Showing papers in "Geophysics in 2006"

Green's function representations for seismic interferometry

Abstract: The term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. The first version of this principle was derived by Claerbout (1968), who showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. For an arbitrary 3D inhomogeneous lossless medium it follows from Rayleigh's reciprocity theorem and the principle of time-reversal invariance that the acoustic Green's function between any two points in the medium can be represented by an integral of crosscorrelations of wavefield observations at those two points. The integral is along sources on an arbitrarily shaped surface enclosing these points. No assumptions are made with respect to the diffusivity of the wavefield. The Rayleigh-Betti reciprocity theorem leads to a similar representation of the elastodynamic Green's function. When a part of the enclosing surface is the earth's free surface, the integral needs only to be evaluated over the remaining part of the closed surface. In practice, not all sources are equally important: The main contributions to the reconstructed Green's function come from sources at stationary points. When the sources emit transient signals, a shaping filter can be applied to correct for the differences in source wavelets. When the sources are uncorrelated noise sources, the representation simplifies to a direct crosscorrelation of wavefield observations at two points, similar as in methods that retrieve Green's functions from diffuse wavefields in disordered media or in finite media with an irregular bounding surface.

Marmousi2 An elastic upgrade for Marmousi

Abstract: The original Marmousi model was created by a consortium led by the Institut Francais du Petrole (IFP) in 1988. Since its creation, the model and its acoustic finite-difference synthetic data have been used by hundreds of researchers throughout the world for a multitude of geophysical purposes, and to this day remains one of the most published geophysical data sets. The advancement in computer hardware capabilities since the late 1980s has made it possible to perform a major upgrade to the model and data set, thereby extending the usefulness of the model for, hopefully, some time to come. This paper outlines the creation of an updated and upgraded Marmousi model and data set which we have named Marmousi2.

Fluid mobility and frequency-dependent seismic velocity — Direct measurements

Abstract: The influence of fluid mobility on seismic velocity dispersion is directly observed in laboratory measurements from seismic to ultrasonic frequencies. A forceddeformation system is used in conjunction with pulse transmission to obtain elastic properties at seismic strain amplitude (10 −7 ) from 5 Hz to 800 kHz. Varying fluid types and saturations document the influence of pore-fluids. The ratio of rock permeability to fluid viscosity defines mobility, which largely controls pore-fluid motion and pore pressure in a porous medium. High fluid mobility permits pore-pressure equilibrium either between pores or between heterogeneous regions, resulting in a low-frequency domain where Gassmann’s equations are valid. In contrast, low fluid mobility can produce strong dispersion, even within the seismic band. Here, the low-frequency assumption fails. Since most rocks in the general sedimentary section have very low permeability and fluid mobility (shales, siltstones, tight limestones, etc.), most rocks are not in the lowfrequency domain, even at seismic frequencies. Only those rocks with high permeability (porous sands and carbonates) will remain in the low-frequency domain in the seismic or sonic band.

The virtual source method: Theory and case study

Abstract: We present a way to image through complex overburden. The method uses surface shots with downhole receivers placed below the most complex part of the troublesome overburden. No knowledge of the velocity model between shots and receivers is required. The method uses time-reversal logic to create a new downward-continued data set with virtual sources (VS's) at the geophone locations. Time reversal focuses energy that passes through the overburden into useful primary energy for the VS. In contrast to physical acoustics, our time reversal is done on a computer, utilizing conventional acquisition with surface shots and downhole geophones. With this approach, we can image below extremely complex (realistic) overburden — in fact, the more complex the better. We recast the data to those with sources where we actually know and can control the waveform that has a downward-radiation pattern that may also be controlled, and is reproducible for 4D even if the near-surface changes or the shooting geometry is altered sl...

Seismic interferometry-turning noise into signal

Abstract: Turning noise into useful data—every geophysicist's dream? And now it seems possible. The field of seismic interferometry has at its foundation a shift in the way we think about the parts of the signal that are currently filtered out of most analyses—complicated seismic codas (the multiply scattered parts of seismic waveforms) and background noise (whatever is recorded when no identifiable active source is emitting, and which is superimposed on all recorded data). Those parts of seismograms consist of waves that reflect and refract around exactly the same subsurface heterogeneities as waves excited by active sources. The key to the rapid emergence of this field of research is our new understanding of how to unravel that subsurface information from these relatively complex-looking waveforms. And the answer turned out to be rather simple. This article explains the operation of seismic interferometry and provides a few examples of its application.

3D interpolation of irregular data with a POCS algorithm

Abstract: Seismic surveys generally have irregular areas where data cannot be acquired. These data should often be interpolated. A projection onto convex sets (POCS) algorithm using Fourier transforms allows interpolation of irregularly populated grids of seismic data with a simple iterative method that produces high-quality results. The original 2D image restoration method, the Gerchberg-Saxton algorithm, is extended easily to higher dimensions, and the 3D version of the process used here produces much better interpolations than typical 2D methods. The only parameter that makes a substantial difference in the results is the number of iterations used, and this number can be overestimated without degrading the quality of the results. This simplicity is a significant advantage because it relieves the user of extensive parameter testing. Although the cost of the algorithm is several times the cost of typical 2D methods, the method is easily parallelized and still completely practical.

3D volumetric multispectral estimates of reflector curvature and rotation

Abstract: One of the most accepted geologic models is the relation between reflector curvature and the presence of open and closed fractures. Such fractures, as well as other small discontinuities, are relatively small and below the imaging rangeofconventionalseismicdata.Dependingonthetectonic regime, structural geologists link open fractures to either Gaussian curvature or to curvature in the dip or strike directions. Reflector curvature is fractal in nature, with different tectonic and lithologic effects being illuminated at the 50-m and1000-m scales.Untilnow,suchcurvatureestimateshave been limited to the analysis of picked horizons. We have developed what we feel to be the first volumetric spectral estimates of reflector curvature. We find that the most positive and negative curvatures are the most valuable in the conventional mapping of lineations — including faults, folds, and flexures.Curvatureismathematicallyindependentof,andinterpretatively complementary to, the well-established coherence geometric attribute. We find the long spectral wavelengthcurvatureestimatestobeofparticularvalueinextracting subtle, broad features in the seismic data such as folds, flexures, collapse features, fault drags, and under- and overmigrated fault terminations. We illustrate the value of these spectral curvature estimates and compare them to other attributes through application to two land data sets — a salt domefromtheonshoreLouisianaGulfCoastandafractured/ karsteddatavolumefromFortWorthbasinofNorthTexas.

Time-shift imaging condition in seismic migration

Abstract: Seismic imaging based on single-scattering approximationisintheanalysisofthematchbetweenthesourceandreceiver wavefields at every image location. Wavefields at depth are functions of space and time and are reconstructed from surface data either by integral methods Kirchhoff migration or by differential methods reverse-time or wavefieldextrapolationmigration.Differentmethodscanbeused toanalyzewavefieldmatching,ofwhichcrosscorrelationisa popular option. Implementation of a simple imaging condition requires time crosscorrelation of source and receiver wavefields, followed by extraction of the zero time lag. A generalized imaging condition operates by crosscorrelation in both space and time, followed by image extraction at zero time lag. Images at different spatial crosscorrelation lags are indicators of imaging accuracy and are also used for imageangle decomposition. In this paper, we introduce an alternative prestack imaging condition in which we preserve multiple lags of the time crosscorrelation. Prestack images are described as functions of time shifts as opposed to space shifts betweensourceandreceiverwavefields.Thisimagingcondition is applicable to migration by Kirchhoff, wavefield extrapolation, or reverse-time techniques. The transformation allows construction of common-image gathers presented as functionsofeithertimeshiftorreflectionangleateverylocationinspace.Inaccuratemigrationvelocityisrevealedbyangle-domain common-image gathers with nonflat events. Computational experiments using a synthetic data set from a complex salt model demonstrate the main features of the method.

Waveform inversion using a logarithmic wavefield

Abstract: Although waveform inversion has been studied extensively since its beginning 20 years ago, applications to seismic field data have been limited, and most of those applications have been for global-seismology- or engineering-seismology-scale problems, not for exploration-scale data. As an alternative to classical waveform inversion, we propose the use of a new, objective function constructed by taking the logarithm of wavefields, allowing consideration of three types of objective function, namely, amplitude only, phase only, or both. In our waveform inversion, we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function. We compute the steepest-descent directions by using a matrix formalism derived from a frequency-domain, finite-element/finite-difference modeling technique. Our numerical algorithms are similar to those of reverse-time migration and waveform inversion based on the adjoint state of the wave equation. In order to demonstrate the practical applicability of our algorithm, we use a synthetic data set from the Marmousi model and seismic data collected from the Korean continental shelf. For noisefree synthetic data, the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion. When random noise is added, the inverted velocity model is also close to the true Marmousi model, but when frequencies below 5 Hz are removed from the data, the velocity structure is not as good as those for the noise-free and noisy data. For field data, we compare the time-domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short-period features of the subsurface. Although we use wrapped phases in our examples, we still obtain reasonable results. We expect that if we were to use correctly unwrapped phases in the inversion algorithm, we would obtain better results.

Inverse Q-filter for seismic resolution enhancement

Abstract: A principal limitation on seismic resolution is the earth attenuation, or Q -effect, including the energy dissipation of high-frequency wave components and the velocity dispersion that distorts seismic wavelets. An inverse Q -filtering procedure attempts to remove the Q -effect to produce high-resolution seismic data, but some existing methods either reduce the S/N ratio, which limits spatial resolution, or generate an illusory high-resolution wavelet that contains no more subsurface information than the original low-resolution data. In this paper, seismic inverse Q -filtering is implemented in a stabilized manner to produce high-quality data in terms of resolution and S/N ratio. Stabilization is applied to only the amplitude compensation operator of a full inverse Q -filter because its phase operator is unconditionally stable, but the scheme neither amplifies nor suppresses high frequencies at late times where the data contain mostly ambient noise. The latter property makes the process invertible, differ...

Mapping thin resistors and hydrocarbons with marine EM methods: Insights from 1D modeling

Abstract: The use of marine controlled-source electromagnetic EM (CSEM) sounding to detect thin resistive layers at depths below the seafloor has been exploited recently to assess the resistivity of potential hydrocarbon reservoirs before drilling. We examine the sensitivity of the CSEM method to such layers with forward and inverse modeling in one and three dimensions. The 3D modeling demonstrates that if both source and receivers are over a tabular 3D target, 1D modeling predicts the observed response to very high accuracy. Experimental design can thus be based on 1D analysis in which hundreds of range and frequency combinations can be computed to find the optimal survey parameters for a given target structure. Modeling in three dimensions shows that the vertical electric-field response is largest over the edges of a 3D target. The 3D modeling also suggests that a target body needs to have a diameter twice the burial depth to be reliably seen by CSEM sounding. A simple air-wave model (energy propagating from source to receiver via the atmosphere) allows the effects of the target layer and atmosphere to be separated and shows where sensitivity to the target is diminished or lost because of finite water depth as a function of range, frequency, and seafloor resistivity. Unlike DC resistivity sounding, the marine CSEM method is not completely T-equivalent and, in principle, can resolve resistivity and thickness separately. Smooth inversion provides an estimate of the method’s resolving power and highlights the fact that although the radial CSEM fields contain most of the sensitivity to the thin resistive target, inverted alone they produce only increasing resistivity with depth. Inclusion of the radial mode CSEM data forces the recovery of the thin resistor, but magnetotelluric data can be used more effectively to achieve the same result.

Robust estimates of 3D reflector dip and azimuth

Abstract: Much of seismic stratigraphy is based on the morphology of seismic textures. The identification of reflector terminations and subtle changes in dip and azimuth allows us to infer coherent progradational and transgressive packages as well as more chaotic slumps, fans, and braided-stream complexes; infill of karsted terrains; gas seeps; and, of course, faults and angular unconformities. A major difficulty in estimating reflector dip and azimuth arises at discrete lateral and vertical discontinuities across which reflector dip and azimuth change. The smearing across these boundaries produced by traditional dip and azimuth estimations is avoided by using temporally and spatially shifted multiple windows that contain each analysis point. This more robust estimation of dip and azimuth leads to increased resolution of well-established algorithms such as coherence, coherent amplitude gradients, and structurally oriented filtering. More promising still is the analysis of high-resolution dip and azimuth through vol...

Spurious multiples in seismic interferometry of primaries

Abstract: Seismic interferometry is a technique for estimating the Green’s function that accounts for wave propagation between receivers by correlating the waves recorded at these receivers. We present a derivation of this principle based on the method of stationary phase. Although this derivation is intended to be educational, applicable to simple media only, it provides insight into the physical principle of seismic interferometry. In a homogeneous medium with one horizontal reflector and without a free surface, the correlation of the waves recorded at two receivers correctly gives both the direct wave and the singly reflected waves. When more reflectors are present, a product of the singly reflected waves occurs in the crosscorrelation that leads to spurious multiples when the waves are excited at the surface only. We give a heuristic argument that these spurious multiples disappear when sources below the reflectors are included. We also extend the derivation to a smoothly varying heterogeneous background medium.

P-wave seismic attenuation by slow-wave diffusion: Effects of inhomogeneous rock properties

Abstract: Recent research has established that the dominant P-wave attenuation mechanism in reservoir rocks at seismic frequencies is because of wave-induced fluid flow (mesoscopic loss). The P-wave induces a fluid-pressure difference at mesoscopic-scale inhomogeneities (larger than the pore size but smaller than the wavelength, typically tens of centimeters) and generates fluid flow and slow (diffusion) Biot waves (continuity of pore pressure is achieved by energy conversion to slow P-waves, which diffuse away from the interfaces). In this context, we consider a periodically stratified medium and investigate the amount of attenuation (and velocity dispersion) caused by different types of heterogeneities in the rock properties, namely, porosity, grain and frame moduli, permeability, and fluid properties. The most effective loss mechanisms result from porosity variations and partial saturation, where one of the fluids is very stiff and the other is very compliant, such as, a highly permeable sandstone at shallow depths, saturated with small amounts of gas (around 10% saturation) and water. Grain- and frame-moduli variations are the next cause of attenuation. The relaxation peak moves towards low frequencies as the (background) permeability decreases and the viscosity and thickness of the layers increase. The analysis indicates in which cases the seismic band is in the relaxed regime, and therefore, when the Gassmann equation can yield a good approximation to the wave velocity.

Correlation of random wavefields: An interdisciplinary review

Abstract: This paper presents an interdisciplinary review of the correlation properties of random wavefields. We expose several important theoretical results of various fields, ranging from time reversal in acoustics to transport theory in condensed matter physics. Using numerical simulations, we introduce the correlation process in an intuitive manner. We establish a fruitful mapping between time reversal and correlation, which enables us to transpose many known results from acoustics to seismology. We show that the multiple-scattering formalism developed in condensed matter physics provides a rigorous basis to analyze the field correlations in disordered media. We discuss extensively the various factors controlling and affecting the retrieval of the Green's function of a complex medium from the correlation of either noise or coda. Acoustic imaging of complex samples in the laboratory and seismic tomography of geologic structures give a glimpse of the promising wide range of applications of the correlation method.

Electrical resistivity tomography applied to geologic, hydrogeologic, and engineering investigations at a former waste-disposal site

Abstract: A former dolerite quarry and landfill site was investigated using 2D and 3D electrical resistivity tomography (ERT), with the aims of determining buried quarry geometry, mapping bedrock contamination arising from the landfill, and characterizing site geology. Resistivity data were collected from a network of intersecting survey lines using a Wenner-based array configuration. Inversion of the data was carried out using 2D and 3D regularized least-squares optimization methods with robust (L1-norm) model constraints. For this site, where high resistivity contrasts were present, robust model constraints produced a more accurate recovery of subsurface structures when compared to the use of smooth (L2-norm) constraints. Integrated 3D spatial analysis of the ERT and conventional site investigation data proved in this case a highly effective means of characterizing the landfill and its environs. The 3D resistivity model was successfully used to confirm the position of the landfill boundaries, which appeared as electrically well-defined features that corresponded extremely closely to both historic maps and intrusive site investigation data. A potential zone of leachate migration from the landfill was identified from the electrical models; the location of this zone was consistent with the predicted direction of groundwater flow across the site. Unquarried areas of a dolerite sill were imaged as a resistive sheet-like feature, while the fault zone appeared in the 2D resistivity model as a dipping structure defined by contrasting bedrock resistivities.

Fast simulated annealing inversion of surface waves on pavement using phase-velocity spectra

Abstract: The conventional inversion of surface waves depends on modal identification of measured dispersion curves, which can be ambiguous. It is possible to avoid mode-number identification and extraction by inverting the complete phase-velocity spectrum obtained from a multichannel record. We use the fast simulated annealing (FSA) global search algorithm to minimize the difference between the measured phase-velocity spectrum and that calculated from a theoretical layer model, including the field setup geometry. Results show that this algorithm can help one avoid getting trapped in local minima while searching for the best-matching layer model. The entire procedure is demonstrated on synthetic and field data for asphalt pavement. The viscoelastic properties of the top asphalt layer are taken into account, and the inverted asphalt stiffness as a function of frequency compares well with laboratory tests on core samples. The thickness and shear-wave velocity of the deeper embedded layers are resolved within 10% deviation from those values measured separately during pavement construction. The proposed method may be equally applicable to normal soil site investigation and in the field of ultrasonic testing of materials.

Gassmann's fluid substitution and shear modulus variability in carbonates at laboratory seismic and ultrasonic frequencies

Abstract: Carbonates have become important targets for rock property research in recent years because they represent many of themajoroilandgasreservoirsintheworld.Someareundergoing enhanced oil recovery. Most laboratory studies to understand fluid and pressure effects on reservoir rocks have been performed on sandstones, but applying relations developed for sandstones to carbonates is problematic, at best.We measure in the laboratory nine carbonate samples from the same reservoir at seismic 3‐3000 Hz and ultrasonic 0.8 MHz frequencies. Samples are measured dry humidified and saturated with liquid butane and brine. Our carbonate samples showed typical changes in moduli as a function of porosity andfluid saturation. However, we explore the applicability of Gassmann’s theory on limestone and dolomite rocks in the context of shear- and bulk-modulus dispersion andGassmann’stheoryassumptions.Forourcarbonatesetat high differential pressures and seismic frequencies, the bulk modulus of rocks with high-aspect-ratio pores and dolomite mineralogy is predicted by Gassmann’s relation.We also explore in detail some of the assumptions of Gassmann’s relation,especiallyrock-framesensitivitytofluidsaturation.Our carbonate samples show rock shear-modulus change from dry to brine saturation conditions, and we investigate several rock-fluid mechanisms responsible for this change. To our knowledge, these are the first controlled laboratory experimentsoncarbonatesintheseismicfrequencyrange.

Accuracy of heterogeneous staggered-grid finite-difference modeling of Rayleigh waves

Abstract: Heterogeneous finite-difference (FD) modeling assumes that the boundary conditions of the elastic wavefield between material discontinuities are implicitly fulfilled by the distribution of the elastic parameters on the numerical grid. It is widely applied to weak elastic contrasts between geologic formations inside the earth. We test the accuracy at the free surface of the earth. The accuracy for modeling Rayleigh waves using the conventional standard staggered-grid (SSG) and the rotated staggered grid (RSG) is investigated. The accuracy tests reveal that one cannot rely on conventional numerical dispersion discretization criteria. A higher sampling is necessary to obtain acceptable accuracy. In the case of planar free surfaces aligned with the grid, 15 to 30 grid points per minimum wavelength of the Rayleigh wave are required. The widely used explicit boundary condition, the so-called image method, produces similar accuracy and requires approximately half the sampling of the wavefield compared to heterogeneous free-surface modeling. For a free-surface not aligned with the grid (surface topography), the error increases significantly and varies with the dip angle of the interface. For an irregular interface, the RSG scheme is more accurate than the SSG scheme. The RSG scheme, however, requires 60 grid points per minimum wavelength to achieve good accuracy for all dip angles. The high computation requirements for 3D simulations on such fine grids limit the application of heterogenous modeling in the presence of complex surface topography.

Direct reservoir parameter estimation using joint inversion of marine seismic AVA and CSEM data

Abstract: A new joint inversion algorithm to directly estimate reservoir parameters is described. This algorithm combines seismic amplitude versus angle (AVA) and marine controlled source electromagnetic (CSEM) data. The rock-properties model needed to link the geophysical parameters to the reservoir parameters is described. Errors in the rock-properties model parameters, measured in percent, introduce errors of comparable size in the joint inversion reservoir parameter estimates. Tests of the concept on synthetic one-dimensional models demonstrate improved fluid saturation and porosity estimates for joint AVA-CSEM data inversion (compared to AVA or CSEM inversion alone). Comparing inversions of AVA, CSEM, and joint AVA-CSEM data over the North Sea Troll field, at a location with well control, shows that the joint inversion produces estimated gas saturation, oil saturation and porosity that is closest (as measured by the RMS difference, L1 norm of the difference, and net over the interval) to the logged values whereas CSEM inversion provides the closest estimates of water saturation.

Early arrival waveform tomography on near-surface refraction data

Abstract: We develop a waveform-tomography method for estimating the velocity distribution that minimizes the waveform misfit between the predicted and observed early arrivals in space-time seismograms. By fitting the waveforms of early arrivals, early arrival waveform tomographyEWT naturally takes into account more general wave-propagation effects compared to the high-frequency method of traveltime tomography, meaning that EWT can estimate a wider range of slowness wavenumbers. Another benefit of EWT is more reliable convergence compared to full-waveform tomography, because an early-arrival misfit function contains fewer local minima. Synthetic test results verify that the waveform tomogram is much more accurate than the traveltime tomogram and that this algorithm has good convergence properties. For marine data from the Gulf of Mexico, the statics problem caused by shallow, gassy muds was attacked by using EWT to obtain a more accurate velocity model. Using the waveform tomogram to correct for statics, the stacked section was significantly improved compared to using the normal moveout NMO velocity, and moderately improved compared to using the traveltime tomogram. Inverting high-resolution land data from Mapleton, Utah, showed an EWT velocity tomogram that was more consistent with the ground truth trench log than the traveltime tomogram. Our results suggest that EWT can provide supplemental, shorter-wavelength information compared to the traveltime tomogram for both shallow and moderately deep seismic data.

On bias and noise in passive seismic data from finite circular array data processed using SPAC methods

Abstract: The finite nature of typical small seismic arrays used in conjunction with spatial autocorrelation SPAC processing for observing the microtremor wavefield causes predictable perturbationsoftheSPACspectrumwhensourcesofseismic noiseareconfinedtoarestrictedrangeofazimuthsSuchperturbations are especially evident at higher frequencies where wavelengths are on the order of the array radius The effects arereadilymodeledandshowthatthetriangulararraygeometries commonly used for microtremor studies require azimuthal distributions of wave energy on the order of 60° or greatertohaveahighprobabilityofbeingfreeofsuchperturbations The imaginary component of the SPAC spectrum, which is ideally zero for a sufficiently dense circular array and/or a sufficiently isotropic wavefield, is in practice often nonzero and provides three quality-control indicators: 1 an indication of insufficient spatial averaging, 2 an empirical measure of the level of statistical uncertainty in SPAC spectralestimates,and3anindicationofdeparturesfromplanewavestationarityoftheseismicnoisewavefield

Bayesian lithology/fluid prediction and simulation on the basis of a Markov-chain prior model

Abstract: A technique for lithology/fluid (LF) prediction and simulation from prestack seismic data is developed in a Bayesian framework The objective is to determine the LF classes along 1D profiles through a reservoir target zone A stationary Markov-chain prior model is used to model vertical continuity of LF classes along the profile The likelihood relates the LF classes to the elastic properties and to the seismic data, and it introduces vertical correlation because the seismic data are band-limited An approximation of the likelihood model provides an approximate posterior model that is a Markov chain The approximate posterior can be assessed by an exact and efficient recursive algorithm The LF inversion approach is evaluated on a synthetic 1D profile that is inspired by a North Sea sandstone reservoir With a realistic wavelet-colored noise model and a S/N ratio of three in the seismic data, the results are reliable The LF classes and the interfaces between zones are largely correct The prediction unce

Wave-equation-based seismic illumination analysis

Abstract: We present a wave-equation-based method for seismic illumination analysis. A one-way wave-equation-based, generalized screen propagator is used to extrapolate the wavefields from sources and receivers to the subsurface target. A local plane-wave analysis is used at the target to calculate localized,directionalenergyfluxesforbothsourceandreceiver wavefields. We construct an illumination matrix using these energy fluxes to quantify the target illumination conditions. The target geometry information is used to manipulate the illumination matrix and generate different types of illumination measures. The wave-equation-based approach can properly handle forward multiple-scattering phenomena, including focusing/defocusing, diffraction, and interference effects.Itcanbedirectlyappliedtocomplexvelocitymodels. Velocity-model smoothing and Fresnel-zone smoothing are not required. Different illumination measurements derived from this method can be applied to target-oriented or volumetric illumination analyses. This new method is flexible and practical for illumination analysis in complex 2D and 3D velocity models with nontrivial acquisition and target

Mapping thin resistors and hydrocarbons with marine EM methods, Part II -Modeling and analysis in 3D

Abstract: The electromagnetic fields surrounding a thin, subseabed resistive disk in response to a deep-towed, time-harmonic electric dipole antenna are investigated using a newly developed 3D Cartesian, staggered-grid modeling algorithm. We demonstrate that finite-difference and finite-volume methods for solving the governing curl-curl equation yield identical, complex-symmetric coefficient matrices for the resulting N×N linear system of equations. However, the finite-volume approach has an advantage in that it naturally admits quadrature integration methods for accurate representation of highly compact or exponentially varying source terms constituting the right side of the resulting linear system of equations. This linear system is solved using a coupled two-term recurrence, quasi-minimal residual algorithm that doesnot require explicit storage of the coefficient matrix, thus reducing storage costs from 22N to 10N complex, double-precision words with no decrease in computational performance. The disk model serve...

Joint estimation of porosity and saturation using stochastic rock-physics modeling

Abstract: Sediment porosity and saturation affect bulk modulus, shearmodulus,anddensity.Consequently,estimatinghydrocarbon saturation and reservoir porosity from seismic data is a joint estimation problem: Uncertainty in porosity will lead toerrorsinsaturationprediction,andviceversa.Porosityand saturation can be jointly estimated using stochastic rockphysicsmodelingandformalBayesianestimationmethodology. Knowledge of shear impedance reduces the uncertainty inporosityandthusalsoreducesuncertaintyinsaturationestimation. This study investigates joint estimation of porosity and saturation by using rock-physics, stochastic modeling, and Bayesian estimation theory to derive saturation and porosity maps of expected pay sands. In the field example, the uncertainty in porosity, quantified by the standard deviation STDassociatedwiththeposteriorprobabilitydensityfunctionpdf,derivedfrominversionofseismicdataismuchless than the uncertainty in the derived saturation. For a typical case, the STD associated with saturation is 24% while porositySTDisabout1.34porosityunitsgivenseismic-derived inversionattributeswithreasonableaccuracy.Comparisonof these numbers with prior estimates showed that inversion of seismic data decreased the uncertainty in porosity to 15% of the prior uncertainty while saturation uncertainty was only reduced to 92% of the prior uncertainty. Although these resultsmayvaryfromonelocationtoanother,themethodology isgeneralandcanbeappliedtootherlocations.

Permeability prediction from MICP and NMR data using an electrokinetic approach

Abstract: Theaccuratemodelingofoil,gas,andwaterreservoirsdependsfundamentallyuponaccesstoreliablerockpermeabilitiesthatcannotbeobtaineddirectlyfromdownholelogs.Instead, a range of empirical models are usually employed.We propose a new model that has been derived analytically from electrokinetic theory and is equally valid for all lithologies. The predictions of the new model and four other common models Kozeny-Carman, Berg, Swanson, and van Baaren have been compared using measurements carried out on fusedandunfusedglassbeadpacksaswellason91rocksamples representing 11 lithologies and three coring directions. The new model provides the best predictions for the glass beadpacksaswellforallthelithologies.Thecruxofthenew modelistohaveagoodknowledgeoftherelevantmeangrain diameter,forexample,fromMICPdata.Hence,wehavealso predictedthepermeabilitiesof21NorthSeawellcoresusing all five models and five different measures of relevant grain size. These data show that the best predictions are provided by the use of the new model with the geometric mean grain size.Wehavealsoappliedthenewmodeltothepredictionof permeability from NMR data of a 500 m thick sand-shale succession in the North Sea by inverting the T2 spectrum to provide a value for the geometric mean grain size. The new model shows a good match to all 348 core measurements fromthesuccession,performingbetterthantheSDR,TimurCoates,HSCM,andKozeny-Carmanpredictions.

Understanding 3D analytic signal amplitude

Abstract: The concept of the analytic signal goes back at least to Ville (1948). The analytic signal a ( x ) of function f ( x ) is a complex quantity defined as where H [ f ( x ) ] represents the Hilbert transform of f ( x ) . Nabighian (1972, 1974) applies the analytic signal concept to potential-field data in two dimensions. For a potential field ϕ ( x ) measured along the x -axis at a constant observation height z and generated by a 2D source aligned parallel to the y -axis, the horizontal derivative ϕ x and the vertical derivative ϕ z are a Hilbert transform pair.

Spatial Orientation And Distribution Of Reservoir Fractures From Scattered Seismic Energy

Abstract: Wepresentthedetailsofanewmethodfordeterminingthereflection and scattering characteristics of seismic energy from subsurface fractured formations. The method is based upon observations we have made from 3D finite-difference modeling of the reflected and scattered seismic energy over discrete systems of vertical fractures. Regularly spaced, discrete vertical fracture corridors impart a coda signature, which is a ringing tail of scatteredenergy,toanyseismicwaveswhicharetransmittedthrough or reflected off of them. This signature varies in amplitude and coherence as a function of several parameters including: 1 the difference in angle between the orientation of the fractures and the acquisition direction, 2 the fracture spacing, 3 the wavelength of the illuminating seismic energy, and 4 the compliance, or stiffness, of the fractures. This coda energy is most coherent when the acquisition direction is parallel to the strike of thefractures.Ithasthelargestamplitudewhentheseismicwavelengths are tuned to the fracture spacing, and when the fractures have low stiffness. Our method uses surface seismic reflection tracestoderiveatransferfunctionthatquantifiesthechangeinan apparent source wavelet before and after propagating through a fracturedinterval.Thetransferfunctionforanintervalwithnoor low amounts of scattering will be more spikelike and temporally compact. The transfer function for an interval with high scattering will ring and be less temporally compact. When a 3D survey is acquired with a full range of azimuths, the variation in the derived transfer functions allows us to identify subsurface areas with high fracturing and to determine the strike of those fractures.Wecalibratedthemethodwithmodeldataandthenapplied ittotheEmiliofieldwithafracturedreservoir.Themethodyielded results which agree with known field measurements and previously published fracture orientations derived from PS anisotropy.

Flattening without picking

Abstract: We present an efficient full-volume automatic dense-picking method for flattening seismic data. First local dips (stepouts) are calculated over the entire seismic volume. The dips are then resolved into time shifts (or depth shifts) using a nonlinear Gauss-Newton iterative approach that exploits fast Fourier transforms to minimize computation time. To handle faults (discontinuous reflections), we apply a weighted inversion scheme. The weight identifies locations of faults, allowing dips to be summed around the faults to reduce the influence of erroneous dip estimates near the fault. If a fault model is not provided, we can estimate a suitable weight (essentially a fault indicator) within our inversion using an iteratively reweighted least squares (IRLS) method. The method is tested successfully on both synthetic and field data sets of varying degrees of complexity, including salt piercements, angular unconformities, and laterally limited faults.