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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE International Petroleum Conference and Exhibition in Mexico, February 1–3, 2000

Paper Number: SPE-59012-MS

... contains acquisition noise, such as white and truncation errors,

**Backus**and Gilbert´s method will perform badly unless we use a**filtering**technique11-13 or the pressure integral function proposed by Blasingame et. al.14. The problem to reproduce the initial distribution with noisy data is in agreement with...
Abstract

Abstract Most of the procedures available in the literature for well tests analysis assume a uniform initial pressure distribution. In this paper the influence of a non-uniform initial condition in pressure data is presented. Several solutions, which consider a non-uniform initial distribution and different conditions at the inner and outer boundaries, are presented. These solutions were obtained by using a combination of Laplace transformation and Green's function methods. Integral equations relating the well response to the initial distribution function are obtained. These equations, which represent inverse problems, are solved recursively by using Backus and Gilbert solution. Numerical experiments of the pressure response in homogeneous and naturally fractured reservoirs with different initial pressure distributions are presented. The theory and numerical results are compared and found good agreement demonstrating the applicability of the proposed method. For radial systems it is found that the semi logarithmic straight line is not generally evident during the transient period. Also during the boundary dominated flow period, with no-flow outer boundary, it is found that an additional pressure drop is present for the case of a non-uniform initial distribution. An expression for this additional pseudo-skin is provided. Introduction A cornerstone for the well-test analyses procedures is the hypothesis of constant initial pressure throughout the reservoir. However, this assumption cannot always be justified. We know that the response of build up tests is controlled by the pressure profile at shut-in 1,2. Thus, we could expect that drawdown responses would be affected by non-uniform initial condition, which could be due to previous production from the tested well and/or surrounding wells. The determination of the original pressure state from wellbore pressure observations is an inverse problem. An obvious motivation for studying this problem is to find out how the initial state influences the wellbore pressure response. Cars law and Jaeger 3 presented an analytical solution to the heat radial problem with an arbitrary initial condition by using separation of variables. Recently, Oliver 4,5 presented a method to estimate a radial permeability distribution from well-test data. This inverse problem was solved by applying the Backus and Gilbert procedure 6, which is an alternative to the clasical inversion methods. The computed permeability profile was shown to be a smoothed version of the actual profile. In this work, the influence of an arbitrary initial distribution on the drawdown response is explored and analytical solutions are derived, for both homogeneous and naturally fractured systems, by using a combination of Laplace transformation and Green s function methods. This procedure yields integral equations, relating the well response to the initial distribution function, which are solved recursively for this function by using Backus and Gilbert procedure 6. The results presented in this work considered a fully penetrating well in the center of a cylindrical reservoir producing slightly compressible liquid, under laminar flow conditions, at a variable flow rate. The reservoir could be an infinite or a closed system.

Journal Articles

Journal:
SPE Formation Evaluation

Publisher: Society of Petroleum Engineers (SPE)

*SPE Formation Evaluation*7 (04): 290–296.

Paper Number: SPE-20555-PA

Published: 01 December 1992

...

**filtered**them with our resolving kernel, we would obtain the solutions shown in this paper. In deriving the theory for this inversion procedure, I assumed single-phase flow of a slightly compressible fluid, constant-rate drawdown, small permeability variation, constant porosity, and reservoir thickness...
Abstract

Summary This paper presents a method of estimating a radial permeabilitydistribution that would reproduce the pressure data permeability distributionthat would reproduce the pressure data obtained in a well test. The method isapplied to three examples: permeability variation in a composite reservoir, porosity variation permeability variation in a composite reservoir, porosityvariation in a composite reservoir, and permeability variation with inaccuratedata. The permeability estimates obtained are shown to be smoothed versions ofthe actual permeability distribution, and an estimate for the resolution widthof the smoothing is provided. One significant advantage of the solution methodapplied in this paper is the ability to estimate permeability variation withoutpaper is the ability to estimate permeability variation without dividing thereservoir into zones of constant permeability. Introduction If permeability, net thickness, and porosity are known throughout areservoir, it is fairly simple to estimate the pressure history at any point inthe reservoir for a given production history. This is the "forwardproblem" for pressure estimation when parameters are known. The accuracy ofpressure prediction given knowledge of the reservoir parameters has nopractical limit. Contrast this with the "inverse problem," which is toestimate the distribution of reservoir properties (i.e., porosity, permeability, and net thickness) that could result in the observedpermeability, and net thickness) that could result in the observed pressures ata well location. The inverse problem is not unique pressures at a welllocation. The inverse problem is not unique because the finite frequency ofmeasurements imposes a limit to the amount of data that can be obtained. Conventional well-test analysis is a solution method with a goal to estimate afew parameters that characterize the reservoir in the area of parameters thatcharacterize the reservoir in the area of investigation. Usually, one uniformpermeability is considered inadequate to describe the entire region; in thiscase, the skin is used to characterize the different permeability of thenear-wellbore region. If two parameters, skin and constant permeability. arenot sufficient to explain the pressure history, permeability. are notsufficient to explain the pressure history, then faults intersecting at variousangles, impermeable regions, or a second permeability region sometimes areadded, either by layering or as a concentric ring. These methods of creatingmodels that match observed pressures can be classified as parameteridentification. The important characteristic of this type of problem is thatthe dimension of the parameter space is small. problem is that the dimension ofthe parameter space is small. If we accept that permeability and porosity arefunctions of reservoir location, then we recognize that the parameter space forwell testing is infinite-dimensional. The problem of estimating a variablepermeability distribution has not been ignored. Previous methods, however, haveused finite-difference or finite-element methods to reduce the parameterdimension from infinite-dimensional to a relatively small dimension that wouldgive unique or stable results when an inverse calculation is attempted. In thispaper, I show that it is possible to retain the functional flavor of paper, Ishow that it is possible to retain the functional flavor of the permeabilityfield by using the Backus and Gilbert approach to solving the inverse problem. For a small variation in permeability, the part of the pressure response causedby variation in absolute permeability can pressure response caused by variationin absolute permeability can be written as (1) where F(r) is the inverse permeability variation defined by (2a) (2b) The primary motivation for this definition of F(r) is the linearrelationship between inverse permeability and the pressure derivative foruniform permeability reservoirs. Except for Eqs. 2, in which I differentiatebetween dimensionless and dimensional permeability, all variables in this paperare dimensionless. The permeability, all variables in this paper aredimensionless. The definitions of the dimensionless variables are thoseconventionally used in petroleum literature. The data kernels, Gi (r), in Eq. 1are influence functions because they specify the influence of permeability onmeasured pressures. For a constant-rate drawdown test, Gi (r) is large near thewell and decreases approximately as 1/r until the radius of investigation isreached. Beyond that distance, Gi (r) vanishes rapidly. This behavior isreasonable because we know that drawdown depends strongly on skin (permeabilitynear the well) and is insensitive to permeability beyond the radius ofinvestigation. The problem in well testing is to estimate the function F(r) or, equivalently, the permeability given a finite set of pressures at times (i =l, n). The theory of Fredholm integral equations of the first kind suggeststhat, when only a finite data set is supplied, F(r) cannot be determineduniquely. Data inaccuracy adds to the difficulty because it is possible that nofunction F(r) will satisfy Eq. 1 with inaccurate data. Also, because theinverse problem often is unstable, the calculated solution may be highlyoscillatory. The most common method of solving this problem (given therelationship in Eq. 1) is to assume that F(r) is piecewise constant, in whichcase we obtain a system of linear algebraic equations instead of an integralequation. If only one value of permeability is to be estimated, because the integralof Gi (r) from r= 1 to r= is approximately 0.5[log(ti) +c], the problem ofpermeability estimation from well-test data reduces to solving the followingequation for the average value, F. A serious problem with any method that relies on parameter dimensionreduction for a unique solution is to determine the optional zonation thatagrees with permeability zonation in the reservoir. One alternative to reducingthe parameter dimension arbitrarily by zonation is to apply the Backus and Gilbert solution to the inverse problem. This method allows one to obtain acontinuouspermeability-field solution to the problem and to calculateproperties of the permeability field that all solutions must share. The Backus and Gilbert Solution. The primary goal of well testing is toestimate the permeability of the formation. In this case, it is to estimate theunknown inverse permeability distribution, F(r), with the data relationshipdescribed by Eq. 1.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-1993-0642

... wavelet superposition basis function thickness interface seismic wavelet seismic data thin layer A Matched-

**Filter**Approach to Impedance Estimation S13.2 James L. Simmons, Jr.* and Milo M.**Backus**, University of Texas at Austin Summary Conventional poststack inversion algorithms parameterize the...
Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2019-3211053

... Zoep- pritz equations (Aki and Richards, 1980; Wiggins et al., 1983; Shuey, 1985; Fatti et al., 1994) instead of the Zoeppritz equa- tions themselves. However, linearization results in a less ac- curate representation of the wave behavior. They can only

**es**- timate the variation of reflection...
Abstract

ABSTRACT We propose a nonlinear AVO inversion to estimate P- and S-wave velocities and density. It is based on exact Zoeppritz solutions for P-wave reflection amplitudes. Reformulation of the parameters appearing in the Zoeppritz equation and application of an adjoint technique make the nonlinear inversion possible. In contrast to traditional AVO inversions using linearized approximation of the reflection coefficient, the inversion does not require any assumptions such as a linear relationship between parameters or the background ratio between P- and S-wave velocities. Instead, the nonlinear Zoeppritz inversion will independently estimate contrasts of target parameters. It consequently leads to better estimation of velocities and density. In order to show the superiority of the method, we present inversion results with field seismic data from the Gulf of Mexico. The results show that the inversion more accurately determines P-wave and S-wave velocities, density, and the ratio between P- and S-wave velocities compared to conventional linearized inversion. Presentation Date: Monday, September 16, 2019 Session Start Time: 1:50 PM Presentation Time: 4:45 PM Location: 217B 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-2019-3211060

.... Chavent , 1979 , Identification de param tres r partis dans les quations aux d riv

**es**partielles : RAIRO , 13 , 115 – 126 . Fatti , J. L. , G. C. Smith , P. J. Vail , P. J. Strauss , and P. R. Levitt , 1994 , Detection of gas in sandstone reservoirs...
Abstract

ABSTRACT A new seismic attribute, , provides a method to more practically estimate seismic anisotropy from real seismic data. We derive an expression for this quantity from analyses of amplitude variation with offset (AVO) inversion with full Zoeppritz solutions for P-wave reflection amplitudes. Then we present a sensitivity test with various source-receiver offsets (i.e., angles of incidence) based on a simple two layer synthetic model. The anisotropy of the model is related to the kerogen volume fraction values using measured laboratory data, and we utilize public domain data for ten different shale formations. When two different AVO ranges (i.e., relatively near and far angle ranges) are applied as inputs for the Zoeppritz AVO inversion, the inversion gives significantly different P-wave velocities. In addition, once the two inverted values are subtracted from each other, the difference, which is the seismic attribute (), increases with increase of model anisotropy. Subsequently, we demonstrate the effectiveness of the attribute with a field seismic data from the Gulf of Mexico. is well correlated with the values of gamma-ray (GR) log, which in turn is related to the amount of clay or shale content and should be highly correlated with seismic anisotropy. Therefore, these results support the effectiveness of the attribute for inference of the degree of seismic anisotropy. Presentation Date: Tuesday, September 17, 2019 Session Start Time: 8:30 AM Presentation Time: 10:35 AM Location: 217D 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-2019-3214459

... , D. , C. Puhrsch , and R. Fergus , 2014 , Depth map prediction from a single image using a multi-scale deep network : Advances in Neural Information Processing Systems , 2366 – 2374 . Fomel , S. , 2002 , Applications of plane-wave destruction

**filters**...
Abstract

ABSTRACT We propose applying a deep learning technique to directly and automatically generate Relative Geologic Time (RGT) volumes from seismic images. In this method, a multi-layer convolutional neural network (CNN) is constructed and trained with synthetic input seismic images and target RGT images. Although the network is trained using only synthetic images, it generates accurate results on real seismic images. The method automatically captures complex geologic structures in the input, including multiple crossing faults and significantly folded horizons, without any need for manual picking. Presentation Date: Tuesday, September 17, 2019 Session Start Time: 8:30 AM Presentation Time: 8:30 AM Location: 221C 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-2017-17495603

... timeshifts. Use of high frequency components mitigate problems associated with sidelobe interference. We use amplitude-adjusted plane-wave destruction (APWD)

**filters**to invert for both timeshifts and amplitude changes between the time-lapse seismic images at each frequency. Plane-wave destruction can...
Abstract

ABSTRACT Time-lapse timeshifts are difficult to measure from seismic data in the presense of low frequencies or thin beds causing tuning effects. We propose to decompose time-lapse seismic images into discrete frequency components using the local time-frequency transform before estimating timeshifts. Use of high frequency components mitigate problems associated with sidelobe interference. We use amplitude-adjusted plane-wave destruction (APWD) filters to invert for both timeshifts and amplitude changes between the time-lapse seismic images at each frequency. Plane-wave destruction can efficiently measure small shifts between seismic traces, making this algorithm particularly effective. The effectiveness of the proposed workflow is confirmed using a 1D synthetic example and a field data example from the Cranfield CO sequestration project. Presentation Date: Wednesday, September 27, 2017 Start Time: 3:05 PM Location: 351F Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2013-0291

... stratigraphic

**filtering**. Stovas et al. (2013) proposed a method to extend the**Backus**upscaling method to low-frequencies and used the wavelet amplitude spectrum to weight averaging of the frequency-dependent effective parameters. In this paper, we extend this method to high-contrast media and TTI anisotropy...
Abstract

Summary In this paper, an extension of low-frequency upscaling methods to handle more complicated media is developed. Increased variability and anisotropy with a tilted symmetry axis (TTI) are now handled. We show that strong contrasts in elastic properties have a dramatic effect on seismic upscaling regardless of anisotropy. In particular, the low-frequency upscaling method (Stovas et al., 2013) developed for isotropic and transversely isotropic media does not work due to discontinuities in the effective slowness surface. In this case, the application of a new method is required. The vertical energy flux computed for the stack of layers can be considered as an AVO signature for the overburden. The new upscaling methods are also defined for a tilted TI medium. The developed methods are tested on a real dataset from the Faroes-Shetland Basin.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2012-0950

...

**filters**in X-T domain or F-X deconvolution applied after flattening the first arrivals. We also apply a divergence correction using of (Newman 1973). As this correction does require velocity information, we use first break picks to estimate interval and RMS velocity. 2. Computation of attributes related...
Abstract

Summary Understanding of seismic attenuation plays an important role in successful application of seismic reservoir characterisation techniques based on amplitude analysis. Zero-offset vertical seismic profiling (VSP) is one of the principal tools which can be used to study seismic attenuation. A comprehensive set of zero-offset VSPs and wireline log data was acquired as a part of CO2CRC Otway project. In this study we estimate apparent attenuation from these VSP data and quantify contribution of intrinsic and scattering components of attenuation using both mathematical modeling and generalized O’Doherty-Anstey theory. Having significant redundancy in the VSP data provides the means to evaluate reliability of our estimates.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2009-2307

... upper half. fA Deconvolution

**filtering**in the local wavenumber domain. Due to the calculation of the kernels for the resolution operator (resolving kernel) (**Backus**and Gilbert, 1970; Tarantola, 1984; 2005; Wu, 2007) and volume deconvolution in space domain are intractable, we deconvolve the image with...
Abstract

Summary The tomography inversion is a process of backpropagation plus filtering in the local wavenumber domain. The backpropagation is a double focusing process and the filtering is a deconvolution in the local wavenumber domain. The filter function is forward model dependent. Through the tests of data sets generated by both the Born approximation and by the finite-difference simulations for low frequencies, we see that the qualities of the local spectra have significant improvement in both coverage and uniformity in the local wavenumber domain. Through the test using a simple model, we see that the generalized diffraction tomography is valid even for strong-contrast media with velocity perturbations less than or around 10 percent with respect to the background velocity in the model. Introduction Inversion theories and methods are forward model dependent. Different forwards models have different parameters of the models and may obtain quite different inversion results finally. Different from the traditional Born model with homogeneous background (Devaney, 1982, 1984; Saney, 1984;Wu and Toks?z, 1987), the scattered wave field can be calculated by distorted-wave Born approximation in heterogeneous media (Taylor, J. R., 1972) and in inhomogeneous background media (Schultz and Jaggard, 1987; Gelius et al., 1991). Wu (2007) derived the formulation of generalized diffraction tomography in heterogeneous media for volume scattering and the formulation uses the Green’s function based on De Wolf approximation( De Wolf, 1971, 1985; Wu, 1996, 2003; Wu et al., 2007) and includes the correction for finite frequency-band and finite spatial aperture of acquisition system. In this paper, first we present the theory and method of generalized diffraction tomography, the imaging condition and deconvolution filtering in the local wavenumber domain; then we use several numerical examples to test the spectrum recover and the validity of the generalized diffraction tomography; finally we give some conclusions. Theory and method of generalized diffraction tomography Distorted-wave Born modeling for volume scattering model. In the Born model, the parameters to be inverted are volume perturbations of unknown parameters with respect to a given reference medium. Due to the Born model only being valid for weak scattering, that is, small parameter perturbations and small integration volume, the inversion based on Born scattering is questionable for strong contrast media or large volume heterogeneities. We use forward scattering renormalized Green’s function in the model based on the De Wolf approximation which is a multiple forward scattering, single back scattering approximation (De Wolf, 1971, 1985; Wu, 1996, 2003; Wu et al., 2007). Hence in the De Wolf approximation, both the incident field and the Green’s function are forward scattering renormalized. The approximation in a type of the local Born approximation and can overcome some drawbacks and limitations of the Born modeling. Imaging condition in the local wavenumber domain. In order to be symmetric for the source array focusing and receiver array focusing, we use the modified imaging condition in the form of cross-correlation in the space domain (Wu and Chen, 2001, 2006; Wu, 2007),

Journal Articles

Journal:
SPE Journal

Publisher: Society of Petroleum Engineers (SPE)

*SPE Journal*14 (04): 746–758.

Paper Number: SPE-110771-PA

Published: 23 September 2009

... seismic trace (Gunning and Glinsky 2004). Synthetic traces corresponding to particular realizations are shown in black with the actual seismic data (gray). Impedance, Layer 1 (gm/cc) (m/s) Impedance, Layer 1 (gm/cc) (m/s) Impedance, Layer 1 (gm/cc) (m/s) Net-to-Gross, Layer 2 Th ic kn

**es**s, L ay er 2 (m...
Abstract

Summary Well data reveal reservoir layering with high vertical resolution but are areally sparse, whereas seismic data have low vertical resolution but are areally dense. Improved reservoir models can be constructed by integrating these data. The proposed method combines stochastic seismic inversion results, finer-scale well data, and geologic continuity models to build ensembles of flow models. Stochastic seismic inversions operating at the mesoscale generate rock property estimates, such as porosity, that are consistent with regional rock physics and true-amplitude imaged seismic data. These can be used in a cascading workflow to generate ensembles of fine-scale reservoir models wherein each realization from the Bayesian seismic inversion is treated as an exact constraint for a subensemble of fine-scale models. Exact constraints ensure that relevant interproperty and interzone correlations implied by rock physics and seismic data are preserved in the downscaled models. Uncertainty in the rock physics and seismic response is included by using multiple stochastic inversions in a cascading workflow. In contrast, inexact constraints generally do not preserve these correlations. We use two-point covariance at the fine scale to provide prior model thickness and porosity distributions of multiple facies. A Bayesian formulation uses the kriged data as the prior with the coarse constraints as the likelihood, and this posterior is sampled using a Markov Chain Monte Carlo (MCMC) method in a sequential simulation framework. These methods generate rich pinchout behavior and flexible spatial connectivities in the fine-scale model. These flow models are easily represented on a cornerpoint grid. 2D examples illustrate the interactions of prior and constraint data, and 3D examples demonstrate algorithm performance and the effects of stratigraphic variability on flow behavior.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2008 SEG Annual Meeting, November 9–14, 2008

Paper Number: SEG-2008-2998

... SUMMARY Conventional semblance methods can be avoided for a number of imaging tasks if local slopes can be directly extracted from prestack data, for example, by

**filtering**schemes. Recent literature shows a revival of the idea for various purposes, such as velocity analysis, tau-p imaging...
Abstract

SUMMARY Conventional semblance methods can be avoided for a number of imaging tasks if local slopes can be directly extracted from prestack data, for example, by filtering schemes. Recent literature shows a revival of the idea for various purposes, such as velocity analysis, tau-p imaging, migration to zero offset and time migration. Here, we discuss several different ways of extracting the desired slope information from the data. We propose a simple, straightforward correction to linear planewave destructors. The correction is based on the observation that additionally to the local slope, also its inverse can be extracted from the data in a fully analogous way. Combining the information of both extractions yields a simple but powerful correction to the local slopes. In our numerical examples, the naive application of simple linear plane-wave destructors with our simple, straightforward correction produced results of high quality, even in an example with a rather high noise level and interfering events. INTRODUCTION The estimation of kinematic attributes of locally coherent events in seismic data or seismic images, is an essential step for several recent developments in seismic data processing and velocity model building. Perhaps, the most visible ones are those connected with seismic tomography in which, not only traveltimes but also slowness components of events and possible other time-domain attributes are used for velocity model building. Famous examples are stereotomography (Billette and Lambaré, 1998; Billette et al., 2003) and NIP-wave tomography (Duveneck, 2004). Locally coherent events are also applied to velocity-independent time imaging (Fomel, 2007b). The estimation of kinematic attributes is usually performed in two steps. The first one is a detection step based on local coherence analysis and the second one is an extraction step based on the coherence level and continuity of the event. Here, we investigate different implementations of plane-wave destructors for automatic detection of locally coherent events. Two implementations use small moving windows through data. In the first algorithm, a single slope at the center of the window is computed by linear least squares. The second algorithm implements the prediction-error filter approach proposed by Fomel (2002). We compare these moving-window strategies with a global inversion of the slope field proposed by Fomel (2002). The global slope estimation admits different alternatives of smoothing the slowness field (Fomel, 2007a) by regularization, but is computationally demanding. The slope estimation using local windows is computationally very fast in comparison with the global estimation alternative and less dependent on prior information. We present numerical experiments using the local and global strategies for slope estimation on a simple synthetic data, corrupted by white noise. These initial results suggest that the estimation of event slopes using local windows can be a very efficient alternative to the detection of locally coherent events. PLANE-WAVE DESTRUCTORS The extraction of local slopes is done by so-called plane-wave destructors (Fomel, 2002; Claerbout, 2004). Our goal is to estimate the local slope p(x, t) for any seismic section which, in general, containing not only plane-wave events but also curved ones. The first approach is basically the technique presented in Claerbout(2004).

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2005-2123

... in- verse

**filter**applied to remove the residual multiple (Paf- fenholz and Barr, 1995), K(f) = (1 + r (f))2 [ 1 2 , 1 2 ] . (9) After the direct sum, the remaining multiple response has a finite-length inverse**filter**which happens to be the**Backus****filter**. New Techniques and SNR Bounds Optimal...
Abstract

ABSTRACT Ocean bottom cable (OBC) multiple suppression can be posed as a multi-input single-output deconvolution (MISO-D) problem, with the OBC hydrophone and geophone data as inputs and the multiple-free data as the output. We propose a powerful two-step framework, called the Texas Two-step, to solve this problem. For the case where the multiple-free reflectivity and noises in our convolutional model are stationary Gaussian random processes, we derive an upper bound on the output signal-to-noise ratio (SNR) of any OBC multiple suppression technique by invoking the Van Trees inequality, a Bayesian form of the Crame´r-Rao bound. We demonstrate that the Texas Two-step achieves the SNR upper bound, whereas other conventional methods under-perform the bound by about 2 dB or more. We also propose a new correlation model for the noise corrupting OBC data, and new SNR-optimized scalar weights for summing hydrophone and geophone data.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2003-2449

... since wavelet errors propagate through the whole process. Figure 1 shows the elements of a well tie. A broadband primaries synthetic seismogram (trace 2) constructed from a calibrated acoustic impedance log (trace 1) is matched to a seismic trace segment (traces 4 and 6). The

**filter**that converts the...
Abstract

Summary In general terms the prerequisites for a close tie between a well-log synthetic seismogram and a seismic data volume are accurate sonic and density logs and good quality seismic data. This poster discusses the key factors that underlie this generality and illustrates them with practical examples. Q,C. of the well-log and seismic data, timing and log calibration, well tie location, seismic bandwidth and S/N ratio, and the use of well tie diagnostics all play an important part in making close well ties. While attention to these factors generally leads routinely to good well ties, there remain some problem cases and areas that currently defy all attempts to produce a close tie. The poster briefly explores reasons behind these difficult cases.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-2002-0273

... and random error, respectively. Of particular interest is R = HW, (4) the resolution R. Rows of the resolution matrix can be considered as

**filters**acting on the real model to give the observed model. Consequently, we could design the in- verse operator such that the resolution is closest to the...
Abstract

Summary Conventional AVO inversion utilizes seismic data alone. However, by including prior information on the subsurface model, the AVO inversion presented herein arrives at an optimal posterior model of the subsurface - optimal in the sense that it utilizes both sets of data, weighted with their respective uncertainties, to produce the posterior model with the smallest uncertainty. Furthermore, the AVO uncertainty itself is independent of actual data and, hence, is ideally suited for survey evaluation and design (SED). In particular, a survey can be designed so that the AVO uncertainty in the future seismic acquisition will meet a preset threshold as, for example, a time-lapse AVO change.

Journal Articles

*Petrophysics - The SPWLA Journal of Formation Evaluation and Reservoir Description*43 (02).

Paper Number: SPWLA-2002-v43n2a4

Published: 01 March 2002

... assumed pattern of cycles within the data series. Secondly, based on the prediction error calculation, Prediction Error

**Filter**Analysis (PEFA) calculates the position and amplitude of breaks in the frequency successions or breaks in the phase of each cycle present within the total frequency. Finally, the...
Abstract

Parameters in Archie's equation are usually determined in labs through experiments on the electric properties of rocks. We discuss a new method using saturation analysis data to determine the parameters. Correlations among saturation, resistivity, and porosity derived from the two Archie equations convert calculation for values of electric parameters to a problem of calculation for the coefficients of an equation with several unknowns. Based on calculation and study on actual saturation analysis data in several oilfields in the Junggar basin, the calculated parameters are all within the theoretical range. which can be used to obtain a water saturation value using logging data. We discuss the factors that influence Archie's parameters, especially the influence of petrophysical properties and wettability. This can be proved using saturation analysis data for a wide range of Archie's parameters. Archie's parameters determined through electric property experiments can't prove this. More importantly, to determine Archie's parameters using saturation analysis data makes it unnecessary to calculate the resistivity of the formation water, Saturation should be measured in well preserved core since large errors can exist between the measured values and the original values due to degasification and volatilization. This will influence the effectiveness of the saturation data. Therefore, the key to the problem is to correct the measured saturation values.

Proceedings Papers

Paper presented at the 9th ISRM Congress, August 25–28, 1999

Paper Number: ISRM-9CONGRESS-1999-190

... wird die Wellenausbreitung manchmal stark behindert durch die Interferenz mehrfach gestreuter Wellen (sogenanntes "stop-pass" Verhalten).

**Es**konnte gezeigt werden, dass Wellen, welche sich parallel zu den Kluften ausbreiten, mehrere gebundelte Eigenfunktionen aufweisen mit Geschwindigkeiten und...
Abstract

ABSTRACT: Frequency-dependent acoustic wave propagation in fractured rock is examined for a set of equally-spaced, parallel fractures. Exact solutions for the velocity of the waves are obtained as a function of wave frequency and fracture stiffness and spacing. Waves propagating obliquely to the fractures show strongly anisotropic velocities for low fracture stiffnesses and high frequencies. For high frequencies, propagation of the waves is sometimes prohibited due to the interference of multiply scattered waves (stop-pass behavior). For the waves propagating parallel to the fractures, multiple guided modes are shown to exist with velocities and particle motions that are dependent on fracture stiffness and frequency. RÉSUMÉ: Ici, on examine la propagation des ondes acoustiques dans une roche fissuree avec une serie de fissures parallèles et egalement espacer, dependant de la frequence d'onde. Des solutions exactes pour la vitesse des ondes sont decritent comme fonction de frequence d'onde, la rigidite des fissures, et la distance entre fissures. Les ondes qui se propagent de direction oblique au fissures demontrent des vitesses fortement anisotrope en cas de fissures avec peu de rigidite et des frequences elevees. En cas des frequences elevees, la propagation des ondes est parfois arrêtee à cause de l'interference entre ondes multiple, dispersees (comportement arrête-aller). En cas d'ondes qui se propagent de direction parallèle au fissures, on demontre qu'il existe des modes multiples guides avec des vitesses and movement de particles dependant de la frequence et la rigidite des fissures. ZUSAMMENFASSUNG: In dieser Abhandlung untersuchen wir die frequenzabangige Ausbreitung akustischer Wellen in Festgesteinen mit parallel verlaufenden, aequidistanten Klueften, Exakte Lösungen wurden gefunden fuer die Geschwindigkeit der Wellen als Funktion der Frequenz, der Steifigkeit der Kluft sowie des Kluftabstandes. Wellen, die unter einem flachen Winkel auf die Kluefte treffen zeigen stark anisotrope Geschwindigkeiten bei geringen Steifigkeiten und hohen Frequenzen. Bei hohen Frequenzen wird die Wellenausbreitung manchmal stark behindert durch die Interferenz mehrfach gestreuter Wellen (sogenanntes "stop-pass" Verhalten). Es konnte gezeigt werden, dass Wellen, welche sich parallel zu den Klueften ausbreiten, mehrere gebuendelte Eigenfunktionen aufweisen mit Geschwindigkeiten und Teilchenbewegungen, welche von der Kluftsteifigkeit und Frequenz abhangen. 1. INTRODUCTION In recent years, fractures in reservoir rock have been recognized as important conduits for hydrocarbon production (Nelson, 1987). Fractures that serve as conduits for fluid and gas transport must be partially open. This imperfect contact can result in large normal and tangential compliances when filled with gas and large tangential compliances when filled With fluid. Compliant fractures are seismically detectable by the changes they impart to wave velocities, amplitudes, and Spectral content. By examining these characteristics, reservoir properties that arise from fractures can be investigated. One of the common geologic structures encountered in reservoir rock is that of closely-spaced parallel fractures (Laubach, 1991; Lorenz & Finley, 1991). Such structures are possibly formed by large regional compressive stresses (Lorenz et al., 1991). Gas, fluid flow and seismic wave propagation in rock with a single set of parallel fractures can exhibit strong transverse isotropy. When the seismic wavelength is much longer than the fracture spacing, the medium can be replaced by an equivalent transversely Isotropic medium (Schoenberg and Douma, 1988; Schoenberg and Muir, 1989; Hood and Schoenberg, 1989). Such an approximation is possible because the stress distribution in a representative volume containing fractures is nearly uniform because of the small spatial variations in stress.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1997 SEG Annual Meeting, November 2–7, 1997

Paper Number: SEG-1997-0175

.... Equations (10) and (11) may be readily solved in the frequency domain: = + = (14) (15) S,(w) is the power spectrum of the noise, and Ss(w) is the power spectrum of the underlying reflection ensemble. An

**es**- sential difference between this approach and Corcoran s is the presence of the H1**filter**, which...Journal Articles

Journal:
SPE Formation Evaluation

Publisher: Society of Petroleum Engineers (SPE)

*SPE Formation Evaluation*12 (02): 137–144.

Paper Number: SPE-30589-PA

Published: 01 June 1997

... better resolve lo- cal permeabilities, and the degree of averaging associated with our

**es**- timates will be minimized. In this paper, we first develop a formalism to quantify the resolu- tion and spatial averaging associated with permeability estimates us- ing interwell tracer and transient-pressure data...
Abstract

Summary This paper examines the sensitivities of interwell tracer and transient pressure response to spatial distribution of permeability heterogeneity. Based on the sensitivities, we describe a formalism to quantify the spatial resolution and averaging (smearing) associated with estimates of permeabilities derived through inversion of tracer and/or pressure data. The spatial resolution is a measure of the effectiveness of the data in estimating local-scale (grid block) permeabilities. The averaging kernels quantify the inherent averaging associated with our estimates due to limited data or sampling. By examining the spatial resolution and averaging kernels as a function of various data types, we can quantitatively evaluate the relative importance of tracer versus pressure data for heterogeneity characterization and the improvement in estimates obtained by combining the data types. We illustrate the concepts by application to a quarter five-spot geometry and also to an experimental tracer response from a well-characterized slab of Antolini sandstone. Tracer data is found to yield much better resolution compared to transient pressure response. Also, both transient pressure data and tracer data appear to better resolve barriers to flow rather than channels to flow. Introduction Current geostatistical methods for reservoir characterization are well-suited to integrate static data, such as cores, logs, and spatial statistics (semivariograms), but they are limited when applied to dynamic data, such as well tests, tracer history, and production data. Since our ultimate objective is to build a reservoir model that will be used to predict the field production, it is imperative that such models adequately reproduce all existing flow and transport data. Characterizing heterogeneous permeable media using transient pressure and tracer data typically requires the solution of an inverse problem. Such inverse modeling relies on the sensitivities of a given data set on the parameters being estimated. Several authors have examined the sensitivity of transient pressure response to the spatial distribution of permeabilities by employing a variety of techniques. These include finite difference approximation, adjoint state methods and perturbation approaches. However, very little exists in the literature on the sensitivity analysis of interwell tracer data. Such sensitivity analysis can provide crucial information regarding reliability of subsurface permeability estimates based on transient pressure and tracer data. Furthermore, traditional geostatistical approaches cannot adequately address issues such as spatial resolution of subsurface property estimates and the averaging (smearing) associated with reservoir characterization based on limited data. This makes such methods unsuitable for evaluating the relative worth of various data types for subsurface characterization, particularly when dynamic data are involved. The concepts of resolution and uncertainty have been routinely used in solid earth geophysics to assess the reliability of subsurface structures obtained through inversion of geophysical data. Similar concepts can be applied in reservoir characterization whereby transient pressure and tracer data are often used to derive the distribution of permeabilities in the reservoir. The pertinent questions here are: given a set of data, what are the length scales of heterogeneity that we are able to resolve? what are the parameter uncertainties? and what is the relative worth of various types of data e.g. pressure transient vs. tracer data for heterogeneity characterization? Since in general the level of detail that we are interested in is far greater than the amount of data available to us, there is always some degree of spatial averaging associated with local-scale permeabilities estimated through inversion of flow and transport data.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

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

Paper Number: SEG-1995-0111

... scatter in the sand points occurs over the transition from good reservoir (left) to shaley reservoir rocks of 3050% shale. While it is easy to identify these zones based on trends seen in the crossplot, both crossplots show overlap in sand and shale properties. This is

**es**- pecially true for our channel...Advertisement