  
Ursula Iturrarán-Viveros ◽  
Andrés M. Muñoz-García ◽  
Octavio Castillo-Reyes ◽  
Khemraj Shukla
Keyword(s):  
Machine Learning ◽  
Initial Velocity ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Wave Impedance ◽  
P Wave ◽  
Well Log ◽  
Velocity Models ◽  
Full Waveform

AbstractWe use machine learning algorithms (artificial neural networks, ANNs) to estimate petrophysical models at seismic scale combining well-log information, seismic data and seismic attributes. The resulting petrophysical images are the prior inputs in the process of full-waveform inversion (FWI). We calculate seismic attributes from a stacked reflected 2-D seismic section and then train ANNs to approximate the following petrophysical parameters: P-wave velocity ($$V_\mathrm{{p}}$$ V p ), density ($$\rho $$ ρ ) and volume of clay ($$V_\mathrm{{clay}}$$ V clay ). We extend the use of the $$V_\mathrm{{clay}}$$ V clay by constraining it with the well lithology and we establish two classes: sands and shales. Consequently, machine learning allows us to build an initial estimate of the earth property model ($$V_\mathrm{{p}}$$ V p ), which is iteratively refined to produce a synthetic seismogram that matches the observed seismic data. We apply the 1-D Kennett method as a forward modeling tool to create synthetic data with the images of $$V_\mathrm{{p}}$$ V p , $$\rho $$ ρ and the thickness of layers (sands or shales) obtained with the ANNs. A nonlinear least-squares inversion algorithm minimizes the residual (or misfit) between observed and synthetic full-waveform data, which improves the $$V_\mathrm{{p}}$$ V p resolution. In order to show the advantage of using the ANN velocity model as the initial velocity model for the inversion, we compare the results obtained with the ANNs and two other initial velocity models. One of these alternative initial velocity models is computed via P-wave impedance, and the other is achieved by velocity semblance analysis: root-mean-square velocity (RMS). The results are in good agreement when we use $$\rho $$ ρ and $$V_\mathrm{{p}}$$ V p obtained by ANNs. However, the results are poor and the synthetic data do not match the real acquired data when using the semblance velocity model and the $$\rho $$ ρ from the well log (constant for the entire 2-D section). Nevertheless, the results improve when including $$\rho $$ ρ , the layered structure driven by the $$V_\mathrm{{clay}}$$ V clay (both obtained with ANNs) and the semblance velocity model. When doing inversion starting with the initial $$V_\mathrm{{p}}$$ V p model estimated using the P-wave impedance, there is some gain of the final $$V_\mathrm{{p}}$$ V p with respect to the RMS initial $$V_\mathrm{{p}}$$ V p . To assess the quality of the inversion of $$V_\mathrm{{p}}$$ V p , we use the information for two available wells and compare the final $$V_\mathrm{{p}}$$ V p obtained with ANNs and the final $$V_\mathrm{{p}}$$ V p computed with the P-wave impedance. This shows the benefit of employing ANNs estimations as prior models during the inversion process to obtain a final $$V_\mathrm{{p}}$$ V p that is in agreement with the geology and with the seismic and well-log data. To illustrate the computation of the final velocity model via FWI, we provide an algorithm with the detailed steps and its corresponding GitHub code.

Reverse time migration in tilted transversely isotropic media

2020 ◽  
Vol 38 (2) ◽  
Author(s):  
Razec Cezar Sampaio Pinto da Silva Torres ◽  
Leandro Di Bartolo
Keyword(s):  
Seismic Anisotropy ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computer Clusters ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Tti Media

ABSTRACT. Reverse time migration (RTM) is one of the most powerful methods used to generate images of the subsurface. The RTM was proposed in the early 1980s, but only recently it has been routinely used in exploratory projects involving complex geology – Brazilian pre-salt, for example. Because the method uses the two-way wave equation, RTM is able to correctly image any kind of geological environment (simple or complex), including those with anisotropy. On the other hand, RTM is computationally expensive and requires the use of computer clusters. This paper proposes to investigate the influence of anisotropy on seismic imaging through the application of RTM for tilted transversely isotropic (TTI) media in pre-stack synthetic data. This work presents in detail how to implement RTM for TTI media, addressing the main issues and specific details, e.g., the computational resources required. A couple of simple models results are presented, including the application to a BP TTI 2007 benchmark model.Keywords: finite differences, wave numerical modeling, seismic anisotropy. Migração reversa no tempo em meios transversalmente isotrópicos inclinadosRESUMO. A migração reversa no tempo (RTM) é um dos mais poderosos métodos utilizados para gerar imagens da subsuperfície. A RTM foi proposta no início da década de 80, mas apenas recentemente tem sido rotineiramente utilizada em projetos exploratórios envolvendo geologia complexa, em especial no pré-sal brasileiro. Por ser um método que utiliza a equação completa da onda, qualquer configuração do meio geológico pode ser corretamente tratada, em especial na presença de anisotropia. Por outro lado, a RTM é dispendiosa computacionalmente e requer o uso de clusters de computadores por parte da indústria. Este artigo apresenta em detalhes uma implementação da RTM para meios transversalmente isotrópicos inclinados (TTI), abordando as principais dificuldades na sua implementação, além dos recursos computacionais exigidos. O algoritmo desenvolvido é aplicado a casos simples e a um benchmark padrão, conhecido como BP TTI 2007.Palavras-chave: diferenças finitas, modelagem numérica de ondas, anisotropia sísmica.

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