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Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2010-3087

... the theory of how to modify the parameters to achieve the best accuracy. We perform the accuracy analysis of reflection and transmission coefficients and find the modification which provides the second order accuracy versus grid size for planar fluid-

**elastic**and**elastic**interfaces parallel to the grid. Two...
Abstract

SUMMARY Inaccurate treatment of sharp medium discontinuities introduces a significant error in finite-difference simulations of wave propagation. Such error can be significantly decreased if medium parameters are modified in the vicinity of the interface in some special way. Here we address the theory of how to modify the parameters to achieve the best accuracy. We perform the accuracy analysis of reflection and transmission coefficients and find the modification which provides the second order accuracy versus grid size for planar fluid-elastic and elastic interfaces parallel to the grid. Two widely used finite different schemes of the second and fourth orders are considered. We validate our theoretical results numerically. INTRODUCTION It is widely known that the main sources of the errors in finite-difference numerical methods are numerical dispersion and anisotropy, e.g. these are the errors that depend on frequency and direction of propagation. However in numerical simulations of wave propagation in complex media other sources of the errors may be important. In particular, for media with discontinuous parameters which is a typical case in geophysics, the errors due to inaccurate treatment of the sharp medium interfaces should be taken into account. Numerical dispersion and anisotropy errors are well understood in theory. They are controlled by the grid size and can be significantly decreased by applying high-order methods in space. One of the most popular techniques to diminish the interface error is a modification of medium parameters in the vicinity of the interface. Several approaches of how to modify the parameters have been developed, e.g., Muir et al. (1992), Kummer et al. (1987), Moczo et al. (2002). However, there is a lack of theoretical understanding of the accuracy of methods, even for the simple case of the interface parallel to the grid. The accuracy analysis performed in most of the papers has been made numerically only and there has been no numerical study of the order of accuracy versus grid size. Various authors, e. g. Graves (1991), Zahradnik et al. (1993), reported the good accuracy of the numerical simulations with the appropriate medium parameters modifications; however, a loss of accuracy was noticed for some modifications. Symes and Vdovina (2009) proved for 1D case that second-order, staggered-grid, finite-difference scheme with no parameters modification loses one order of accuracy in discontinuous medium. Vossen et al. (2002) observed the loss of convergence with the grid size for fourth order staggered-grid scheme for wave propagation along the fluid-elastic interface (Scholte wave). The rigorous accuracy study with a recommendation of how to modify the parameters to achieve the best accuracy has been made by Cohen and Joly (1996) for the 1D acoustic case on a non-staggered grid. Here we expand their approach to a 2D case elastic-elastic and fluid-elastic interfaces for staggered grid schemes of the second (Virieux (1986)) and fourth (Levander (1988)) orders. We support theoretical results with numerical experiments. ACCURACY ANALYSIS To perform the accuracy analysis we compare reflection and transmission coefficients for differential and discretized elastic wave equation.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the SEG/AAPG/SEPM First International Meeting for Applied Geoscience & Energy, September 26–October 1, 2021

Paper Number: SEG-2021-3564832

... the dimensionality of the problem. Using local solvers, we can reduce the size of the computational domain to small areas while preserving the fidelity of the

**elastic**wavefield reconstruction. Both the full waveform and extracted amplitudes and phases from seismic reflections are used in geophysical inversions...
Abstract

In many inverse problems such as Full-Waveform Inversion (FWI) or reverse-time migration (RTM) the key computational cost is the repeated seismic modeling. Due to data and model spaces dimensions, the inversion algorithms become too costly, so that practical approaches are needed to reduce the dimensionality of the problem. Using local solvers, we can reduce the size of the computational domain to small areas while preserving the fidelity of the elastic wavefield reconstruction. Both the full waveform and extracted amplitudes and phases from seismic reflections are used in geophysical inversions to recover elastic parameters in regions of interest. In this study, we compare full-waveform inversion and amplitude-phase versus offset inversion to recover elastic parameters for a reflector of interest using a local elastic solver.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2020-3410057

... Correctly injecting recorded multicomponent seismic data to generate receiver-side wavefield is a major step in

**elastic**reverse time migration (RTM). In land reflection survey, the data are often recorded at the free surface where the traction free condition is naturally maintained. Based...
Abstract

Correctly injecting recorded multicomponent seismic data to generate receiver-side wavefield is a major step in elastic reverse time migration (RTM). In land reflection survey, the data are often recorded at the free surface where the traction free condition is naturally maintained. Based on the representation theorem, we propose a numerical appsoach to inject receiver-side signals from a free surface to reconstruct the receive-side wavefield. By injecting the traction-free time-reversed multicomponent seismic records from the surface, the method can generate correct down-going wavefields, which can further be used in the elastic RTM. Numerical examples are used to validate the injection and wavefield reconstruction procedure. Synthetic dataset is calculated in a model with a free surface boundary condition, and then re-injected to the model with a traction-free boundary condition. The reconstructed wavefields are carefully compared to the original forward propagated waves to evaluate the accuracy of the boundary treatment. By combining the regenerated receiver-side wavefield, the source-side wavefield and a vectorized image condition, we also tested the multicomponent elastic RTM. The PP, PS, SP and SS images are calculated. Presentation Date: Monday, October 12, 2020 Session Start Time: 1:50 PM Presentation Time: 1:50 PM Location: Poster Station 7 Presentation Type: Poster

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2020-3428395

... We combine two inversion techniques to achieve an accurate wave-equation-based

**elastic**-parameter estimation workflow using pressure data. We first apply full-waveform inversion by model extension (FWIME), a robust model-building technique, which provides an accurate migration velocity so...
Abstract

We combine two inversion techniques to achieve an accurate wave-equation-based elastic-parameter estimation workflow using pressure data. We first apply full-waveform inversion by model extension (FWIME), a robust model-building technique, which provides an accurate migration velocity so that flat angle-domain common-image gathers (ADCIGs) can be obtained. Secondly, we employ the retrieved migration velocity to perform a redatuming technique based on an extended least-squares migration process, which allows the reconstruction of elastic pressure data coming from a target area. These reconstructed data are finally employed within an elastic fullwaveform inversion (FWI) procedure to estimate the elastic parameters of the target area with a fraction of the computational cost of inverting the entire surface pressure data. We demonstrate the efficacy of this new workflow on elastic pressure data recorded on the Marmousi2 model and where the goal is the estimation of the elastic parameters of a gas reservoir. Presentation Date: Wednesday, October 14, 2020 Session Start Time: 8:30 AM Presentation Time: 9:45 AM Location: 361F Presentation Type: Oral

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2019-3215341

... ABSTRACT In this paper, the Fourier Coefficients (FCs) expression of azimuthally anisotropic

**elastic**impedance (EI) equation is derived, a three-step workflow is proposed to simultaneously estimate P-wave impedance, S-wave impedance and fracture weaknesses parameters. The first step...
Abstract

ABSTRACT In this paper, the Fourier Coefficients (FCs) expression of azimuthally anisotropic elastic impedance (EI) equation is derived, a three-step workflow is proposed to simultaneously estimate P-wave impedance, S-wave impedance and fracture weaknesses parameters. The first step of the workflow is using the stacked seismic data to separately predict the small, middle, and large incidence angle EI data sets at each azimuth, after which we extract the FCs from all the predicted results of azimuthally anisotropic EI. Finally, the nonlinear iteratively reweighted least squares (IRLS) algorithm is implemented to simultaneously estimate P-wave impedance, S-wave impedance and fracture weaknesses parameters from all the extracted results of FCs. Tests on synthetic data show that inversion results are still estimated reasonably with moderate noise. A test on real data shows that the estimated results are in good agreement with the drilling. Presentation Date: Monday, September 16, 2019 Session Start Time: 1:50 PM Presentation Time: 2:15 PM Location: 217D Presentation Type: Oral

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1983 SEG Annual Meeting, September 11–15, 1983

Paper Number: SEG-1983-0254

... ABSTRACT No preview is available for this paper. reflection refraction approximation elliptical velocity dependence equivalent force diffraction rayleigh different part point source polar axis lobe wavelength upstream oil & gas incidence refraction

**elastic**wave...
Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1983 SEG Annual Meeting, September 11–15, 1983

Paper Number: SEG-1983-0256

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

**elastic**inclusion rayleigh interference factor dynamical variable circular disc vibrator characteristic upstream oil & gas partition sv wave lobe displacement transition zone**elastic**wave ice...
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-2017-17431305

...

**Elastic**least-squares reverse time migration via linearized**elastic**full waveform inversion with pseudo-Hessian preconditioning Ke Chen and Mauricio D. Sacchi, University of Alberta SUMMARY Time domain**elastic**least-squares reverse time migration (LSRTM) is formulated as a linearized**elastic**full...
Abstract

ABSTRACT Time domain elastic least-squares reverse time migration (LSRTM) is formulated as a linearized elastic full waveform inversion (FWI) problem. The elastic Born approximation and elastic reverse time migration (RTM) operators are derived from the time-domain continuous adjoint-state method. Our approach defines P- and S-wave impedance perturbations as elastic images. Our algorithm is obtained using continuous functional analysis where the problem is discretized at the final stage (optimize-before-discretize approach). The discretized numerical versions of the elastic Born operator and elastic RTM operator pass the dot product test. The conjugate gradient least squares (CGLS) method is used to solve the least-squares optimization problem. The diagonal of the pseudo-Hessian is used for preconditioning the elastic LSRTM. Elastic LSRTM provides higher resolution images with fewer artifacts and a superior balance of amplitudes when compared to elastic RTM. Moreover, elastic LSRTM can remove cross-talk between P-and S-wave impedance perturbations. Presentation Date: Monday, September 25, 2017 Start Time: 2:40 PM Location: 361A Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2015-5819774

...Inversion of

**elastic**parameters based on ray-path**elastic**impedance theory and its application in the prediction of tight sand reservoirs Duan Yushun, Wang Peng*, Wang Shicheng, Han Wei, Wang Juan, and Hao Fuzeng, BGP, CNPC Abstract Compared with**elastic**impedance (EI), ray-path**elastic**impedance...
Abstract

Abstract Compared with elastic impedance (EI), ray-path elastic impedance (REI) reduces the requirement for the Vp/Vs velocity ratio to be used as a constant parameter, leading to calculations of greater precision. Based on the REI formula, the analytic calculation of elastic parameters is derived from the objective function. It is not necessary to calculate the elastic parameter by means of iteration. As a result, the inversion of elastic parameters, in theory, is more precise and efficient. The AVO curve of the typical gas reservoir interface in the LD region of the Ordos Basin shows that the relative error of the reflection coefficient calculated by using REI is evidently smaller than that of the Shuey approximation formula. When the angle of incidence is 30°, the REI error is only 3%, whereas the error from the Shuey approximation formula is 13.2%. Therefore, the REI approach can better reflect the features of tight gas reservoirs. The example from the tight sand gas reservoir in the LD region shows that the result matches extremely well with the gas testing results of known wells. Introduction As a generalization of AI, elastic impedance (EI) as defined by Connolly (1999) takes into account the effect of P-wave reflectivity versus incident angle in order to solve the post-stack seismic trace inversion problem at large offsets. When the EI function is used in seismic trace inversion, the ratio of S-wave to P-wave velocities, ?=ß/a, is assumed to be constant, and the seismic data are replaced with a common angle stack or an AVA fitting stack. Ray-path elastic impedance (REI; Wang, 2003; Ma and Morozov, 2004) eliminates the requirement for the Vp/Vs velocity ratio in the EI formula to be a constant variable. It is more precise than the EI formula, and better matches real-world scenarios. Pan et al. (2003) analyzed and compared some EI formulas, and suggest the GEI still has very high precision, even for the special case of REI. Wang (2003) was the first to use the REI formula, influencing many scholars to study similar approaches. Zhang et al. (2011) constructed a new parameter, which is the normalized EI with the strong points of both EI and REI, and used the estimated P-wave impedance. Liu et al. (2011) omitted the high-order term in the REI formula and derived a new REI formula as the function of the P- and Swave impedance. When the incidence angle is small, the precision is similar to that of the REI formula. However, when the incidence angle is large, the error is also large. As a result, it is only suitable for small incidence angles.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2012-1158

... porous media by equivalent visco-

**elastic**solids. In this work, we solve Biot’s equations of motion to perform numerical simulations of seismic wave propagation through porous media containing mesoscopic heterogeneities. We then use an upscaling procedure to replace the heterogeneous poro-**elastic**regions...
Abstract

SUMMARY There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes the predominant attenuation mechanism at seismic frequencies. As a consequence, centimeter-scale perturbations of the subsurface physical properties should be taken into account for seismic modeling whenever detailed and accurate responses of the target structures are desired. This is, however, computationally prohibitive since extremely small grid spacings would be necessary. A convenient way to circumvent this problem is to use an upscaling procedure to replace the heterogeneous porous media by equivalent visco-elastic solids. In this work, we solve Biot’s equations of motion to perform numerical simulations of seismic wave propagation through porous media containing mesoscopic heterogeneities. We then use an upscaling procedure to replace the heterogeneous poro-elastic regions by homogeneous equivalent visco-elastic solids and repeat the simulations using visco-elastic equations of motion. We find that, despite the equivalent attenuation behavior of the heterogeneous poroelastic medium and the equivalent visco-elastic solid, the seismograms may differ due to diverging boundary conditions at fluid-solid interfaces, where there exist additional options for the poro-elastic case. In particular, we observe that the seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an interesting result, which has potentially important implications for wave-equation-based algorithms in exploration geophysics involving fluid-solid interfaces, such as, for example, wave field decomposition.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2011-2762

... ABSTRACT A new algorithm is proposed here to extract

**elastic**parameters from**elastic**impedance (EI) by using linearized Bayesian theory. Rock physics relations are also included as priori information and used to constrain the inversion process. Test on synthetic data shows that all parameters...
Abstract

ABSTRACT A new algorithm is proposed here to extract elastic parameters from elastic impedance (EI) by using linearized Bayesian theory. Rock physics relations are also included as priori information and used to constrain the inversion process. Test on synthetic data shows that all parameters are almost perfectly retrieved when the noise approached abnormal level. The elastic parameter inversion results can be used to predict the lithology and fluid in reservoir. Processing real data collected from carbonate reservoir in southern China, all the elastic parameters are well estimated and match the well data perfectly. The results also show well gas reservoir discrimination in this area.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the 45th U.S. Rock Mechanics / Geomechanics Symposium, June 26–29, 2011

Paper Number: ARMA-11-389

... ABSTRACT Laboratory tests on dry outcrop and artificial sandstone indicate that non-

**elastic**deformation appears quickly upon loading from the forming state or a turning point on the stress path. Upon further loading the non-**elastic**part of the deformation may increase or decrease depending...
Abstract

ABSTRACT Laboratory tests on dry outcrop and artificial sandstone indicate that non-elastic deformation appears quickly upon loading from the forming state or a turning point on the stress path. Upon further loading the non-elastic part of the deformation may increase or decrease depending on the stress history of the rock. Upon unloading from the forming state or from a turning point of the stress path the non-elastic part of the deformation appears to grow linearly with stress alteration, starting from zero. The results may be utilized to obtain values for purely elastic stiffness on the basis of static measurements, at points where the stress path turns from loading to unloading. Combined with dynamic (velocity) measurements, this may allow for estimation of dispersion, or estimation of Thomsen’s d-parameter, without the use of complicated experimental equipment. 1. INTRODUCTION Rock volumes situated in the vicinity of rock altering events are usually subject to stress changes, ranging from next to nothing and up to levels that may even induce failure. For instance, the magnitude of stress changes induced by the drilling of a well depends - according to linear elasticity - on the inverse square of the distance from the well, and hence vanishes asymptotically. Also for the rock around a reservoir, depletion induced stress changes decrease with distance in a similar way. For activities such as modeling of rock deformation and interpretation of time lapse seismics, it is of interest to know where and when the rock behaves like a linearly elastic material, and how the transition from such behavior to non-elastic behavior occurs. We here present results from laboratory tests on relatively weak outcrop sandstone, where both static and dynamic (elastic) moduli are measured simultaneously. Particular attention is given to the behavior when the stress path makes a turn, which for such materials is the closest we get to a field situation where the stress state is shifted from its in situ equilibrium. Previous results [1, 2] show that the difference between static - generally non-elastic - and elastic behavior is small when the stress state is close to a turning point, while the difference grows as the stress state deviates more and more from the turning point. We also present results from tests where artificial sandstone is cemented under stress, and subsequently subjected to stress alterations. In terms of stress path, this situation is even closer to the field situations we are considering. 2. LABORATORY TESTS Some of the laboratory tests were performed on outcrop sandstone [2, 3], while some of the tests were performed on synthetic sandstone formed under stress [4]. The tests were performed on core plugs of size 3” (length) by 1½” (diameter). The test setup is shown schematically in Fig. 1. P-and S-wave velocities were measured in the axial direction by transducers mounted in the pistons, while transducers clamped to the sleeve were used to measure the P-wave velocity in the lateral (radial) direction. Axial deformation was measured by LVDTs while lateral deformation was measured by a chain.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2009-2799

... Summary We use the synthetic

**elastic**Marmousi-II ocean bottom cable (OBC) dataset to compare the results from**elastic**reverse-time migration (RTM) and acoustic RTM. We applied acoustic RTM to the pressure data and applied**elastic**RTM to the horizontal and vertical particle velocity data...
Abstract

Summary We use the synthetic elastic Marmousi-II ocean bottom cable (OBC) dataset to compare the results from elastic reverse-time migration (RTM) and acoustic RTM. We applied acoustic RTM to the pressure data and applied elastic RTM to the horizontal and vertical particle velocity data for simulated OBC data at the sea bottom. The results show clear improvement on the elastic P-wave RTM images compared to the acoustic RTM images. Introduction Reverse-time depth migration (RTM) has become more attractive as computing power has increased with an advantage over less-computationally-intense methods of being able to handle complex subsurface structures for difficult targets adjacent and beneath salt. Compared to conventional one-way wave equation migration that treats multiple scattering as noise, RTM considers multiple scattered energy as signal useful for creating better images. This capability is extremely important in situations where only scattered waves can illuminate the target. Elastic RTM uses the elastic wave equation to propagate source and receiver wave fields and has potential advantages over acoustic RTM for migrating multi-component data. The conventional approximation for multi-component data has been to migrate individual particle-velocity components using an acoustic RTM scheme making the assumption that the vertical geophone records only P waves and that the horizontal geophones only record S waves. Approximate P-P images would be created using the vertical particle velocity component and the P-wave velocity model. Approximate SV-SV images would use the inline particle velocity component and the S-wave velocity model. SH-SH images would use the transverse particle velocity component and the S-wave velocity model. Converted P-SV wave images would be made using a dual velocity model approach where the source-to-image-point propagation used the P-wave velocity model and the receiver-to-image-point propagation used the S-wave velocity model. Such procedures are at most kinematically correct because acoustic wave propagation does not properly treat all of the elastic wave propagation issues needed for optimal imaging. Comparisons need to be made to justify the extra cost associated with elastic RTM compared with acoustic RTM. Although acoustic RTM is faster than its elastic counterpart, it has the intrinsic liability that the actual wave propagation in the earth is elastic. By migrating the elastic wave field using acoustic approximations, inevitably artifacts due to the coupling and conversion between P-wave and S-wave components bring uncertainty to the migrated results. On the other hand, elastic RTM has the correct physics to handle multi-component data and accurate source and receiver features such as radiation patterns, and it can migrate different wave types to their correct subsurface position. Meanwhile, our computational capability has increased dramatically, which makes full elastic RTM more practical for real applications. Yan and Sava (2008) extensively reviewed various conventional elastic imaging conditions, including imaging with vector displacements and imaging with scalar and vector potentials. They also discussed the extended elastic imaging conditions with non-zero cross-correlation lags in space and time for RTM with angle-domain imaging formulated for multi-component elastic data. Denli and Huang (2008) proposed a wavefield-separation imaging condition for elastic RTM that mitigates the low-frequency artifacts associated with migration using conventional cross-correlation imaging condition.

Proceedings Papers

Carlos Alberto Pedroso, Luiz Carlos do Carmo Marques, Paulo Roberto Da Motta Pires, Luiz Carlos Paixao, Euripedes Barsanuplho Luz, Jr.

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the 8th European Formation Damage Conference, May 27–29, 2009

Paper Number: SPE-122180-MS

... to inject large amount of water in dolomites. All these projects were preceded by a fracture growth analysis. Usually, these analyses are carried-out by using simulators which are based in Linear

**Elastic**Fracture Model theory (LEFM) and consider a single planar fracture. However, in the case of IAFP in non...
Abstract

Abstract The Injection Above the Fracture Pressure (IAFP) has became one of the most important alternatives to guarantee high injection rates, even when the quality of the injected water is below the minimum requirements for not damaging the rock-reservoir. For this reason IAFP has found a vast application in both, the discard or re-injection of oily water or water with high solid content and to maintain the injectivity index of injector wells. In Campos Basin, an interesting application of IAFP to assure the injection rate has been done in a pair of parallel horizontal wells completed with HOHGP (horizontal open hole gravel pack) in a Maastrichtian reservoir, where the fracture growth has been monitored through Hall Plots. In the first group (IAFP for water discard) some new projects have been planned, such as an "ecological well" (so called because the reduction of discard) which plan to inject large amount of water in dolomites. All these projects were preceded by a fracture growth analysis. Usually, these analyses are carried-out by using simulators which are based in Linear Elastic Fracture Model theory (LEFM) and consider a single planar fracture. However, in the case of IAFP in non-consolidated sandstones or soft carbonates, these assumptions can be quite unrealistic. Effects of plastic deformation in the fracture tip, compacting or fluidization of porous media, multiple fractures and pore-elastic effects can be predominant in these cases. An example that ratifies this was the attempt to re-inject produced water above the fracture pressure in an unconsolidated Miocene reservoir. Even with injection pressure 800 psi above the fracturing pressure (measured through a previous minifrac), it was impossible to propagate the fracture. In another well, the IAFP was aborted when a completely unexpected fracture gradient greater than 0.83 psi/ft was attained (it was expected 0.52 psi/ft). This behavior can only be explained if we consider the occurrence of any different phenomena of those foreseen by LEFM. This work details the IAPF projects here mentioned and depicts the deviations of LEFM observed in IAFP wells in Campos' Basin. Introduction The analysis of Figure 1 confirms the cliché that "We work in a Water Industry. The oil is just a supporting actor". This data collected in 2006 reflects the historic and the forecasted production and water injection for all the projects on development at that time in Campos Basin. The actual data, which confirmed the forecast, shows that in 2009 the oil production is circa 2,000,000 bbl/day, while the produced water is circa 3,400,000 bbl/day. If we consider that this water is re-injected or properly discarded, the total amount of water handled per day is almost 7,000,000 bbl in Campos Basin. In broad terms: "Managing water is not part of our business. It is our business". And doing that efficiently means to increase oil production at lower cost. Water injection and produced water re-injection play an extremely important role in this process (Furtado, 2005). Basically, water injection is carried out to accomplish the following functions: sweep efficiency improvement, reservoir pressure maintenance and produced water discard.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2007-1908

... Hessian matrix, the pseudo-Hessian matrix has a limitation to scale the gradient of misfit function compared to the approximate Hessian matrix. To validate the new pseudo- Hessian matrix, we perform frequency-domain

**elastic**full waveform inversion using this Hessian matrix. By synthetic experiments, we...
Abstract

Summary For scaling of the gradient of misfit function, we develop a new pseudo-Hessian matrix constructed by combining amplitude field and pseudo-Hessian matrix. Since pseudo- Hessian matrix neglects the calculation of the zero-lag auto-correlation of impulse responses in the approximate Hessian matrix, the pseudo-Hessian matrix has a limitation to scale the gradient of misfit function compared to the approximate Hessian matrix. To validate the new pseudo- Hessian matrix, we perform frequency-domain elastic full waveform inversion using this Hessian matrix. By synthetic experiments, we show that the new pseudo-Hessian matrix can give better convergence to the true model than the old one does. Furthermore, since the amplitude fields are intrinsically obtained in forward modeling procedure, we do not have to pay any extra cost to compute the new pseudo-Hessian. We think that the new pseudo-Hessian matrix can be used as an alternative of the approximate Hessian matrix of the Gauss-Newton method. Introduction One of the main problems of elastic waveform inversion algorithms can be computational costs and time caused from the calculation of the gradient and the Hessian matrix of misfit function. Pratt et al. (1998) showed that the Gauss-Newton method and the full Newton method have an effect of scaling (i.e., normalizing) the gradient of misfit function, which leads to better convergence rates and better results than those of the gradient method. Operto et al. (2004), Ravaut et al. (2004), Sheen et al. (2006) and Xu et al. (2006) applied the Gauss-Newton method in seismic waveform inversion. In spite of the advantages of the Gauss-Newton method and the full Newton method, we still hesitate to apply such algorithms in elastic waveform inversion, because of their huge computational costs and time required for the computation of the Jacobian and Hessian matrices. As an effort to enhance the efficiency of seismic waveform inversion algorithm, a backpropagation algorithm was suggested and has been popularly employed in waveform inversion algorithm (Lailly, 1983; Tarantola, 1984; Pratt et al., 1998; Choi et al., 2005; Shin and Min, 2006). By using the backpropagation algorithm, we can compute the gradient of misfit function without directly computing Jacobian matrices. In the case of using the backpropagation algorithm, it is not an efficient way to employ the Gauss-Newton or the full Newton method, because we need to compute Jacobian matrices additionally which is only used to scale the gradient of misfit function (note that the backpropagation method allows us to circumvent the calculation of Jacobian matrix). In order to scale ( precondition) efficiently the gradient of misfit function for frequency-domain elastic full waveform inversion, we developed a ‘new’ pseudo-Hessian matrix. The new pseudo Hessian matrix is a modification of the pseudo-Hessian matrix that was proposed by Shin et al. (2001). The pseudo Hessian matrix was derived from the approximate Hessian matrix by ignoring an effect of the zero-lag auto-correlation of impulse responses that describes geometrical spreading. To overcome the limitation, we propose a new pseudo-Hessian matrix, which is constructed by using the virtual source and the amplitude fields of impulse response.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 3–6, 2004

Paper Number: OTC-16731-MS

... Abstract The concept of

**Elastic**Inversion (EI) has been generally accepted over the last few years in the exploration and production environment. EI reconstructs**elastic**attributes, such as Poisson's ratio, V p /V s ratio and other attributes using angle stack AVO data. This paper discusses...
Abstract

Abstract The concept of Elastic Inversion (EI) has been generally accepted over the last few years in the exploration and production environment. EI reconstructs elastic attributes, such as Poisson's ratio, V p /V s ratio and other attributes using angle stack AVO data. This paper discusses a 3-point elastic inversion method. As its name suggests the 3-point inversion needs three impedance values at each location for calculating various elastic attributes. First, three angle stacks are calculated and inverted individually to reflectivity impedances using standard seismic software. The three resulting reflectivity impedances are associated with angle-dependent elastic impedance by Connolly's (1999) formula. Unfortunately, this EI formula is strongly dimension-dependent, which makes application of it difficult since it predicts very large values of EI for small angels and small values of EI for large angles. In 2002 Withcombe derived a dimensionless version of Connolly's formula. It contains quantities V p , V s and normalized by the background (average) values of V p , V s and. The background values are derived either from the mudline or from existing logs. We obtain stable results using a slightly modified version of Whitcombe's and Connolly's formulae. Here, we present and discuss real-data results on a Frio reservoir. The Elastic Inversion Concept Elastic Inversion reconstructs elastic attributes, such as V p /V s ratio, Poisson's ratio and other attributes using angle stack AVO data. First, three angle stacks are calculated, e.g. at near (5-15 degrees), middle (15-25 degrees) and far angles (25-35 degrees). Next, each of these angle stacks is inverted to reflectivity impedances, using standard seismic software. The following method is used to associate the three resulting reflectivity impedances with angle dependent elastic impedance. Unfortunately, Connolly's EI formula is strongly dimensiondependent, which makes application of it difficult since it predicts large values of EI for the small angles and small values of EI for large angles. Whitcombe (2002) derived a dimensionless version of the EI formula: (Mathematical equation available in fullpaper) which contains quantities V p , V s and normalized by the background (average) values of V po , V so This is the formula used for this elastic inversion. Assuming that K=2, and taking the logarithm of EI and rearranging the terms, we have: (Mathematical equation available in full paper) Seismic example The Frio reservoir is a stratigraphically trapped sand and shows a large drop in acoustic impedance when gas saturated. This results in a typical bright spot around the gas reservoir. However, amplitude alone does not seem to define the limits of the gas sand sufficiently and elastic attributes were calculated. Figure 1 shows an amplitude horizon map at the top of the Frio reservoir. Around well-2 amplitude anomalies are present, which are most likely caused by the gas. However, this figure does not clearly show the extent of the reservoir. Figure 1: Amplitude map at top of Frio sand. (available in full paper) Figure 2 displays the elastic attribute Poisson's ratio.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2003-0204

... Summary In this paper we first incorporate quality factors (Q p and Qs) into

**elastic**thin-slab propagators, which is a fast one-way**elastic**propagator, using complex velocities to specify intrinsic attenuation effects for**elastic**wave modeling in visco-**elastic**media. The accuracy of the Q...
Abstract

Summary In this paper we first incorporate quality factors (Q p and Qs) into elastic thin-slab propagators, which is a fast one-way elastic propagator, using complex velocities to specify intrinsic attenuation effects for elastic wave modeling in visco-elastic media. The accuracy of the Q-incorporated method at handling attenuation and scattering / reflection due to heterogeneities in both elastic parameters and intrinsic attenuation is numerically investigated. For models with Q contrasts and density and velocity perturbations, the use of complex velocities can improve the wide-angle capacity of the methods at large-angle scatterings. Second, we apply the method to AVO modeling in heterogeneous visco-elastic media and to frequency-dependant amplitude analysis.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the 20th U.S. Symposium on Rock Mechanics (USRMS), June 4–6, 1979

Paper Number: ARMA-79-0541

... ABSTRACT: Comparisons of finite element analyses of "cave" zone growth with longwall face advance using

**elastic**-plastic and**elastic**-brittle material descriptions show some differences in cave zone extent, but the differences are not large relative to the loads on wood cribs used for support...
Abstract

ABSTRACT: Comparisons of finite element analyses of "cave" zone growth with longwall face advance using elastic-plastic and elastic-brittle material descriptions show some differences in cave zone extent, but the differences are not large relative to the loads on wood cribs used for support in the "bleeder" entry adjacent to the longwall starting room. The elastic-plastic description is based on pressure dependent yield and associated flow rules; the elastic brittle description is based on a discontinuing strain softening concept appropriate to diffuse fracturing accompanied by an abrupt change in rock properties. INTRODUCTION The University of Utah, the U.S. Bureau of Mines and the Kaiser Steel Corporation have been engaged in a cooperative study of a single entry longwall development system at the latter''s Sunnyside Mine in central Utah. The purpose of the study is to determine whether a single entry system is as safe or safer than the double entry development system currently in use. The double entry system itself is unusual; the majority of longwall development systems in the United States use multiple entries. The potential advantages and disadvantages of single entry development for longwall mining compared to double and multiple entry development have been described by Poad, Waddell and Ross (1974) and by Ross (1974). The main advantages are: improved ground control, improved ventilation, increased coal recovery and increased development rate. These follow from the elimination of the chain pillars (normally not recovered), crosscuts, intersections and the additional entries associated with multiple entry development systems. One part serves for access and fresh air intake; the second part serves as a belt and exhaust air entry as shown in Fig. 1. A metal brattice separates the two, and a row of cribs along the centerline provides additional roof support beyond that afforded by bolting.

Proceedings Papers

Paper presented at the 1st ISRM Congress, September 25–October 1, 1966

Paper Number: ISRM-1CONGRESS-1966-046

... Summary The so-called borehole-method and the pressure chamber method have been adopted recently to estimate the in-situ

**elastic**modulus of the foundation rock by measuring the deformation of the bored hole or the chamber subjected to internal pressure. In these method, the foundation rock has...
Abstract

Summary The so-called borehole-method and the pressure chamber method have been adopted recently to estimate the in-situ elastic modulus of the foundation rock by measuring the deformation of the bored hole or the chamber subjected to internal pressure. In these method, the foundation rock has been, hitherto, assumed to be homogeneous and isotropic for the determination of elastic modulus from the measured results. Many kinds of rock mass have the orthotropic properties because of the foundation rock being affected by stratification and geological discontinuity. In this study, the states of deformation around a circular hole subjected to internal pressure in the orthotropic medium are theoretically investigated in plane strain condition, and the method of determining the orthotropic elastic moduli (or deformation moduli) by the measured values of the diameter changes of the hole in the three directions are presented. One example is shown as an application of this calculation method by using the results from tests carried out by the radial jack of TlWAG. Resume La methode dite trou-perfore et celie dite galerie en charge ont ete recemment adoptees pour l'estimation in-situ du module d'elasticite d'un rocher de base par la deformation du trou ou de la galerie cause par la pression interne. Dans ces methodes de calcul une hypothèse a ete jusqu'ici retenue que Ie rocher en question soit homogène et isotropique, Plusieurs espèces du rocher ont en realite de la propriete orthotropique à cause de la stratification et de la discontinuite geologique. Dans l'expose present, l'auteur a theoriquement examine la deformation par la pression interne du trou circulaire perfore dans un milieu d'elasticite orthotropique sous l'etat de contraines planes et propose une methode de calcul du module d'elasticite orthotropique (ou module de deformation) par le changement du diamètre du trou, avec un exemple du calcul en partant des valeurs mesurees lors de l'essai effectue avec le verin radial de TIWAG. Zusammenfassung Seit kurzem sind das sogenannte Bohrlochund Druckschachtsverfahren herangezogen worden, um den in-situ-Modul des Gebirges abzuschatzen durch die Abmessung der Formanderung des Bohrlochs oder des Schachtes, die unter Innendruck gesetzt sind. Bei der Bestimmung des Elastizitatsmoduls aus den gemessenen Ergebnissen wurde es bisher angenommen, daβ das Gebirge homogen und isotrop sei. Viele Felsmassen haben orthotrope Eigenschaften, weil das Gebirge durch die Aufschichtung und die geologiscbe Diskontinuitat beeingluβt ist. In dieser Arbeit werden die Formanderungszustande rings eines unter Innendruck gesetzten Kreisschachtes, der in einem orthotrop- elastischen Medium gebohrt und im ebenen Verzerrungszustand ist, theoretisch untersucht, und das Bestimmungsverfahren der orthotrop-elastischen Moduln (oder der Deformations-Moduln) aus den gemessenen Ergebnissen der Durchmesserveranderungen des Lochs in drei Richtungen dargelegt. An einem Beispiel wird es gezeigt, wie mit Hilfe dieses Verfahrens die Berechnung durchzufuehren ist; dabei werden die Zahlenwerte, die sich aus den Versuchsergebnissen unter Verwendung der Radialpresse der TlWAG ergeben, zugrunde gelegt. Introduction The prudent investigation of the geomechanical property of foundation rock is required when the arch dams, underground electric power stations and pressure tunnels are designed. The elastic modulus (or the deformation modulus) of the foundation rock is generally measured in the field by the static deformation tests (the jacking method and the water chamber method etc.) and the elastic wave tests. However, the large scale test like the static deformation test requires a large amount of money and labour, but often gives us the local results only. Therefore, the simple and inexpensive method of measurement became to be demanded and several testing procedures have been adopted recently, and yet some new testing methods are still under investigation. One of these new methods is the so-called borehole method which finds the elastic modulus by measuring the deformation of the bored hole subjected to internal pressure in the deep ground [1]. In the water chamber method, TIWAG'S method [2] (in which the internal pressure is applied by the flat jacks arranged on the inner wall of the hole, instead of the water pressure in the chamber method) and the borehole tests, the foundation rock is assumed to be homogeneous and isotropic for the determination of the elastic modulus from the measured results. Then the elastic modulus can be found theoretically by measuring diameter change in one direction or volume change of the circular hole. The mean value of the measured diameter change in each direction is used practically for the calculation of the elastic modulus. In the case of in-situ measurements of the deformation modulus by a pressure meter used for soil foundation, the volume changes of the boreholes in the ground are measured and used for the calculation of the modulus for the elastic and plastic ranges of the foundation. Many kinds of rock mass have the orthotropic properties because of the foundation rock being affected by stratification and geological discontinuity. Therefore, a circular hole in the foundation rock is not deformed uniformly even under the uniformly distributed internal pressure.

Proceedings Papers

Khalid Obaid, Abdelwahab Noufal, Abdulrahman Almessabi, Atef Abdelaal, Karim Elsadany, Edan Gofer, Omar Aly, Glen Nyein, Anubrati Mukherjee

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Abu Dhabi International Petroleum Exhibition & Conference, November 15–18, 2021

Paper Number: SPE-208090-MS

..., and interpretation to model the stratigraphic/structural framework and link it with reservoir characterization. Hence, ADNOC decided to conduct a trial on state-of-art technique Litho-Petro-

**Elastic**(LPE) AVA Inversion to mitigate the seismic interpretation challenges and delineate the reservoirs. The LPE AVA...
Abstract

This study summarizes the efforts taken to provide reliable reservoir characterizations products to mitigate seismic interpretation challenges and delineation of the reservoirs. ADNOC has conducted seismic exploration activities to assess Miocene to Upper Cretaceous aged reservoirs in East Onshore Abu Dhabi. The Oligo-Miocene section comprises of interbedded salt (mainly halite), anhydrite, limestones and marls. Deposited in the foreland basin related to the Oman thrust-belt. Ranging in thickness from nearly 1.5 km in the depocenter to almost nil on the forebulge located to the west of the studied area. The well data based geological model suggests that initially porous rocks (presumably grain-supported carbonates) encompassed polyphase sulfate cementation during recurrent subaerial exposure in which pores and grains were recrystallized sometimes completely too massive, tight anhydrite beds. This heterogeneity of the complex shallow section showing high variation of velocity impact seismic imaging, and interpretation to model the stratigraphic/structural framework and link it with reservoir characterization. Hence, ADNOC decided to conduct a trial on state-of-art technique Litho-Petro-Elastic (LPE) AVA Inversion to mitigate the seismic interpretation challenges and delineate the reservoirs. The LPE AVA inversion provides a single-loop approach to reservoir characterization based on rock physics models and compaction trends, reducing the dependency on a detailed prior the low frequency model, Where the rock modelling and lithology classification are not separate steps but interact directly with the seismic AVO inversion for optimal estimates of lithologies and elastic properties. The LPE inversion scope requires seismic data conditioning such as CMP gathers de-noising, de-multiple, flattening and amplitude preservation, in addition to detailed log conditioning, petro-elastic and rock physics analysis to maximize the quality and value of the results. The study proved that the LPE AVA Inversion can be used to guide seismic interpreters in mapping the structural framework in challenging seismic data, as it managed to improve the prospect evaluation.

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