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.

Computed waveforms in transversely isotropic media

Geophysics ◽  
1982 ◽  
Vol 47 (5) ◽  
pp. 771-783 ◽  
Author(s):  
J. E. White
Keyword(s):  
Asymptotic Theory ◽  
Transversely Isotropic ◽  
Inversion Method ◽  
S Wave ◽  
Fourier Inversion ◽  
P Waves ◽  
Arrival Times ◽  
S Waves ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Radiation of elastic waves from a point force or from a localized torque into a transversely isotropic medium has been formulated in terms of displacement potentials, and transient waveforms have been computed by numerical Fourier inversion. For isotropic sandstone, this procedure yields P‐ and S‐wave pulses whose arrival times and magnitudes agree with theory. For a range of anisotropic rocks, arrival times of quasi‐P‐waves and quasi‐S‐waves agree with asymptotic theory. For extreme anisotropy, some quasi‐S‐wave pulses arrive at times which are not predicted by asymptotic theory. Magnitudes have not been compared with results of asymptotic theory, but decrease with distance appears to be in agreement. This Fourier inversion method gives near‐source changes in waveform which are not obtainable from the asymptotic theory.

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.

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.

Seismic parameters for transversely isotropic media

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 1908-1914 ◽  
Author(s):  
Bok S. Byun
Keyword(s):  
Velocity Structure ◽  
Transversely Isotropic ◽  
Wave Surface ◽  
Seismic Parameters ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
The Media ◽  
Local Properties ◽  
Exploration Seismology ◽  
Seismic Measurements

One of the most important problems in exploration seismology is to relate the surface seismic measurements with the subsurface geologic parameters. The concept of wavefront curvature has been in extensive use for this purpose. Byun (1982) developed relationships between several measurable seismic parameters (e.g., geometrical spreading and normal moveout velocity) and parameters of the media with elliptical velocity dependencies. This paper extends the wavefront curvature concept to more general, transversely isotropic media. After a brief discussion on ray tracing, a procedure is developed to describe the local properties of the ray based on an elliptical surface fit to the actual wave surface. The apparent velocities of the elliptical fit are then used to generalize the seismic parameters developed in Byun (1982). Simple numerical experiments are given to demonstrate the explorational significance of the theory. It is shown that the measurements of the normal moveout velocity are not sufficient to estimate the velocity structure of the transversely isotropic medium. The “side‐slip” effect can lead to significant errors in depth‐mapping dipping reflectors.

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.

scholarly journals Imaging the subsurface using induced seismicity and ambient noise: 3-D tomographic Monte Carlo joint inversion of earthquake body wave traveltimes and surface wave dispersion

2020 ◽  
Vol 222 (3) ◽  
pp. 1639-1655
Author(s):  
Xin Zhang ◽  
Corinna Roy ◽  
Andrew Curtis ◽  
Andy Nowacki ◽  
Brian Baptie
Keyword(s):  
Surface Wave ◽  
Ambient Noise ◽  
Velocity Structure ◽  
Joint Inversion ◽  
Body Wave ◽  
Source Parameters ◽  
Wave Dispersion ◽  
Inversion Method ◽  
Surface Wave Dispersion ◽  
Wave Data

SUMMARY Seismic body wave traveltime tomography and surface wave dispersion tomography have been used widely to characterize earthquakes and to study the subsurface structure of the Earth. Since these types of problem are often significantly non-linear and have non-unique solutions, Markov chain Monte Carlo methods have been used to find probabilistic solutions. Body and surface wave data are usually inverted separately to produce independent velocity models. However, body wave tomography is generally sensitive to structure around the subvolume in which earthquakes occur and produces limited resolution in the shallower Earth, whereas surface wave tomography is often sensitive to shallower structure. To better estimate subsurface properties, we therefore jointly invert for the seismic velocity structure and earthquake locations using body and surface wave data simultaneously. We apply the new joint inversion method to a mining site in the United Kingdom at which induced seismicity occurred and was recorded on a small local network of stations, and where ambient noise recordings are available from the same stations. The ambient noise is processed to obtain inter-receiver surface wave dispersion measurements which are inverted jointly with body wave arrival times from local earthquakes. The results show that by using both types of data, the earthquake source parameters and the velocity structure can be better constrained than in independent inversions. To further understand and interpret the results, we conduct synthetic tests to compare the results from body wave inversion and joint inversion. The results show that trade-offs between source parameters and velocities appear to bias results if only body wave data are used, but this issue is largely resolved by using the joint inversion method. Thus the use of ambient seismic noise and our fully non-linear inversion provides a valuable, improved method to image the subsurface velocity and seismicity.

Sign in / Sign up

Export Citation Format

Share Document