Borehole seismic‐source radiation in layered isotropic and anisotropic media: Real data analysis

Geophysics ◽  
1995 ◽  
Vol 60 (3) ◽  
pp. 748-757 ◽  
Author(s):  
Wenjie Dong ◽  
M. Nafi Toksöz
Keyword(s):  
Body Wave ◽  
Transversely Isotropic ◽  
Seismic Source ◽  
Real Data ◽  
Wave Radiation ◽  
Data Set ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Local Geology ◽  
Borehole Seismic

The source and receiver boreholes in crosshole seismology are usually considered unimportant except for their effects on body wave radiation and reception patterns. We present counter examples by analyzing a real crosswell data set from Buckhorn, Illinois, using computer simulations. The algorithm used is a combination of the boundary element method (for the source borehole) and the borehole coupling theory (for the receiver borehole) in transversely isotropic media. We find that most of the strong events in the data are inexplicable unless both boreholes are included in the modeling. The importance of the boreholes stems from the local geology which consists of highly contrasted sedimentary rocks. At a high‐contrast interface, wave conversion is no longer a negligible secondary effect. In fact, converted waves can be stronger than the primaries.

scholarly journals Frequency domain multiparameter acoustic inversion for transversely isotropic media with a vertical axis of symmetry

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. C1-C14 ◽  
Author(s):  
Ramzi Djebbi ◽  
Tariq Alkhalifah
Keyword(s):  
Frequency Domain ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
The Other ◽  
Sensitivity Analyses ◽  
Data Set ◽  
Trade Off ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Axis Of Symmetry

Multiparameter full-waveform inversion for transversely isotropic media with a vertical axis of symmetry (VTI) suffers from the trade-off between the parameters. The trade-off results in the leakage of one parameter’s update into the other. It affects the accuracy and convergence of the inversion. The sensitivity analyses suggested a parameterization using the horizontal velocity [Formula: see text], Thomsen’s parameter [Formula: see text], and the anelliptic parameter [Formula: see text] to reduce the trade-off for surface recorded seismic data. We aim to invert for this parameterization using the scattering integral (SI) method. The available Born sensitivity kernels, within this approach, can be used to calculate additional inversion information. We mainly compute the diagonal of the approximate Hessian, used as a conjugate-gradient preconditioner, and the gradients’ step lengths. We consider modeling in the frequency domain. The large computational cost of the SI method can be avoided with direct Helmholtz equation solvers. We applied our method to the VTI Marmousi II model for various inversion strategies. We found that we can invert the [Formula: see text] accurately. For the [Formula: see text] parameter, only the short wavelengths are well-recovered. On the other hand, the [Formula: see text] parameter impact is weak on the inversion results and can be fixed. However, a good background [Formula: see text], with accurate long wavelengths, is needed to correctly invert for [Formula: see text]. Furthermore, we invert a real data set acquired by CGG from offshore Australia. We simultaneously invert all three parameters using our inversion approach. The velocity model is improved, and additional layers are recovered. We confirm the accuracy of the results by comparing them with well-log information, as well as looking at the data and angle gathers.

Kirchhoff time migration for transversely isotropic media: An application to Trinidad data

Geophysics ◽  
2006 ◽  
Vol 71 (1) ◽  
pp. S29-S35 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Data Set ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Higher Order Terms ◽  
Isotropic Media ◽  
Migration Method ◽  
Vti Media ◽  
Vertical Inhomogeneity

Using a newly developed nonhyperbolic offset-mid-point traveltime equation for prestack Kirchhoff time migration, instead of the conventional double-square-root (DSR) equation, results in overall better images from anisotropic data. Specifically, prestack Kirchhoff time migration for transversely isotropic media with a vertical symmetry axis (VTI media) is implemented using an analytical offset-midpoint traveltime equation that represents the equivalent of Cheop's pyramid for VTI media. It includes higher-order terms necessary to better handle anisotropy as well as vertical inhomogeneity. Application of this enhanced Kirchhoff time-migration method to the anisotropic Marmousi data set demonstrates the effectiveness of the approach. Further application of the method to field data from Trinidad results in sharper reflectivity images of the subsurface, with the faults better focused and positioned than with images obtained using isotropic methods. The superiority of the anisotropic time migration is evident in the flatness of the image gathers.

Nonlinear traveltime inversion scheme for crosshole seismic tomography in tilted transversely isotropic media

Geophysics ◽  
2008 ◽  
Vol 73 (4) ◽  
pp. D17-D33 ◽  
Author(s):  
Bing Zhou ◽  
Stewart Greenhalgh ◽  
Alan Green
Keyword(s):  
Seismic Tomography ◽  
Velocity Structure ◽  
Body Wave ◽  
Transversely Isotropic ◽  
The Body ◽  
Body Waves ◽  
Inversion Method ◽  
Perturbation Equation ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Crosshole seismic tomography often is applied to image the velocity structure of an interwell medium. If the rocks are anisotropic, the tomographic technique must be adapted to the complex situation; otherwise, it leads to a false interpretation. We propose a nonlinear kinematic inversion method for crosshole seismic tomography in composite transversely isotropic media with known dipping symmetry axes. This method is based on a new version of the first-order traveltime perturbation equation. It directly uses the derivative of the phase velocity rather than the eigenvectors of the body-wave modes to overcome the singularity problem for application to the two quasi-shear waves. We applied an iterative nonlinear solver incorporating our kinematic ray-tracing scheme and directly compute the Jacobian matrix in an arbitrary reference medium. This reconstructs the five elastic moduli or Thomsen parameters from the first-arrival traveltimes of the three seismic body waves (qP, qSV, qSH) in strongly and weakly anisotropic media. We conducted three synthetic experiments that involve determining anisotropic parameters for a homogeneous rock, reconstructing a fault embedded in a strongly anisotropic background, and imaging a complicated four-layer model containing a small channel and a buried dipping interface. We compared results of our nonlinear inversion method with isotropic tomography and the traditional linear anisotropic inversion scheme, which showed the capability and superiority of the new scheme for crosshole tomographic imaging.

Three-parameter normal moveout correction in layered anisotropic media: A stretch-free approach

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. C129-C142 ◽  
Author(s):  
Mohammad Mahdi Abedi ◽  
Mohammad Ali Riahi ◽  
Alexey Stovas
Keyword(s):  
Transversely Isotropic ◽  
Real Data ◽  
Data Sets ◽  
P Waves ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Nmo Correction ◽  
Recorded Data ◽  
Normal Moveout Correction ◽  
Vti Media

In conventional normal moveout (NMO) correction, some parts of the recorded data at larger offsets are discarded because of NMO distortions. Deviation from the true traveltime of reflections due to the anisotropy and heterogeneity of the earth, and wavelet stretching are two reasons of these distortions. The magnitudes of both problems increase with increasing the offset to depth ratio. Therefore, to be able to keep larger offsets of shallower reflections, both problems should be obviated. Accordingly, first, we have studied different traveltime approximations being in use, alongside new parameterizations for two classical functional equations, to select suitable equations for NMO correction. We numerically quantify the fitting accuracy and uncertainty of known nonhyperbolic traveltime approximations for P-waves in transversely isotropic media with vertical symmetry axis (VTI). We select three suitable three-parameter approximations for NMO in layered VTI media as the VTI generalized moveout approximation, a double-square-root approximation, and a perturbation-based approximation. Second, we have developed an extension of the earlier proposed stretch-free NMO method, using the selected moveout approximations. This method involves an automatic modification of the input parameters in anisotropic NMO correction, for selected reflections. Our anisotropic stretch-free NMO method is tested on synthetic and three real data sets from Gulf of Mexico and Iranian oil fields. The results verify the success of the method in extending the usable offsets, by generating flat and stretch-free NMO corrected reflections.

Laboratory results for the features of body‐wave propagation in a transversely isotropic media

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1921-1924 ◽  
Author(s):  
Young‐Fo Chang ◽  
Chih‐Hsiung Chang
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Elastic Anisotropy ◽  
Body Wave ◽  
Transversely Isotropic ◽  
Sedimentary Basins ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Much of the earth’s crust appears to have some degree of elastic anisotropy (Crampin, 1981; Crampin and Lovell, 1991; Helbig, 1993). The phenomena of elastic wave propagation in anisotropic media are more complex than those in isotropic media. Shear‐wave propagation in an orthorhombic physical model is most complex when the direction of the wave is close to the neighborhood of the cusp on the group velocity surfaces (Brown et al., 1991). The first identification of singularities in wave propagation through sedimentary basins occurred in the examination of shear‐wave splitting in multioffset vertical seismic profiles (VSPs) at a borehole site in the Paris Basin (Bush and Crampin, 1991), where large variations in shear‐wave polarizations in propagation directions close to point singularities were observed. Computation of synthetic seismograms for layer sequences showed that the shear‐wave polarizations and amplitudes were irregular near point singularities (Crampin, 1991).

scholarly journals Approximations for traveltime, slope, curvature, and geometrical spreading of elastic waves in layered transversely isotropic media

Geophysics ◽  
2021 ◽  
pp. 1-68
Author(s):  
Mohammad Mahdi Abedi ◽  
David Pardo ◽  
Alexey Stovas
Keyword(s):  
Body Wave ◽  
Transversely Isotropic ◽  
Wave Mode ◽  
Geometrical Spreading ◽  
Converted Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Ray Parameter ◽  
Approximate Equations ◽  
Wave Modes

Each seismic body wave, including quasi compressional, shear, and converted wave modes, carries useful subsurface information. For processing, imaging, amplitude analysis, and forward modeling of each wave mode, we need approximate equations of traveltime, slope (ray-parameter), and curvature as a function of offset. Considering the large offset coverage of modern seismic acquisitions, we propose new approximations designed to be accurate at zero and infinitely large offsets over layered transversely isotropic media with vertical symmetry axis (VTI). The proposed approximation for traveltime is a modified version of the extended generalized moveout approximation that comprises six parameters. The proposed direct approximations for ray-parameter and curvature use new, algebraically simple, equations with three parameters. We define these parameters for each wave mode without ray tracing so that we have similar approximate equations for all wave modes that only change based on the parameter definitions. However, our approximations are unable to reproduce S-wave triplications that may occur in some strongly anisotropic models. Using our direct approximation of traveltime derivatives, we also obtain a new expression for the relative geometrical spreading. We demonstrate the high accuracy of our approximations using numerical tests on a set of randomly generated multilayer models. Using synthetic data, we present simple applications of our approximations for normal moveout correction and relative geometrical spreading compensation of different wave modes.

scholarly journals Body‐wave radiation patterns and AVO in transversely isotropic media

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1409-1425 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Reflection Coefficient ◽  
Radiation Pattern ◽  
Transversely Isotropic ◽  
P Wave ◽  
Wave Radiation ◽  
Reflection Coefficients ◽  
Radiation Patterns ◽  
Avo Analysis ◽  
Transversely Isotropic Media ◽  
Isotropic Media

The angular dependence of reflection coefficients may be significantly distorted in the presence of elastic anisotropy. However, the influence of anisotropy on amplitude variation with offset (AVO) analysis is not limited to reflection coefficients. AVO signatures (e.g., AVO gradient) in anisotropic media are also distorted by the redistribution of energy along the wavefront of the wave traveling down to the reflector and back up to the surface. Significant anisotropy above the target horizon may be rather typical of sand‐shale sequences commonly encountered in AVO analysis. Here, I examine the influence of P‐ and S‐wave radiation patterns on AVO in the most common anisotropic model—transversely isotropic media. A concise analytic solution, obtained in the weak‐anisotropy approximation, provides a convenient way to estimate the impact of the distortions of the radiation patterns on AVO results. It is shown that the shape of the P‐wave radiation pattern in the range of angles most important to AVO analysis (0–40°) is primarily dependent on the difference between Thomsen parameters ε and δ. For media with ε − δ > 0 (the most common case), the P‐wave amplitude may drop substantially over the first 25–40° from vertical. There is no simple correlation between the strength of velocity anisotropy and angular amplitude variations. For instance, for models with a fixed positive ε − δ the amplitude distortions are less pronounced for larger values of ε and δ. The distortions of the SV‐wave radiation pattern are usually much more significant than those for the P‐wave. The anisotropic directivity factor for the incident wave may be of equal or greater importance for AVO than the influence of anisotropy on the reflection coefficient. Therefore, interpretation of AVO anomalies in the presence of anisotropy requires an integrated approach that takes into account not only the reflection coefficient but also the wave propagation above the reflector.

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.

Variation of stacking velocity in transversely isotropic media

1995 ◽  
Vol 26 (2-3) ◽  
pp. 431-436 ◽  
Author(s):  
Patrick N.(Jr). Okoye ◽  
N. F. Uren ◽  
W. Waluyo
Keyword(s):  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Isotropic Media
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