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Journal Articles

*Petrophysics - The SPWLA Journal of Formation Evaluation and Reservoir Description*60 (02): 335–347.

Paper Number: SPWLA-2019-v60n2a10

Published: 01 April 2019

... angle

**of**incidence**of**the reflected arrival is related to the relative**dip**, and the moveout**in**3D across the individual sensors is related to the azimuthal orientation**of**the**reflector**. This information is then used to produce a 3D structural map**of**the**reflector**, which can be readily used for further...
Abstract

A new sonic-imaging technique uses azimuthal receivers to determine individual reflector locations and attributes, such as the dip and azimuth of formation layer boundaries, fractures, and faults. From the filtered waveform measurements, an automated time pick and event-localization procedure is used to collect possible reflected arrival events. An automated ray-tracing and 3D slowness time coherence (STC) procedure is used to determine the raypath type of the arrival event and the reflector azimuth. The angle of incidence of the reflected arrival is related to the relative dip, and the moveout in 3D across the individual sensors is related to the azimuthal orientation of the reflector. This information is then used to produce a 3D structural map of the reflector, which can be readily used for further geomodeling. This new technique addresses several shortcomings in the current state-of-the-art sonic-imaging services within the industry. Similar to seismic processing, the current sonic-imaging workflow consists of iteratively testing migration parameters to obtain a 2D image representing a plane in line with the desired receiver array. The image is then interpreted for features, which is often subjective in nature and does not directly provide quantitative results for the discrete reflections. The technique presented here, besides providing appropriate parameter values for the migration workflow, further complements the migration image by providing dip and azimuth for each event that can be used in further downstream boundary or discontinuity characterization. A field example from the Middle East is presented in which a carbonate reservoir was examined using this technique and subsequently integrated with wellbore images to provide insight to the structural geological setting, which was lacking seismic data due to surface constraints. Structural dips were picked in the lower zone of the main hole and used to update the orientation of stratigraphic formation tops along the well trajectory. 3D surfaces were then created and projected from the main hole to the sidetrack to check for structural conformity. One of the projected surfaces from the main hole matched the expected depth of the formation top in the sidetrack but two were offset due to the possible presence of a fault. This was confirmed by parallel evaluation of the azimuthal sonic-imaging data acquired in the main hole that showed an abrupt change in the relative dip of reflectors above and below the possible fault plane using the 3D STC and ray tracing. Dip patterns from both wells showed a drag effect around the offset formation tops, further confirming the presence of a fault. A comparison of the acquired borehole images pinpointed the depth and orientation of the fault cutting both wells to explain the depth offset of the projected 3D formation top surfaces.

Proceedings Papers

Paper presented at the SPWLA 59th Annual Logging Symposium, June 2–6, 2018

Paper Number: SPWLA-2018-JJJJ

...

**dip**, and the moveout**in**3D across the individual sensors is related to the azimuthal orientation**of**the**reflector**. This information is then used to produce a 3D structural map**of**the**reflector**which can be readily used for further geomodeling. This new technique addresses several shortcomings**in**the...
Abstract

ABSTRACT A new sonic imaging technique uses azimuthal receivers to determine individual reflector locations and attributes such as the dip and azimuth of formation layer boundaries, fractures, and faults. From the filtered waveform measurements, an automatic time pick and event localization procedure is used to collect possible reflected arrival events. An automatic ray tracing and 3D slowness time coherence (STC) procedure is used to determine the ray path type of the arrival event and the reflector azimuth. The angle of incidence of the reflected arrival is related to the relative dip, and the moveout in 3D across the individual sensors is related to the azimuthal orientation of the reflector. This information is then used to produce a 3D structural map of the reflector which can be readily used for further geomodeling. This new technique addresses several shortcomings in the current state-of-the-art sonic imaging services within the industry. Similar to seismic processing, the current sonic imaging workflow consists of iteratively testing migration parameters to obtain a 2D image representing a plane in line with the desired receiver array. The image is then interpreted for features, which is often subjective in nature and does not directly provide quantitative results for the discrete reflections. The technique presented here, besides providing appropriate parameter values for the migration workflow, further complements the migration image by providing dip and azimuth for each event that can be used in further downstream boundary or discontinuity characterization. A field example is presented from the Middle East in which a carbonate reservoir was examined using this technique and subsequently integrated with wellbore images to provide insight to the structural geological setting, which was lacking seismic data due to surface constraints. Structural dips were picked in the lower zone of the main hole and used to update the orientation of stratigraphic well tops along the well trajectory. 3D surfaces were then created and projected from the main hole to the sidetrack to check for structural conformity. One of the projected surfaces from the main hole matched the expected depth of the well top in the sidetrack but two were offset due to the possible presence of a fault. This was confirmed by parallel evaluation of the azimuthal sonic imaging data acquired in the main hole that showed an abrupt change in the relative dip of reflectors above and below the possible fault plane using the 3D STC and ray tracing. Dip patterns from both wells showed a drag effect around the offset well tops, further confirming the presence of a fault. A comparison of the acquired borehole images pinpointed the depth and orientation of the fault cutting both wells to explain the depth offset of the projected 3D well top surfaces.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012

Paper Number: SEG-2012-0507

... DSR formula valid for media with the symmetry axis normal to the

**dip****of**the**reflector**(DTI). The accuracy**of**this approximate solution is enhanced using Shanks transform to a point where the errors are extremely small for practical anisotropic values. Under this assumption, we also do not need to...
Abstract

Summary The double-square-root (DSR) formula is an integral part of many wavefield based imaging tools. A transversely isotropic medium with a titled symmetry axis (TI) version of the DSR formula is nearly impossible to obtain analytically. As a result, we develop an approximate version of the DSR formula valid for media with the symmetry axis normal to the dip of the reflector (DTI). The accuracy of this approximate solution is enhanced using Shanks transform to a point where the errors are extremely small for practical anisotropic values. Under this assumption, we also do not need to compute the symmetry axis field as it is inherently included in the formulation.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015

Paper Number: SEG-2015-5807160

... non- uniqueness. We therefore must make some assumptions about the anisotropy symmetry axes. I assume that anisotropy axes are perpendicular to the

**dipping****reflectors**. This is called a**dip**-constrained transverse-isotropic (DTI) model (Alkhakifah and Sava, 2010). Dix-type inversion**of**walkaway first...
Abstract

Summary Walkaway vertical seismic profiling (WVSP) data potentially provides the most reliable anisotropy estimates. In many cases, a 1D depth velocity model is not adequate for WVSP data inversion. If the walkaway first break function is not symmetrical with respect to the well then a velocity model with lateral velocity changes is needed. In this paper, I present a first break constrained traveltime inversion approach for a 3D tilted transverse isotropy (TTI) parameter estimation that takes into account lateral velocity changes above the shallowest receiver. A new methodology, based on the constrained first break inversion, was developed to estimate anisotropic parameters in a 3D model. This method includes residual source statics calculation, walkaway first break correction due to zero-offset misfit for different walkaway lines, lateral velocity changes above the shallowest receiver, dipping boundaries and visual uncertainty analysis of estimated anisotropic parameters. Dipping boundaries, interval velocities and anisotropic TI parameters are simultaneously estimated through the least squares method with adaptive stabilizing weights. This approach was applied to a four-line walkaway dataset. The results showed small residual time differences between actual and synthetic first breaks with a standard deviation of 2 msec. Introduction Walkaway vertical seismic profiling (WVSP) data is often used as a tool for high-resolution imaging in areas where surface seismic resolution is low. Depth velocity model building is a key step for WVSP imaging. Lateral velocity changes above the shallowest receiver lead to a nonsymmetrical first break function t(x): t(-x) ¹ t(x) where x is the offset. The velocity model in the overburden must therefore compensate for the non-symmetrical first arrivals. Simultaneous inversion for dipping boundaries and tilted TI anisotropy with unknown tilt axes leads to strong nonuniqueness. We therefore must make some assumptions about the anisotropy symmetry axes. I assume that anisotropy axes are perpendicular to the dipping reflectors. This is called a dip-constrained transverse-isotropic (DTI) model (Alkhakifah and Sava, 2010). Dix-type inversion of walkaway first breaks provides explicit estimates for anisotropic parameters e and d (Blias, 2012a). In this inversion, the use of averaged first breaks for symmetrical points was suggested to suppress the influence of the dipping boundaries in the overburden. Dix-type inversion requires accurate estimates of an NMO non-hyperbolic term. As the Dix-type inversion does not provide error control, anisotropy estimates can be used as initial values for anisotropic parameters for further improvement.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2005 SEG Annual Meeting, November 6–11, 2005

Paper Number: SEG-2005-0116

.... Numbers around the outer circle denote azimuth (

**in**degrees) from the**reflector****dip**plane. The radial scale corresponds to the magnitude**of**hyperbolic moveout**term**av- eraged over azimuth . 0.02 0.04 0.06 0.08 0.1 30 210 60 240 90 270 120 300 150 330 180 0 Fig. 2: TNH, num ( marks negative and N...
Abstract

Summary Deviations of P-wave reflection traveltimes from a hyper- bola, called the nonhyperbolic or quartic moveout, need to be properly handled while processing the long-spread seismic data. As observed nonhyperbolic moveout is usu- ally attributed to the presence of anisotropy, we devote our paper to deriving and analyzing a general formula that describes azimuthally varying quartic moveout co- e±cient in a homogeneous, weakly anisotropic medium above a dipping, mildly curved reflector. Our result incorporates all known weak anisotropy ap- proximations of the quartic moveout coe±cient and ex- tends them further to triclinic media. By comparing our approximation with nonhyperbolic moveout obtained from the ray-traced reflection traveltimes, we ¯find that the former satisfactory predicts azimuthal variations of the quartic moveout when its magnitude is less or about 20% of the corresponding hyperbolic moveout term. We also study the influence of reflector curvature on non- hyperbolic moveout. It turns out that the curvature as such produces no quartic moveout in the reflector strike direction, where the anisotropy-induced moveout nonhy- perbolicity is usually non-negligible. Thus, the presence of nonhyperbolic moveout along the reflector strike might serve as an indication of effective anisotropy. Introduction Measuring nonhyperbolic (or quartic) reflection moveout is a necessary step in processing of long-spread P-wave re- flection data. Proper corrections for nonhyperbolic move- out have to be made both to improve imaging and to per- form amplitude-versus-offset analysis at large incidence angles. Flattening the P-wave traveltimes at long offsets is relatively easy in 2D because it can be accomplished by applying almost any moveout equation that has some built-in deviation from a hyperbola. Nonhyperbolic velocity analysis is more involved when 3D multiazimuth reflection data are available, and one has to account for azimuthal variations of quartic move- out. The difficulty is caused by a relatively complicated dependence of the quartic moveout coefficient A 4 on az- imuth acompared to that of the normal moveout (NMO) velocity, V nmo. While V nmo(a) is an ellipse described by three parameters, azimuthal dependence of A 4(a) is gen- erally determined by five quantities. To the best of our knowledge, this result was first obtained by Sayers and Ebrom (1997), who employed expansions of the P-wave group velocities in spherical harmonics. Further progress in understanding the nonhyperbolic moveout in realistic earth models was made by Pech et al. (2003). They presented an expression for A 4 applicable to any anisotropy, heterogeneity, and reflector shape pro- vided that required forth-order traveltime derivatives ex- ist. Pech et al. (2003) also derived a weak anisotropy ap- proximation for transversely isotropic layer with a tilted symmetry axis above a plane dipping reflector. They demonstrated that A 4( a ) can change sign and form in- tricate cloverleaf patterns. Even though complexity and variability of these patterns increases as the layer symme- try reduces from TI to orthorhombic (Pech and Tsvankin, 2004), the weak anisotropy approximations of A 4 seem to reproduce them, at least in a qualitative fashion. Here we continue the work of Pech et al. (2003) and Pech and Tsvankin (2004).

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the SEG International Exposition and Annual Meeting, October 11–16, 2020

Paper Number: SEG-2020-3424784

... investigation on capability

**of**LSRTM, to image a deep geological setting which includes steep**dip****reflectors**, major subduction zone, was performed. Applying a finite faults and thrusts. The LSRTM process was conducted**in**difference modelling on the high resolution GO_3D_OBS two steps due to the memory shortage...
Abstract

Imaging of crustal-scale complex structures causing subduction zones namely major faults, low-velocity zones and steep dips is a challenge in seismic exploration. Various depth imaging techniques including Kirchhoff migration, reverse time migration (RTM), etc. have been utilized to reconstruct reflectivity images of those geological targets. However, depth migration methods strongly rely on the accuracy of the velocity model and imaging aperture and have further limitations in terms of amplitude treatment. This issue becomes more serious when short-offset multichannel seismic (MCS) data are employed. In this research, the efficiency of a well-developed least-squares RTM (LSRTM) to image a complex crustal-scale geological setting, is examined using a high-resolution velocity model of the subduction zone, inspired by the geology of the Nankai Trough, Japan. Comparison of the results obtained with LSRTM and conventional Kirchhoff prestack depth migration (PSDM) demonstrated that the LSRTM algorithm succeeded to image accurately the steeply dipping faults, remove migration artefacts and enhance the resolution of deep targets reducing potential ambiguity of geological interpretation. Presentation Date: Wednesday, October 14, 2020 Session Start Time: 1:50 PM Presentation Time: 2:40 PM Location: 362D Presentation Type: Oral

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012

Paper Number: SEG-2012-0053

...-midpoint

**traveltime**pyramid**in**transversely isotropic media: Geophysics, 65, 1316 1325. Alkhalifah, T., 2000b, Prestack phase-shift migration**of**separate offsets: Geophysics, 65, 1179 1194. Alkhalifah, T., and S. Fomel, 2010, Source-receiver two-way wave extrapolation for prestack exploding**reflector**...
Abstract

SUMMARY A two-way time extrapolation of the DSR-derived phase operator allows for up and down down going wavefields, but suffers from an essential singularity for horizontally traveling waves. This singularity is also associated with an anisotropic version of the DSR extrapolator. Perturbation theory allows us to separate the isotropic contribution, as well as the singularity. As a result, the anisotropic residual operator is free from the singularity and can be applied as a stand alone operator to correct for anisotropy. This is achieved even if the original image was obtained using, for example, reverse time migration (RTM). The residual correction is useful for parameter estimation. Applications to initial simple synthetic data demonstrate the accuracy of the new prestack modeling and migration approach.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2009 SEG Annual Meeting, October 25–30, 2009

Paper Number: SEG-2009-0211

....

**In**addition, we can use least-**square**fitting**of**any NMO approximation, which will provide a more stable and accurate result. From walkaway VSP data, virtual reflected**traveltimes**are created, using each receiver as a virtual horizontal**reflector**.**Traveltimes**are approximated using several three-**term**...
Abstract

Summary The purpose of this paper is to present a new method for accurate interval VTI anisotropic parameter estimation from walkaway VSP data. The method creates a virtual horizontal reflector at each receiver depth by calculating reflected traveltimes as the sum of first arrival times from the two symmetrical source points. A three-term NMO approximation function is used to estimate NMO velocity and a non-hyperbolic parameter. Assuming that the interval vertical velocity is known from zero-offset VSP data, Dixtype inversion is applied to the three parameters to invert them to generate interval anisotropic parameters e, d. Modeling results show that different approximations have different accuracy for different VTI models. Introduction Inversion of reflection traveltimes can provide anisotropic parameters required for depth seismic processing and imaging. Non-hyperbolic P-wave moveout for a transverse isotropic model with a vertical axis (VTI) depends on the parameter ?. To determine this parameter from surface seismic data, three-term semblance velocity analysis is used. Knowing ? and the vertical velocity from zero-offset VSP data, we can invert for the Thomsen parameters e and d, Grechka and Tsvankin (1998). Alkhalifah (1997) suggested estimating the coefficient ? and NMO velocity through semblance velocity analysis using a non-hyperbolic equation, suggested by Tsvankin and Thomsen (1995) and rewritten by Alkhalifah and Tsvankin (1995) in terms of coefficient ?. Tsvankin and Thomsen (1995), discussed the feasibility of non-hyperbolic NMO inversion for ? estimation. Non-hyperbolic three-term semblance velocity analysis provides the estimation of a third coefficient, but for this we need long-offset data, up to and exceeding 2.5 times the reflector depth H. Another problem with using semblance analysis is regular noise, multiple reflections, and AVO effects. This paper suggests using first arrival times picked from walkaway VSP data to determine NMO velocity and a nonhyperbolic term within the receiver array interval. Because first breaks can be picked with much higher accuracy than the moveout from semblance velocity analysis, NMO velocity and the third parameter estimates are more accurate and reliable. In addition, we can use least-square fitting of any NMO approximation, which will provide a more stable and accurate result. From walkaway VSP data, virtual reflected traveltimes are created, using each receiver as a virtual horizontal reflector. Traveltimes are approximated using several three-term functions (Blias, 2009) to estimate the vertical time t0, NMO velocity and the third parameter. Next, a Dix-type inversion of these three parameters is done to determine the interval anisotropic parameters e and d, using the vertical velocity computed from zero-offset VSP data. Theory and Method Fig.1. shows surface seismic geometry with sources at the surface and the receivers in a well. Let t(x,z) be the first break time (time arrival for downgoing P wave) where x is the offset and z is the receiver depth. We can find the reflected traveltimes t1(x) and t2(x) for two virtual boundaries at the depth z1 and z2 of two receivers (Fig. 1b): Figures 1a and 1b show that times t1(x) and t2(x) are the same as the times of the waves reflected from the top and the bottom of layer number n.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2000-2229

... Summary P-wave reflection

**traveltimes**may be used to constrain the depth scale**of**transversely isotropic models with a vertical symmetry axis (VTI) if the medium above the**reflector**is laterally heterogeneous**In**Part I**of**this work w e examined the inversion**of**P-wave normal-moveout (NMO...
Abstract

Summary P-wave reflection traveltimes may be used to constrain the depth scale of transversely isotropic models with a vertical symmetry axis (VTI) if the medium above the reflector is laterally heterogeneous In Part I of this work w e examined the inversion of P-wave normal-moveout (NMO) ellipses for the vertical velocity V P 0 and anisotropic coefficients e and d in VTI models with plane dipping interfaces in the overburden. Here, w e extend these results to stratified VTI media with irregular (e.g., curved) interfaces. Despite the higher complexity of the model, non-planar in terfaces increase the angle cover- age of reflected rays, which helps to resolve trade-offs between the medium parameters. By employing singular-value decomposition (SVD), we show that there exists a subset of VTI models for which all parameters needed for anisotropicdepth processing can be obtained solely from P-wave reflection traveltimes.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015

Paper Number: SEG-2015-5792516

... Thomsen (1988). The result

**of**Alkhalifah and Tsvankin (1995) based on the 2D NMO equation**of**Tsvankin (1995) can be applied only if the symmetry axis lies**in**the**dip**plane**of**the**reflector**. Tsvankin (1997) suggested obtaining anisotropic parameter by inverting**dip**-dependent P-wave moveout**in**the vertical...
Abstract

Summary Seismic inversion, one of the most significant technologies for seismic reservoir characterization, provides the most detailed view of underground structure and rock properties. Over the past few decades, many different inversion techniques, from post-stack inversion to pre-stack inversion, have been greatly improved, especially the azimuth anisotropy inversion, in which the transversely isotropic model with a horizontal symmetry axis (HTI media) has been extensively used in seismological studies of fractured reservoirs. The inversion of P -wave data in HTI media is normally carried out with azimuthally-dependent P-wave normalmoveout (NMO) velocities (Contreras et al ., 1999), and can be used to estimate the crack density and orientation. In this paper, a parameter estimation technique is originally proposed for HTI media, which is based on Rüger equation, and the Thomsen-style anisotropic coefficients responsible for P -wave reflection coefficient can be obtained directly by two-step inversion of reflection P -wave data acquired over HTI formations. Introduction Horizontal transverse isotropy (HTI) is the most commonly occurring type of anisotropy (Krey and Helbig, 1956), typical associated with vertical or steeply dipping fracture systems (Thomsen, 1988). The crack density leads to the subtle differences between S-wave velocities and P-wave velocities with different incidence azimuth, which provides important insight into the properties of the fractured reservoir (Thomsen, 1995). Typically, P-wave data is easier to obtain than S -wave data, so the inversion based on azimuthally-dependent reflection traveltimes or NMO velocities of P -wave is the most reliable approach for anisotropic parameter estimation of HTI media. In most cases of interest to geophysicists the anisotropy is weak (Thomsen, 1986), allowing the equations to simplify considerably. Weak-anisotropy approximations for moveout in HTI media was discussed by Thomsen (1988). The result of Alkhalifah and Tsvankin (1995) based on the 2D NMO equation of Tsvankin (1995) can be applied only if the symmetry axis lies in the dip plane of the reflector. Tsvankin (1997) suggested obtaining anisotropic parameter by inverting dip-dependent P-wave moveout in the vertical plane contains the symmetry axis, which can be used to estimate the crack density and investigate the contents of the fracture network (Rüger and Tsvankin, 1997). Al-Dajani and Tsvankin (1998) devoted to an analytic description of long-spread reflection moveout in HTI media. The method of Grechka and Tsvankin (1999, 2000) can be applied to the moveout inversion in HTI media because horizontal transverse isotropy can be considered as a special case of the more general orthorhombic model, and subsequently the method was extended the inversion algorithm to vertically heterogeneous TTI media above a dipping reflector using the generalized Dix equation, which shows a high accuracy of the inversion for a strongly anisotropic, stratified TTI medium. Despite these developments, the current study of seismic signatures in general azimuthally anisotropic media is hardly sufficient just by using reflection traveltime or NMO velocity, we should consider using the P-wave amplitude variation with the azimuth anisotropy.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2000-2225

... estimating the vertical velocity and depth scale

**of**the model from surface data. For laterally homogeneous VTI (transversely isotropic with a vertical symmetry axis) media above the target**reflector**, P-wave reflection**traveltimes**alone are insufficient to obtain the vertical v elocityVP0 and Thomsen...
Abstract

Summary A major complication caused by anisotropy in velocity analysis and imaging is the uncertainty in estimating the vertical velocity and depth scale of the model from surface data. For laterally homogeneous VTI (transversely isotropic with a vertical symmetry axis) media above the target reflector, P-wave reflection traveltimes alone are insufficient to obtain the vertical v elocityVP0 and Thomsen anisotropic parameters e and d. As a result, P-wave surface data have to be combined with other information (e.g., borehole data or converted waves) to build velocity models for depth imaging. The presence of lateral heterogeneity in the overburden may create the dependence of P-wave reflection data on all three relevant parameters (V P 0 , e and d) and, therefore, may help to determine the depth scale of the velocity field.

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-2017-17795790

... (1956) and Taner and Koehler (1969).

**In**horizontally layered media, for source-receiver spread-length**of**up to approximately a depth to the**reflector**, the well known hyperbolic approximation is used to describe the reflection**traveltimes**. Normal-moveout (NMO) velocity is the only parameter that controls...
Abstract

ABSTRACT Traveltime parameters, defined as the series coefficients of the traveltime squared as a function of the horizontal offset projections, play an important role in moveout approximations and corrections, and in media parameters inversion. We present an approach to derive the traveltime parameters in vertically heterogeneous anisotropic media for one- and two-way traveling waves. The approach allows to obtain the traveltime parameters of pure and converted wave modes. As a practical case, we consider tilted orthorhombic anisotropy and use a numerical model to illustrate the dependence of the high-order traveltime parameters on the Euler angles. Presentation Date: Wednesday, September 27, 2017 Start Time: 8:30 AM Location: 360D Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2011-3017

... conven- tional eikonal is, however, a one way

**traveltime**map that does not reflect directly the source/receiver setup associated with our typical surface seismic reflection ex- periment. For horizontal**reflectors**, such travelimes**in**homogenous media is given by a simple hyperbolic sur- face. To include...
Abstract

ABSTRACT Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2003 SEG Annual Meeting, October 26–31, 2003

Paper Number: SEG-2003-2100

... improved velocity estimate. n n 1 n 1 n n 1 n n h (h 39=Bh Figure 6: Moreni velocity grid (courtesy

**of**IFP). Examples We begin with a simple laterally-varying TI velocity model,**in**which the strata**dip**to the right at , overlaying a**dipping****reflector**R (Figure 1). The auxiliary horizon M is immersed...
Abstract

Summary We study a data-driven approach to multi-mode interval velocity analysis in laterally inhomogeneous and anisotropic media. We obtain a simple model-independent description of long-spread reflection moveout versus offset for both symmetric and asymmetric wave modes. It resolves a trade-off between anisotropy and lateral heterogeneity. This is done using offset-dependent arrival-angle and wavefront-curvature ( P-Q ) attributes. These attributes are estimated by transforming common-shot (CS) or common-receiver (CR) data with local slant and beam stacks for various offsets. The relationship between interval parameters and the P-Q attributes is provided by the generalized Dix-type layer-stripping formula. This formula is implemented as a recursive CS or CR wave-equation downward continuation process.

Proceedings Papers

Patrice Guillaume, Mathieu Reinier, Gilles Lambaré, Alexandre Cavalié, Monica Iren Adamsen, Benny Munch Bruun

Publisher: Society of Exploration Geophysicists

Paper presented at the 2013 SEG Annual Meeting, September 22–27, 2013

Paper Number: SEG-2013-0559

...

**dip**constraint is structural and does not constrain the position**of**the seismic**reflectors**. A shallow channel example Migration velocity analysis usually fails to identify velocity variations caused by very shallow channels (Figures 1 and 4) because RMO picks are sparse**in**shallow parts and resolution...
Abstract

Summary Ray based migration velocity analysis from pre-stack seismic reflection data is based on the characterization of the migrated reflected events by their position, dips and residual move-out. Such approaches update the depth velocity model through an optimization process, where the residual move-out of the picked migrated events is minimized while obeying some regularization constraints related to the depth or to the shape of some horizons or to the smoothness or structural conformity of the velocity field. We propose to introduce an additional term in the cost function involving the dip of kinematically migrated locally coherent events. The velocity is then updated to match the expected dip of the re-migrated offset-dependent events. We develop here the conceptual aspects of this approach within the frame of non-linear slope tomography and present a first application, on a North Sea dataset, to the characterization of very shallow channels creating pull-up and pull-down effects in deeper parts of the migrated image. Due to the very limited offset range of the residual move-out picks in shallow subsurface, these effects could not be solved by residual move-out based tomography. We demonstrate that the introduction of the dip constrained inversion allows the correction of these pull-up and pull-down effects, resulting in improved depth imaging.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-1998-1855

... used to help iden- tify the phase

**of**the seismic wavelet associated with each**reflector**. For the correct velocity model the central event**in**the gather will appear flat across all offsets because**of**the effective subtraction**of**the ray-trace moveout. Otherwise, the**traveltime**residuals for non-zero...
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-2017-17657381

... the acceptable error limit through successive iterations

**of**inversion and parameter update, which result**in**sufficient flattening**of**the reflected events**in**the common image gathers (CIG's). This is a powerful and stable methodology to handle large tilts (? = 60°)**of**the steeply**dipping****reflectors****in**...
Abstract

ABSTRACT Imaging below the tilted transversely isotropic (TTI) media pose serious problem and distortions of the subsurface geological targets for hydrocarbon exploration, which is very common in fold-thrust belts or active tectonic areas like the Foothills of Himalaya or Rocky Mountain Foothills of Canada. To model and image below the TTI media having symmetry-axis orthogonal to the dipping anisotropic layers, a TTI thrust sheet is considered for elastic anisotropic finite-difference full-wave modeling to generate synthetic seismic data using the robust staggeredgrid scheme of wave propagation. Free-surface boundary conditions at the top and absorbing boundary conditions for other three sides of the model have been imposed to reduce undesirable edge effects and suppress dispersions. The synthetic seismic data generated for the TTI thrust model are migrated using the anisotropic Kirchhoff pre-stack depth migration (PSDM) technique followed by migration velocity analysis (MVA) algorithm with traveltime computations using anisotropic ray-tracing for the model to image below the thrust sheet. The MVA algorithm adopted also estimate the anisotropic parameters e and d accurately within the acceptable error limit through successive iterations of inversion and parameter update, which result in sufficient flattening of the reflected events in the common image gathers (CIG's). This is a powerful and stable methodology to handle large tilts (? = 60°) of the steeply dipping reflectors in complex geological structures like TTI thrust sheet without much distortion of CIG's for which the symmetry-axis of each TTI block is set orthogonal to bottom of the reflectors having different tilts. This paper has been withdrawn from the Technical Program and will not be presented at the 87th SEG Annual Meeting.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1988 SEG Annual Meeting, October 30–November 3, 1988

Paper Number: SEG-1988-1061

...

**reflector**depth. Yet progress**in**velocity estimation has been slow and tortuous.**In**1955 Oix developed a procedure for estimating velocity from seismic**traveltimes**when the geology consists**of**flat homogeneous beds that are parallel to one another; each bed is**of**uniform thickness. It was not until 1974...
Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2018 SEG International Exposition and Annual Meeting, October 14–19, 2018

Paper Number: SEG-2018-2987198

... when it comes to complex subsurface structure such as steeply

**dipping****reflectors**, overthrust strata and so on. However, due to irregular illumination and acquisition footprint, RTM can t generate amplitude preserved imaging and artifacts exist**in**migration section. The concept**of**inversion was...
Abstract

ABSTRACT Least-squares reverse time migration (LSRTM) is inversion based method which can remove artificial imaging and produce amplitude preserved reflectivity section. It has shown significant advantages in lithological reservoir exploration and 4-D seismic. However, LSRTM needs the solution for Hessian matrix in iterative way. Huge requirement of computational quantity and memory storage can be obstacle limiting its application in industry. LSRTM in pseudo-depth domain was provided here to lower calculating cost while maintaining its precision. After converting velocity field from depth domain to pseudo domain, total vertical sampling number gets much reduced. Therefore, oversampling effect can be avoided when calculating wavefield in pseudo-depth domain, which leads to higher efficiency. Test result on synthetic data demonstrates the validity and effectiveness of LSRTM in pseudo-depth domain. The method has huge potentials to explore further when dealing with field data. Presentation Date: Tuesday, October 16, 2018 Start Time: 1:50:00 PM Location: 207A (Anaheim Convention Center) Presentation Type: Oral

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-2017-17680865

... popular least

**squares**reverse time migration, has the advantage**of**being fast enough to be applied**in**a production environment, and flexible enough to be applied without data regularization. This last characteristic makes it a good candidate to understand benefits**in****terms****of**footprint acquisition and...
Abstract

ABSTRACT Least squares migration has been an important research topic in the academia for about two decades, but only recently it has attracted interest from the industry. The main reason is that from a practical point of view its ratio of benefit/cost has not been sufficient for its use in seismic exploration. Another problem is that these benefits are mixed with effects from the filtering techniques used to regularize the inversion, which are computationally much cheaper. In this paper, I discuss some challenges with least squares Kirchhoff depth migration. This algorithm, although less precise than the more popular least squares reverse time migration, has the advantage of being fast enough to be applied in a production environment, and flexible enough to be applied without data regularization. This last characteristic makes it a good candidate to understand benefits in terms of footprint acquisition and aliasing. In addition, its limitations in terms of modelling/imaging accuracy make more evident some problems that exist but are often ignored when using reverse time migration with synthetic data. Presentation Date: Wednesday, September 27, 2017 Start Time: 3:55 PM Location: 361A Presentation Type: ORAL

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