Skip Nav Destination
Filter
Filter
Filter
Filter
Filter

Search Results for
Diffraction and ray theory for wave propagation

Update search

Filter

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

### NARROW

Peer Reviewed

Format

Subjects

Journal

Publisher

Conference Series

Date

Availability

1-20 of 726 Search Results for

#### Diffraction and ray theory for wave propagation

**Follow your search**

Access your saved searches in your account

Would you like to receive an alert when new items match your search?

*Close Modal*

Sort by

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2004 SEG Annual Meeting, October 10–15, 2004

Paper Number: SEG-2004-2180

... ABSTRACT

**Ray****theory**is inadequate to explain the behavior of finite-frequency**wave****propagation**in media with structures smaller in size than wavelength and the Fresnel zone. In such complex structures,**wave****diffraction**effects are important. By performing an ultrasonic**wave**experiment, a newly...
Abstract

ABSTRACT Ray theory is inadequate to explain the behavior of finite-frequency wave propagation in media with structures smaller in size than wavelength and the Fresnel zone. In such complex structures, wave diffraction effects are important. By performing an ultrasonic wave experiment, a newly developed theory for finite-frequency wave propagation is successfully validated. The presented wave theory has a large potential in high-resolution seismic crosswell and VSP tomographic experiments.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2002 SEG Annual Meeting, October 6–11, 2002

Paper Number: SEG-2002-1348

... the coherent-state. Also, an early test of acoherent-state migration is shown. amplitude

**wave**equation chevrontexaco salt lake city phillips petroleum coherent-state approximation**wave**equation douglas asymptotic solution reservoir characterization**diffracted****wave****ray****theory**charles mosher...
Abstract

Summary The coherent-state transform is used in obtaining a global, uniform asymptotic solution of the wave equation. This solution approximates high-frequency wave propagation in generally heterogeneous media. The coherent-state approximation has an advantage over more traditional ray methods (direct and Fourier transform), because it leads to a well-defined approximation independent of the complexity of the caustics. As an illustration the edge diffraction problem is discussed. The diffracted wave has the correct asymptotic form but the accuracy depends on a parameter that controls the coherent-state. Also, an early test of acoherent-state migration is shown.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1993 SEG Annual Meeting, September 26–30, 1993

Paper Number: SEG-1993-0860

... coverage (Kendall & Thomson 1993). Waveform Results The

**ray**-**theory**and Maslov-**theory**synthetics are shown in Figures 2( top) and 2(bottom) respectively. There is no S-**wave**separation for**rays****propagating**horizontally, but with increasing declination, the delay time between the two (is-**waves**increases...
Proceedings Papers

Paper presented at the The Fourth International Offshore and Polar Engineering Conference, April 10–15, 1994

Paper Number: ISOPE-I-94-200

... crests. In the ocean of deep depth to moderate depth, with the assumption of small

**wave**amplitude, the**ray****theory**has been widely adopted to describe**wave**transformation by tracing**wave****rays**.**Ray****theory**claims that**wave**energy**propagates**merely along a**ray**; hence no energy flux transverse to**wave****ray**...
Abstract

ABSTRACT The objective of this paper is to provide a summary of the development of governing equations for wave diffraction and refraction in ocean of shallow water. The nonlinear mild-slope equations for the Fourier components of weakly nonlinear shallow-water waves as well as the parabolic approximation will be reviewed and discussed. A two-dimensional generalization of cnoidal waves in shallow water based on a multi -parameter family of exact solutions of KP equation is also included in content. WAVES EVOLUTION IN SHALLOW WATER In the ocean, the surface waves possess a wide spectrum of wavelength and period. The ocean waves undergo severe transformation due to the water depth variation and the influence of coastal currents, artificial structures, and geological features. In the course of evolution, waves change their propagation direction and speed and redistribute their energy along wave crests. In the ocean of deep depth to moderate depth, with the assumption of small wave amplitude, the ray theory has been widely adopted to describe wave transformation by tracing wave rays. Ray theory claims that wave energy propagates merely along a ray; hence no energy flux transverse to wave ray occurs. Therefore, the effects on wave evolution of wave amplitude variation along wave crests are totally Ignored by the ray theory. During the last decade, some numerical models based on ray theory have been developed m an attempt to tackle the phenomenon near caustics, where the ray theory breaks down (Bouws, 1982, Southgate, 1984). However, the wave diffraction nature is not properly considered by them. Improved wave theories and associated numerical models have been developed to consider the combined effects of refraction and diffraction. The mud - slope equation is known as an adequate model for describing the combined refraction and diffraction from deep water to shallow water.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1995 SEG Annual Meeting, October 8–13, 1995

Paper Number: SEG-1995-1301

... with the angular dis- tance from the shadow boundary.

**Diffracting**edges can termi- nate at vertices. In this case the edge-**diffracted****waves**have shadows of their own and the evanescent field in th- ows is represented by spherical vertex**waves****propagating**along vertex-**diffracted****rays**. The**diffracted**fields can...
Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1995 SEG Annual Meeting, October 8–13, 1995

Paper Number: SEG-1995-1317

... ABSTRACT No preview is available for this paper. wavelength amplitude

**diffraction**upstream oil & gas wavefront traveltime inclusion**wave**receiver reservoir characterization incident**ray**scatterer snapshot frequency modeling shadow zone**ray****theory****ray**method**ray**...
Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2007 SEG Annual Meeting, September 23–28, 2007

Paper Number: SEG-2007-2215

... been extensively employed in

**wave**field modeling and imaging due to its algorithmic understandability and computational efficiency. However, this method has some shortcomings. For example,**ray****theory**could not be used to describe the critical point, head**wave**,**diffraction**and so on. Maslov method keeps...
Abstract

Summary On the basis of the Helmoholtz equation for inhomogeneous media, we have deduced wave propagation formula using beamlet decomposition of wave field in general frame and employing the pseudo-differential operator, and obtain the marching algorithm of wave propagation in phase space (local angle domain). And also we have more freedom when choosing the frame of beamlet decomposition in one-way wave marching algorithm. Taking the scale-variable Gabor-Daubechies tight frame as an example, the specific expression of oneway wave propagator and corresponding marching algorithm are derived. And the high-frequency asymptotic problem of propagator based on Gabor-Daubechies tight frame is discussed in detail and its validity conditions are investigated, which could be used to increase the computation efficiency. The wave propagation results respectively by integrated propagator and high-frequency asymptotic one are compared by numerical examples, which demonstrates that the error of wave fields is quite small in certain high-frequency asymptotic conditions and the computation cost is averagely reduced by 30%. Introduction As the high-frequency asymptotic solution of wave equation, ray theory has been extensively employed in wave field modeling and imaging due to its algorithmic understandability and computational efficiency. However, this method has some shortcomings. For example, ray theory could not be used to describe the critical point, head wave, diffraction and so on. Maslov method keeps the availability of propagation in the critical point, Airy caustics and Fresnel shadowing domain, whereas it will lose validity when there are more caustic points (Foster and Jau-Inn, 1991). Gauss beam method (Cervený, Popov and PšencÍk, 1982) not only has the advantage of ray theory, but also keeps the dynamics characteristic of wave to a certain extent. However, in heterogeneous medium the wave beam will diverge when the distance of propagation increases. Subsequently, local propagator and corresponding marching method have been introduced (Steinberg, (1993(a), 1993(b)), Steinberg and Birman, (1995)). Since taking windowed Fourier transform as a tool to decompose the operator and wave field, their method is too time-consuming to use for seismic wave field and imaging. Moreover, their method can’t work well in strongly cross-varying medium, because of using global perturbation in partial equation (Wu, Wang and Gao, 2000). In order to overcome the above-mentioned disadvantage, the wave propagator in local-angle domain and corresponding marching algorithm are developed, based on frame theory, local background velocity and local disturbance (Wu and Chen, 2006). The one-way wave propagation based on Gabor-Daubechies frame (including tight frame, G-D frame for short below) is discussed (Wu et al., 2000, Wu and Chen, 2006).In this work, we investigate the one-way wave propagation problem and its marching algorithm based on the theory of general frame and pseudo-differential operator. We obtain the wave propagator in phase space and corresponding marching algorithm of wave field for a general frame. Taking the scale-variable Gabor-Daubechies tight frame as an example, our results give a specific propagator termed G-D propagator. By using the integrated and approximate wave propagator in wave propagation respectively, we compare their precision and cost.

Proceedings Papers

Paper presented at the The Fifteenth International Offshore and Polar Engineering Conference, June 19–24, 2005

Paper Number: ISOPE-I-05-245

... treated in electromagnetic

**waves**. The first successful**theory**that works for arbitrary shape of objects is proposed by J. B. Keller. His Geometric**Theory**of**Diffraction**(GTD) is based on the so-called model problems of some simplified geometries and advances the concept of**diffraction****rays**. Through...
Abstract

ABSTRACT Unlike wave models which analyze each individual wave, phase-averaged wave models focus only on the wave amplitude and can simulate a much larger area. However, its application to a sheltered zone is limited because the diffraction effect is not included. To improve the Phase-Averaged Wave Model, the Geometrical Theory of Diffraction (GTD) is introduced and complex coastlines are replaced by simple geometries such as semi-infinite breakwaters or wedges. By expanding the exact solution with respect to the non dimensional distance to the pointed end of the wedge, kr, the diffraction wave can be represented by a source on the pointed end. The asymptotic solution for totally absorbent wedge boundaries is implemented in the NOAA Wave Watch III (NWW III) model as a new wave source at the end of the wedge. Two other approaches on implementing the diffraction effect are also discussed. INTRODUCTION Wind-wave forecasting models can be divided into two groups, some forecast only the significant wave height and the others forecast the whole wave spectrum. The former group, including e.g. the classical SMB (Sverdrup, Munk and Bretschneider) method and its modifications, has been discussed in most coastal engineering textbooks. The later group, including the WAM, SWAN, and NWW III models, can describe much more of the wave phenomena in both time and space. However, these models are phase-averaged and formulated on the radiative-transfer equation based on energy conservation. The diffraction effect is neglected and, consequently, they can be used only outside the sheltered zone. Including diffraction effects in the forecast of wind wave is important for both theoretical and engineering purposes, and a diffraction-included wind wave model is of special importance to Taiwan. The most populated western coast, comprising almost all of the commercial harbors, power plants, recreational beaches, and industrial parks, next to the Taiwan Strait.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1998 SEG Annual Meeting, September 13–18, 1998

Paper Number: SEG-1998-1531

... ABSTRACT No preview is available for this paper.

**diffraction**term kirchhoff-born migration steve hildebrand wavefield extrapolation slowness vector kirchhoff-born equation**ray****theory**equation reservoir characterization perturbation approximation slowness model upstream oil...
Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010

Paper Number: SEG-2010-0307

... process. Velocity continuation has found application in migration velocity analysis (Fomel, 2003a; Schleicher et al., 2008) and

**diffraction**imaging (Fomel et al., 2007). Fomel (1994) and Hubral et al. (1996) point out that velocity continuation is a**wave****propagation**process where, instead of wavefronts...
Abstract

SUMMARY Velocity continuation describes how a seismic image changes given a change in migration velocity. This description turns out to be a wave propagation process, in which images propagate along a velocity axis. In the anisotropic case, the velocity model is multi-parameter. Therefore, anisotropic image propagation is multi-dimensional. We extend time-domain velocity continuation to the 3D azimuthally anisotropic case. We use a three-parameter slowness model, which can be related to azimuthal variations in velocity, as well as their principal directions. This information is useful for fracture and reservoir characterization from seismic data. We provide synthetic diffraction imaging examples to illustrate the concept of azimuthal continuation and to analyze the impulse response of the 3D velocity continuation operator. INTRODUCTION Velocity continuation, introduced by Fomel (1994, 2003b), provides a framework for describing how a seismic image changes given a change in the migration velocity model. Similar in concept to residual migration (Rothman et al., 1985) and cascaded migrations (Larner and Beasley, 1987), velocity continuation is a continuous formulation of the same process. Velocity continuation has found application in migration velocity analysis (Fomel, 2003a; Schleicher et al., 2008) and diffraction imaging (Fomel et al., 2007). Fomel (1994) and Hubral et al. (1996) point out that velocity continuation is a wave propagation process where, instead of wavefronts propagating as a function of time, images propagate as a function of migration velocity. Recent work has extended the concept to heterogeneous and anisotropic velocity models (Alkhalifah and Fomel, 1997; Adler, 2002; Iversen, 2006; Schleicher and Alexio, 2007; Duchkov and de Hoop, 2009). To account for anisotropy, the seismic velocity model must become multi-parameter. Consequentially, velocity continuation generalizes to a process of implementing image transformations caused by changes in multiple parameters rather than velocity alone. In 3D, azimuthal variation in velocity has been shown to be an indicator of preferentially aligned vertical fractures (Crampin, 1984), lateral heterogeneity (Levin, 1985), regional stress (Sicking et al., 2007), or a combination of these factors. Accounting for azimuthal variations in velocity results in better event focusing and improved imaging (Sicking and Nelan, 2008). With these benefits as motivation, we extend time-domain velocity continuation to 3D, accounting for the case of azimuthally variable migration velocity. THEORY The theory of velocity continuation formulates the connection between the seismic velocity model and the seismic image as a wave propagation process. In doing so, the process can be implemented in the same variety of ways as seismic migration. Seismic migration in its many forms is commonly derived starting at the wave equation, which is broken into the eikonal and transport equations, and if necessary, a system of ray tracing equations. Velocity continuation is derived in the opposite order (Fomel, 2003b). Starting with a traveltime equation which describes the image, a corresponding kinematic equation is derived to describe how the image moves according to a change in imaging parameters. Subsequently, the kinematic equation is used to derive a corresponding wave equation, which describes the dynamic behavior of the image as a propagation through imaging parameter coordinates.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 32nd U.S. Symposium on Rock Mechanics (USRMS), July 10–12, 1991

Paper Number: ARMA-91-407

... that interface

**waves**and multiply scat- tered**waves**will not be included in Kirchhoff method solution. The Kirchhoff method has several advantages over geometric**ray****theory**: it includes**diffractions**from surface irregularities and does not break down when the receiver is located on a caustic. Application...
Abstract

1 INTRODUCTION Interconnected fractures can serve as major conduits for fluid flow and can significantly alter the mechanical properties of rock. Information about the location, orientation, and mechanical and hydrologic properties of fractures are therefore of great importance in many problems encountered in the earth sciences. To obtain this information, crosshole seismic imaging methods such as ray tomography (Majer, 1990) and diffraction tomography (Tura, 1990) are currently being developed. The success of seismic imaging methods for locating and characterizing fractures depends on our understanding of the interaction of an elastic wave with a fracture. In this study, the effects of spatial variations in the mechanical properties of fractures are investigated. A numerical approach based on the elastic Kirchhoff method is presented for modeling elastic wave transmission and reflection from fractures with arbitrary shapes and stiffness distributions. 2 THEORY For wave propagation problems involving reflection and transmission of waves from surfaces, it is often convenient to work with an integral form of the elastodynamic equation. The advantage of using the integral representation for seismic waves is that it does not require absorbing boundary conditions and extensive gridding of the entire medium that are necessary in finite difference and finite element methods. A potential drawback of the method is that a Green's function is needed to propagate waves between surfaces. However, if the medium is homogeneous and isotropic, the simple whole-space Green's function can be used. Numerical evaluation of equation (1) for the displacement at a point in the medium requires a knowledge of the terms appearing in the integral. When the medium is homogeneous and isotropic, the whole-space expressions for G and Ó can be used. Once the values of stress and displacement are known along S for a particular source location, the displacement can be evaluated for a receiver located anywhere in the medium. 2.2 Kirchhoff Approximation A problem with the BIEM approach is that for high frequency, three-dimensional, elastic problems typically encountered in fracture studies it requires large matrix inversions that are computationally intensive. A more feasible approach is to approximate the surface displacements and tractions using ray theory and plane wave reflection and transmission coefficients. This approximation, which is called the Kirchhoff or tangent plane approximation, is valid when the incident wave is of sufficiently high frequency (i.e., the wavelength is much smaller than the correlation distance of any variation in material properties) that locally its amplitude decay is described by geometric ray theory and plane-wave reflection and transmission coefficients (Scott, 1985). The Kirchhoff approximation has the following implications: (1) that every point on the surface of material discontinuity reflects the incident wave as though there were an infinite plane tangent to the surface at that point, and (2) that the values of displacement and traction at a point are independent of the boundary values at other points. This independence of displacement and traction between neighboring elements suggests that interface waves and multiply scattered waves will not be included in Kirchhoff method solution.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1990 SEG Annual Meeting, September 23–27, 1990

Paper Number: SEG-1990-1037

... applications in modeling driven geophysical inversion schemes. All these factors pose stringent reguirements on the modeling algorithm. Asymptotic

**ray**tracing is the most widely used method for modeling of seismic**wave****propagation**in the geophysical industry today. Its popularitycanbe attributedtothe fact...
Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the SEG International Exposition and Annual Meeting, September 15–20, 2019

Paper Number: SEG-2019-3216391

... with the wavefront attributes. Since

**rays****propagated**downward from a focusing curve focus at a particular point on the edge, this method allows for grouping the central midpoints in order to use the edge**diffractions**in a focusing based tomography. ACKNOWLEDGMENTS The authors appreciate the support of the**Wave**...
Abstract

ABSTRACT Wavefront attributes, among others NIP- and N-wavefront curvature matrices, are routinely retrieved during 3D CRS processing of seismic data. NIP-wave is a wave induced by a source that is placed at the normal-incidence-point on the reflector. N-wave is triggered by the exploding reflector element. In this abstract, we give a general criterion for identifying edge diffraction that we formulate in terms of the NIPand N-wavefront curvatures. This allows us to complement the wavefront curvature based classification of possible wave phenomena present in seismic datasets. It has a potential for identification, separation from reflections, and dedicated processing of the point and edge diffraction modes. Additionally, we explain how to group central midpoints on the acquisition surface to obtain ray families focusing at a specific point on the edge. This paves the way for using the edge diffraction in a tomography based on the criterion of ray focusing. We illustrate the concept with a synthetic example comprising a linear edge in a 3D gradient medium. However, the method is valid for arbitrarily oriented curved edge embedded in a 3D heterogeneous medium, which could be either isotropic or anisotropic. Presentation Date: Wednesday, September 18, 2019 Session Start Time: 1:50 PM Presentation Start Time: 3:55 PM Location: 303B Presentation Type: Oral

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016

Paper Number: SEG-2016-13874023

... investigate the localized

**wave****propagation**in complex acoustic media to show its directional property with limited**diffraction**and capability to retain its geometric shape. Second, we apply the Gaussian**wave**packet (GWP) to invert for the spacing of fractures in an acoustic medium. The GWP is an exact...
Abstract

ABSTRACT We develop the method using exact localized waves to detect the spacing between fractures from the idea of the earlier Double focusing Gaussian beams. First, we investigate the localized wave propagation in complex acoustic media to show its directional property with limited diffraction and capability to retain its geometric shape. Second, we apply the Gaussian wave packet (GWP) to invert for the spacing of fractures in an acoustic medium. The GWP is an exact solution to the wave equation and should be distinguished from the traditional asymptotic Gaussian beam or Gaussian packet. A directional localized wave illuminates the fracture targets and the multiply scattered waves can be captured in a time-space window using the multiple-scattering theory of plane waves upon a local periodic structure. The scattered wave depends on the fracture orientation and spacing. We scan all possible fracture parameters such that the predicted scattered waves match our observation. Because this method is not a seismic migration/imaging method, its dependence on background velocity accuracy is not stringent. Finally, our numerical examples will illustrate these points. Presentation Date: Tuesday, October 18, 2016 Start Time: 4:10:00 PM Location: 155 Presentation Type: ORAL

Proceedings Papers

Paper presented at the The Seventh ISOPE Pacific/Asia Offshore Mechanics Symposium, September 17–21, 2006

Paper Number: ISOPE-P-06-006

... current. In the past, Several researchers (e.g. Longuet-Higgins & Stewart,1961; Bretherton & Garrett,1969) studied the

**wave**current interaction using the conventional**wave**-action equation, which is equivalent to the geometrical**ray****theory**and cannot be applied to the regions where**wave****diffraction**...
Abstract

ABSTRACT: Two different time-dependent hyperbolic mild-slope equations each with a dissipation term for wave propagation on non-uniform currents are transformed into wave action and eikonal equations. By considering their respective performance, the mathematical formulation is selected that is more rigorous and complete with regard to intrinsic frequency and wave number. Using a perturbation method, a parabolic form of the time-dependent mild-slope equation is derived from the selected hyperbolic version, and solved using the alternating direction implicit method. The resulting numerical model is applicable to wave propagation on non-uniform currents and depth. Making comparisons between the numerical solutions with the theoretical solutions of collinear waves and current, the results show that the numerical solutions are in good agreement with the exact ones. Calculating the interactions between incident wave and current on a sloping beach(Arthur,1950), the differences of wave number vector between refraction and combined refraction-diffraction of waves are discussed quantitatively, while the effects of different methods of calculating wave number vector on numerical results are shown. INTRODUCTION In the past, Several researchers (e.g. Longuet-Higgins & Stewart,1961; Bretherton & Garrett,1969) studied the wave-current interaction using the conventional wave-action equation, which is equivalent to the geometrical ray theory and cannot be applied to the regions where wave diffraction becomes important. To overcome the shortcomings of wave-action equation, many researchers (e.g. Booij, 1981; Liu, 1983; Kirby, 1984; Kirby, 1986; Hong, 1996) proposed different time dependent hyperbolic mild slope equations for wave propagation on non-uniform currents. Kirby(1984)'s equation is not only different from Booij(1981)'s one but also different from Liu (1983)'s one. Kirby (1984) pointed out that Booij (1981) didn't use the correct form of the dynamic free surface boundary condition and the error of Liu (1983)'s equation was due to the limitations in the procedure deriving the equation.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1985 SEG Annual Meeting, October 6–10, 1985

Paper Number: SEG-1985-0480

..., if the specular point is not to be found (according to geometrical optics) either in the element or in its smooth con- tinuation, then the

**ray**field u (M- ,M+) is assumed to be zero. In most cases this is equivalent to neglecting exponentially de- caying**diffracted**tripping**waves**. Function W in expression (2...
Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017

Paper Number: SEG-2017-17794193

...- mization of geometrical spreading of all the

**diffracted**and nor- mal incidence point**waves**presented in the kinematic**wave**- field attributes dataset. For the true velocity model geometri- cal spreading vanishes when is back**propagated**at arrival time because diffractors and normal incidence points...
Abstract

ABSTRACT A stable and fast automatic workflow for smooth velocity model retrieval is of interest for subsequent depth migration and as a source of initial models for full-waveform inversion. At the same time, seismic data enhancement by means of stacking is widely performed. The idea of utilizing kinematic wavefield attributes representing an extra stacking output as input data for a fast smooth velocity model inversion was first proposed in a paper of Duveneck (2004b). Common-reflection-surface (CRS) stack attributes (Mann et al., 1999; Jäger et al., 2001) form a data vector for nonlinear least-square optimization. Recently, this method of zero-offset wavefront tomography has found its application to passive seismic source localization (Schwarz et al., 2016) and diffraction imaging (Bauer et al., 2017). The inverse problem was formulated similarly to stereotomography (Lambaré, 2008) with velocity model, diffractors and scattering angles as unknowns. This is a redundant set for the zero-offset wavefront tomography because in contrast to the pre-stack stereotomography the CRS processing produces zero-offset travel times to diffractors before the inversion. To fully exploit this fact we developed a novel kinematic wavefield attributes inversion workflow. It performs an overall minimization of diffracted and normal incidence point waves geometrical speading at emergence time. We refer this procedure as dynamic focusing. During the optimization the wavefield attributes remain constant and serve as initial conditions and travel time for kinematic and dynamic ray tracing. Transition to velocity as the only unknown significantly decreases tomographic matrix dimension and improves a ratio of data points number and a number of unknowns. After a velocity model is retrieved reflectors and diffractors are localized with ray tracing. Fréchet derivatives together with adjoint-state method gradient are adduced. The algorithm was tested on a full of diffrated energy marine dataset from the Levantine Basin (Netzeband et al., 2006). Presentation Date: Wednesday, September 27, 2017 Start Time: 2:15 PM Location: Exhibit Hall C, E-P Station 1 Presentation Type: EPOSTER

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2011 SEG Annual Meeting, September 18–23, 2011

Paper Number: SEG-2011-2860

... of simulating different events including primaries, internal multiples, converted

**waves**,**diffractions**, etc. However, the computational speed of such methods is considerably less than**ray**based-methods. Now, the question is do we require highly accurate modeling to seismically detect fluid flow...
Abstract

ABSTRACT Time-lapse seismic modeling is an essential step for any seismic reservoir monitoring prospect. Different algorithms with various degrees of accuracy can be utilized to image fluid flow. Highly accurate seismic modeling techniques, e.g., finite difference (FD), are capable of simulating different events including primaries, internal multiples, converted waves, diffractions, etc. However, the computational speed of such methods is considerably less than ray based-methods. Now, the question is do we require highly accurate modeling to seismically detect fluid flow or are approximate, ray-based and hybrid, modeling techniques adequate. To investigate this problem, we conducted a systematic modeling study over a recently developed petro-elastic model. A base and two monitor surveys were simulated and the corresponding time-lapse signatures were analyzed. Our analyses demonstrated that internal multiples behind the waterfront, flooded zones, partially subtract out in time-lapse differencing. We also found that for time-lapse seismic modeling, acoustic modeling of an elastic medium is a good approximation from near to middle offsets. From middle to far offsets, differences between elastic and acoustic wave propagation is the dominant effect rather than internal multiples and converted waves. We also found that time-lapse modeling of the reservoir using split-step Fourier plane-wave (SFPW) approach is computationally fast compared to FD. It is capable of handling higher frequencies than FD and provides an accurate image of the waterflooding process comparable to FD.

Journal Articles

Journal:
SPE Production & Operations

Publisher: Society of Petroleum Engineers (SPE)

*SPE Prod & Oper*17 (03): 149–159.

Paper Number: SPE-78812-PA

Published: 01 August 2002

...

**propagation**, two**diffractions**are measured, which we interpret as coming from the fluid-front and fracture-tip positions. From the travel time of these**diffractions**and the material velocities, we can construct the**ray**path and calculate the fracture radius and the size of the nonpenetrated zone...
Abstract

Summary We performed scaled laboratory experiments of hydraulic fracture propagation and closure in soft artificial rock and outcrop rock samples. We also performed numerical simulations of the fracture behavior in plastic rocks with independently measured rock properties. The simulations aided in interpreting the measurements and extrapolating the results to field scale. Compared with elastic rock, plasticity induces a larger width for a given net pressure. However, the pressure to propagate fractures is only marginally increased and, in the case of the laboratory tests, was actually lower than expected from elastic behavior. The most dramatic effect of plasticity is that closure is much lower than the confining stress because of strong stress redistribution along the fracture. Introduction Rock is characterized by a very low tensile strength compared to its compressive strength. Often, tensile fracturing will, therefore, prevail if rock is loaded to rupture. This is also expected for fluid-driven fractures in which the high fluid pressures will lead to extensile loading of the rock ahead of the fracture tip. Straight ahead of the crack, the stresses will go to zero, but at some offset from the fracture plane, the stress decreases strongly in the direction perpendicular to the fracture plane, whereas the stress along it will be much higher. This loading induces shearing of the rock, which gives rise to deviations from brittle tensile failure. Shear failure can be described on a global scale by plasticity theory, although on a small scale, the plastic deformation consists either of so-called axial cleavage fractures along the maximum stress or of small shear fractures. In view of the large shear stress, fracture propagation in weak rocks is expected to induce a significant plastic (shear) deformation around the fracture tip, as depicted in Fig. 1 . It has been proposed that such plastic behavior may induce a high tip pressure 1,2 that could lead to high wellbore pressures and a fracture that is much wider and shorter compared with elastic behavior. In fact, there is evidence that the propagation pressure in soft formations is much larger than the elastic models predicted. Apart from a high tip pressure, the apparently high net pressures can also be explained by underestimation of the rock modulus. Net propagation pressure is almost proportional to the rock modulus, and the modulus (especially in soft rock) can be underestimated by a factor of two to three. Also, underestimation of fracture closure pressure could lead to significant errors because the absolute net pressure level is low in soft rocks. In routine jobs, the net pressure is used for estimating fracture penetration. Significant errors in the relation between net pressure and fracture width could result in poor coverage of the interval or insufficient fracture length. Also, fracturing is used nowadays for waste disposal in shallow, unconsolidated formations. It is obvious that a correct prediction of fracture geometry is vital for safely designing such a process. Apart from fracture geometry, it is important to establish the stress development after fracturing soft formations. Sandface stabilization in unconsolidated formations is an important byproduct of fracturing. Insight into the induced stress changes can aid in optimizing such treatments. This paper presents an overview of a study of rock plasticity in hydraulic fracturing (for details, refer to Refs. 3 through 13). We performed physical model tests to determine the relevant phenomena and to validate numerical models of fracture propagation. Small-scale lab tests cannot be directly applied to field applications: one needs to use a numerical model that is checked against experiments that represent the essential physics of the process. Validation of the numerical code gives confidence in the field application of the numerical model. Of course, it is always possible that field behavior is governed by phenomena, such as formation heterogeneity (e.g., layering and small-scale faults), that are neglected in the current model. We first review the most important experimental observations. Then, we describe the results of simulations with the two (independent) numerical models. The two models are based on the same physical assumptions, but we use the first model for comparison with the experiments; the second model is used for extrapolation of the results to field scale. Finally, we discuss the practical implications of the results. Experimental Setup and Method Fig. 2a shows a schematic view of the experimental setup used for the hydraulic fracturing experiments. Cubic blocks 0.30 m in size are loaded in a true triaxial machine to simulate in-situ stress states; no pore pressure can be applied. We used 0.1-mm-thick polyfluoroethylene sheets greased with petroleum jelly to reduce friction between the block and the loading platens. Six linear voltage differential transformers (LVDTs) measure the block deformation. During fracture propagation, a high-pressure pump injects fluid into the wellbore, and the wellbore pressure is measured at a dead string. An LVDT, mounted with clamps in the wellbore, measures the fracture width with a measuring error of approximately 10%. The block extension during propagation is a measure for the fracture volume. The fracturing fluid used is silicon oil, which behaves approximately in a Newtonian fashion at the shear rates of interest. Fig. 2b shows a schematic view of the ultrasonic measurements. Direct transmissions through the fracture yield its width profile. 14 The fracture tip acts as a diffractor. During fracture propagation, two diffractions are measured, which we interpret as coming from the fluid-front and fracture-tip positions. From the travel time of these diffractions and the material velocities, we can construct the ray path and calculate the fracture radius and the size of the nonpenetrated zone. In experiments on plaster with nonpenetrated zone sizes of 1 to 2 cm, the nonpenetrated zone size agreed well with the size of the dry zone measured after opening the block. When the fracture stops growing, the diffraction disappears. The ultrasonic shear-wave transmissions then gave us the radius over which the fracture was open. These measurements have an accuracy of approximately ±1 cm. We used artificial rock samples made of cement, plaster, and diatomite as natural rock (see Table 1 ). The strength of the plaster blocks depends on the water content. We did experiments with strong and weak plaster. The diatomite blocks were obtained from a quarry in Lompoc, California. In diatomite, the hydraulic fracture plane is oriented approximately parallel with the bedding plane.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2000 SEG Annual Meeting, August 6–11, 2000

Paper Number: SEG-2000-0988

... kirchhoff image

**propagation**traveltime image point image point displacement equation migration velocity analysis perturbation**propagated**image kirchhoff image**propagation**frank adler**diffraction**point reservoir characterization velocity**ray**velocity model Kirchhoff image**propagation**Frank...
Abstract

Summary Kirchhoff image propagation is a new Kirchhoff migration/inversion technique which predicts subsurface images for perturbations of 3D laterally inhomogeneous velocity models from a single application of migration/inversion. The technique is based on the prediction of image point displacements determined from the traveltime perturbations and the matrix of the Beylkin determinant. Correct interval velocities can be picked directly from common-image-gathers of perturbed images during migration velocity analysis.

Advertisement