Showing papers in "Geophysics in 2012"
TL;DR: In this paper, a rank-reduction process was used to reduce the rank of the prestack seismic tensor, and the higher-order singular value decompostion was used for rank reduction.
Abstract: A patch of prestack data depends on four spatial dimensions ( x , y midpoints and x , y offsets) and frequency. The spatial data at one temporal frequency can be represented by a fourth-order tensor. In ideal conditions of high signal-to-noise ratio and complete sampling, one can assume that the seismic data can be approximated via a low-rank fourth-order tensor. Missing samples were recovered by reinserting data obtained by approximating the original noisy and incomplete data volume with new observations obtained via the rank-reduction process. The higher-order singular value decompostion was used to reduce the rank of the prestack seismic tensor. Synthetic data demonstrated the ability of the proposed seismic data completion algorithm to reconstruct events with curvature. The synthetic example allowed to quantify the quality of the reconstruction for different levels of noise and survey sparsity. We also provided a real data example from the Western Canadian sedimentary basin.
187 citations
TL;DR: In this paper, a robust concept for the calculation of depth of investigation (DOI) that is valid for any 1D electromagnetic (EM) geophysical model is proposed, which can be used on any model type for which a sensitivity matrix can be calculated.
Abstract: We tested a new robust concept for the calculation of depth of investigation (DOI) that is valid for any 1D electromagnetic (EM) geophysical model. A good estimate of DOI is crucial when building geologic and hydrological models from EM data sets because the validity of the models varies strongly with data noise and the resistivity of the layers themselves. For diffusive methods, such as groundbased and airborne electromagnetic, it is not possible to define an unambiguous depth below which there is no information on the resistivity structure and a measure of DOI is therefore to what depth the model can be considered reliable. The method we presented is based on the actual model output from the inversion process and we used the actual system response, contrary to assuming, e.g., planar waves over a homogeneous half-space, the widely used skin depth calculation. Equally important, the data noise and the number of data points are integrated into the calculation. Our methodology is based on a recalculated sensitivity (Jacobian) matrix of the final model and thus it can be used on any model type for which a sensitivity matrix can be calculated. Unlike other sensitivity matrix methods, we defined a global and absolute threshold value contrary to defining a relative (such as 5%), sensitivity limit. The threshold value will apply to all 1D inverted data and will thus produce comparable numbers of DOI.
185 citations
TL;DR: In this paper, the Radon transform was used for separating diffraction from reflections and noise in the dip-angle domain, and the separation procedure can be performed after either time migration or depth migration.
Abstract: Common-reflection angle migration can produce migrated gathers either in the scattering-angle domain or in the dip-angle domain. The latter reveals a clear distinction between reflection and diffraction events. We derived analytical expressions for events in the dip-angle domain and found that the shape difference can be used for reflection/diffraction separation. We defined reflection and diffraction models in the Radon space. The Radon transform allowed us to isolate diffractions from reflections and noise. The separation procedure can be performed after either time migration or depth migration. Synthetic and real data examples confirmed the validity of this technique.
176 citations
TL;DR: In this article, a joint inversion of seismic first-arrival traveltimes and gravity data is proposed to recover causative slowness and density distributions. But the authors do not consider the effect of the coupling to avoid potential convergence issues, and automatically adjust two Tikhonov tradeoff parameters to achieve a desired fit to both d...
Abstract: Seismic methods continue to receive interest for use in mineral exploration due to the much higher resolution potential of seismic data compared to the techniques traditionally used, namely, gravity, magnetics, resistivity, and electromagnetics. However, the complicated geology often encountered in hard-rock exploration can make data processing and interpretation difficult. Inverting seismic data jointly with a complementary data set can help overcome these difficulties and facilitate the construction of a common earth model. We considered the joint inversion of seismic first-arrival traveltimes and gravity data to recover causative slowness and density distributions. Our joint inversion algorithm differs from previous work by (1) incorporating a large suite of measures for coupling the two physical property models, (2) slowly increasing the effect of the coupling to help avoid potential convergence issues, and (3) automatically adjusting two Tikhonov tradeoff parameters to achieve a desired fit to both d...
174 citations
TL;DR: In this article, the authors review important contributions that have been made in developing these techniques for the mining industry with focus on four main regions: Australia, Europe, Canada, and South Africa.
Abstract: Due to high metal prices and increased difficulties in finding shallower deposits, the exploration for and exploitation of mineral resources is expected to move to greater depths. Consequently, seismic methods will become a more important tool to help unravel structures hosting mineral deposits at great depth for mine planning and exploration. These methods also can be used with varying degrees of success to directly target mineral deposits at depth. We review important contributions that have been made in developing these techniques for the mining industry with focus on four main regions: Australia, Europe, Canada, and South Africa. A wide range of case studies are covered, including some that are published in the special issue accompanying this article, from surface to borehole seismic methods, as well as petrophysical data and seismic modeling of mineral deposits. At present, high-resolution 2D surveys mostly are performed in mining areas, but there is a general increasing trend in the use of 3...
164 citations
TL;DR: In this paper, the authors demonstrate that the requirement of having an actual receiver inside the medium can be circumvented, going beyond seismic interferometry, by using inverse scattering theory.
Abstract: With seismic interferometry one can retrieve the response to a virtual source inside an unknown medium, if there is a receiver at the position of the virtual source. Using inverse scattering theory, we demonstrate that, for a 1D medium, the requirement of having an actual receiver inside the medium can be circumvented, going beyond seismic interferometry. In this case, the wavefield can be focused inside an unknown medium with independent variations in velocity and density using reflection data only.
153 citations
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Abstract: A Summary of Part 1 and Introduction to Part 2 Our complex earth has a continuum of all scales of ordered heterogeneities. Ordered heterogeneities give rise to three types of seismic observations, depending upon the relationship between the wavelength and the scale length of the ordered heterogeneity: Reflections that arise from layers 3/8ths wavelength thick or greater. Azimuthal scattering, azimuthal attenuation, and azimuthal dispersion that arise from aligned ordered heterogeneities with scale lengths ∼0.01 – ∼0.4 wavelength. Azimuthal anisotropy = azimuthal variations of traveltimes (and amplitude) that show a 90° variation between fast-to-slow on offsets approximately equal to target depth that arise from aligned ordered heterogeneities that are very small relative to the wavelength. Unequal horizontal stresses and/or aligned ordered heterogeneities (fractures) can cause azimuthal anisotropy. Equivalent media theory and “their penny-shaped cracks” are used to model and explain these observations. In...
152 citations
TL;DR: In this paper, the non-local means algorithm is used to attenuate random noise in seismic data, which is a noise attenuation filter that was originally developed for the purposes of image denoising.
Abstract: The nonlocal means algorithm is a noise attenuation filter that was originally developed for the purposes of image denoising. This algorithm denoises each sample or pixel within an image by utilizing other similar samples or pixels regardless of their spatial proximity, making the process nonlocal. Such a technique places no assumptions on the data except that structures within the data contain a degree of redundancy. Because this is generally true for reflection seismic data, we propose to adopt the nonlocal means algorithm to attenuate random noise in seismic data. Tests with synthetic and real data sets demonstrate that the nonlocal means algorithm does not smear seismic energy across sharp discontinuities or curved events when compared to seismic denoising methods such as f-x deconvolution.
151 citations
TL;DR: In this article, a sign factor is introduced to represent the polarity distribution of the S-wave component, which can be computed using the energy flux density vector to improve the quality of the migration events.
Abstract: Polarity reversals in PS and SP images of elastic reverse time migration will cause destructive interference in the final stacked results, which may lead to an erroneous interpretation. We derive a polarity reversal correction based on an analysis of the polarity distribution of PS and SP images. The key aspect for a polarity reversal correction is the polarity distribution of the S-wave component. Polarity reversal correction methods can be performed according to the actual patterns of the polarity distribution in gathers. For the 2D isotropic case, a sign factor is introduced to represent the polarity distribution of the S-wave component; this sign factor can be computed using the energy flux density vector. We present a procedure to correct the polarity reversal for elastic reverse time migration in the common-shot domain. First, the sign factor is computed during the wavefield reconstruction for every imaging point. Then, the polarity reversal is corrected by multiplying the PS and SP images with the sign factor at every time step when an elastic imaging condition is applied. We also design a filter algorithm for the sign factor to improve its consistency along an event and thereby to diminish the impact of the inaccuracy of the energy flux density vector and to improve the imaging results. Numerical examples have shown that the polarity reversal correction procedure works and that the sign filter algorithm successfully eliminates the consequences of the inaccuracy of the energy flux density vector. The quality of the migration events is effectively improved.
151 citations
TL;DR: A new and simple multidirectional vector-median filter (MD-VMF) is introduced to separate the blended seismic shot gathers to achieve the highest seismic image quality and for standard prestack processing, such as filtering, statics computation, and velocity analysis.
Abstract: Simultaneous source acquisition technology, also referred to as “blended acquisition,” involves recording two or more shots simultaneously. Despite the fact that the recorded data has crosstalk from different shots, conventional processing procedures can still produce acceptable images for interpretation. This is due to the power of the stacking process using blended data with its increased data redundancy and inherent time delays between various shots. It is still desirable to separate the blended data into single shot gathers and reduce the crosstalk noise to achieve the highest seismic image quality and for standard prestack processing, such as filtering, statics computation, and velocity analysis. This study introduced a new and simple multidirectional vector-median filter (MD-VMF) to separate the blended seismic shot gathers. This method extended the well-known conventional median filter from a scalar implementation to a vector version. More specifically, a vector median filter was applied in...
149 citations
TL;DR: In this article, a novel method for random noise attenuation in seismic data by applying regularized nonstationary autoregression (RNA) in the frequency-space (f-x) domain was developed.
Abstract: We have developed a novel method for random noise attenuation in seismic data by applying regularized nonstationary autoregression (RNA) in the frequency-space (f-x) domain. The method adaptively predicts the signal with spatial changes in dip or amplitude using f-x RNA. The key idea is to overcome the assumption of linearity and stationarity of the signal in conventional f-x domain prediction technique. The conventional f-x domain prediction technique uses short temporal and spatial analysis windows to cope with the nonstationary of the seismic data. The new method does not require windowing strategies in spatial direction. We implement the algorithm by an iterated scheme using the conjugate-gradient method. We constrain the coefficients of nonstationary autoregression (NA) to be smooth along space and frequency in the f-x domain. The shaping regularization in least-square inversion controls the smoothness of the coefficients of f-x RNA. There are two key parameters in the proposed method: filter length ...
TL;DR: In this paper, the authors combined poroelasticity theory, amplitude variation with offset (AVO) inversion, and identification of P- and S-wave moduli to present a stable and physically meaningful method to estimate the fluid term, with no need for density information from prestack seismic data.
Abstract: The fluid term in the Biot-Gassmann equation plays an important role in reservoir fluid discrimination. The density term imbedded in the fluid term, however, is difficult to estimate because it is less sensitive to seismic amplitude variations. We combined poroelasticity theory, amplitude variation with offset (AVO) inversion, and identification of P- and S-wave moduli to present a stable and physically meaningful method to estimate the fluid term, with no need for density information from prestack seismic data. We used poroelasticity theory to express the fluid term as a function of P- and S-wave moduli. The use of Pand S-wave moduli made the derivation physically meaningful and natural. Then we derived an AVO approximation in terms of these moduli, which can then be directly inverted from seismic data. Furthermore, this practical and robust AVO-inversion technique was developed in a Bayesian framework. The objective was to obtain the maximum a posteriori solution for the P-wave modulus, S-wave modulus, and density. Gaussian and Cauchy distributions were used for the likelihood and a priori probability distributions, respectively. The introduction of a low-frequency constraint and statistical probability information to the objective function rendered the inversion more stable and less sensitive to the initial model. Tests on synthetic data showed that all the parameters can be estimated well when no noise is present and the estimated P- and S-wave moduli were still reasonable with moderate noise and rather smooth initial model parameters. A test on a real data set showed that the estimated fluid term was in good agreement with the results of drilling.
TL;DR: In this article, a forward code and inversion algorithm was developed using the full-time decay of the induced polarization response, together with an accurate description of the transmitter waveform and of the receiver transfer function, to reconstruct the distribution of the Cole-Cole parameters of the earth.
Abstract: Time-domain-induced polarization has significantly broadened its field of reference during the last decade, from mineral exploration to environmental geophysics, e.g., for clay and peat identification and landfill characterization. Though, insufficient modeling tools have hitherto limited the use of time-domain-induced polarization for wider purposes. For these reasons, a new forward code and inversion algorithm have been developed using the full-time decay of the induced polarization response, together with an accurate description of the transmitter waveform and of the receiver transfer function, to reconstruct the distribution of the Cole-Cole parameters of the earth. The accurate modeling of the transmitter waveform had a strong influence on the forward response, and we showed that the difference between a solution using a step response and a solution using the accurate modeling often is above 100%. Furthermore, the presence of low-pass filters in time-domain-induced polarization instruments af...
TL;DR: In this article, a model-space preconditioning technique based on directional Laplacian filters is proposed to preserve most of the details of the velocity model while smoothing the solution along known geological dips.
Abstract: The waveform inversion problem is inherently ill-posed. Traditionally, regularization schemes are used to address this issue. For waveform inversion, where the model is expected to have many details reflecting the physical properties of the Earth, regularization and data fitting can work in opposite directions: the former smoothing and the latter adding details to the model. We propose constraining estimated velocity fields by reparameterizing the model. This technique, also called model-space preconditioning, is based on directional Laplacian filters: It preserves most of the details of the velocity model while smoothing the solution along known geological dips. Preconditioning also yields faster convergence at early iterations. The Laplacian filters have the property to smooth or kill local planar events according to a local dip field. By construction, these filters can be inverted and used in a preconditioned waveform inversion strategy to yield geologically meaningful models. We illustrate with 2D syn...
TL;DR: In this paper, the authors inverted airborne time-domain electromagnetic (ATEM) data over a porphyry deposit in central British Columbia, Canada and recovered the 3D electrical conductivity structure.
Abstract: We inverted airborne time-domain electromagnetic (ATEM) data over a porphyry deposit in central British Columbia, Canada and recovered the 3D electrical conductivity structure. Full 3D inversion was required because of the circular geometry of the deposit. Typical analysis, which assumes a homogeneous or layered earth, produces conductive artifacts that are contrary to geologic expectations. A synthetic example showed that those misleading artifacts arise by assuming a 1D layered earth and that a 3D inversion can successfully solve the problem. Because of the computational challenges of solving the 3D inversion with many transmitters of airborne survey, we introduced a work flow that uses a multimesh strategy to handle the field data. In our inversion, a coarse mesh and a small number of soundings are first used to rapidly reconstruct a large-scale distribution of conductivity. The mesh is then refined and more soundings are incorporated to better resolve small-scale features. This strategy significantly ...
TL;DR: In this article, a unified approach for denoising and interpolation of seismic data in the frequency-wavenumber (f-k) domain is proposed, which can be used to interpolate regularly sampled data as well as randomly sampled data on a regular grid.
Abstract: I introduce a unified approach for denoising and interpolation of seismic data in the frequency-wavenumber (f-k) domain. First, an angular search in the f-k domain is carried out to identify a sparse number of dominant dips, not only using low frequencies but over the whole frequency range. Then, an angular mask function is designed based on the identified dominant dips. The mask function is utilized with the least-squares fitting principle for optimal denoising or interpolation of data. The least-squares fit is directly applied in the time-space domain. The proposed method can be used to interpolate regularly sampled data as well as randomly sampled data on a regular grid. Synthetic and real data examples are provided to examine the performance of the proposed method.
TL;DR: In this article, the authors inverted 3D amplitude variation with offset (AVO) data from the Alvheim field in the North Sea into lithology/fluid classes, elastic properties, and porosity.
Abstract: Seismic 3D amplitude variation with offset (AVO) data from the Alvheim field in the North Sea are inverted into lithology/fluid classes, elastic properties, and porosity. Lithology/fluid maps over hydrocarbon prospects provide more reliable estimates of gas/oil volumes and improve the decision concerning further reservoir assessments. The Alvheim field is of turbidite origin with complex sand-lobe geometry and appears without clear fluid contacts across the field. The inversion is phrased in a Bayesian setting. The likelihood model contains a convolutional, linearized seismic model and a rock-physics model that capture vertical trends due to increased sand compaction and possible cementation. The likelihood model contains several global model parameters that are considered to be stochastic to adapt the model to the field under study and to include model uncertainty in the uncertainty assessments. The prior model on the lithology/fluid classes is a Markov random field that captures local vertical/horizonta...
TL;DR: In this paper, the authors proposed a recursive joint migration inversion (JMI) algorithm, which combines the full waveform inversion process for velocity estimation with a recursive, optionally blended, anisotropic multiple-scattering algorithm.
Abstract: The next generation seismic migration and inversion technology considers multiple scattering as vital information, allowing the industry to derive significantly better reservoir models — with more detail and less uncertainty — while requiring a minimum of user intervention. Three new insights have been uncovered with respect to this fundamental transition. Unblended or blended multiple scattering can be included in the seismic migration process, and it has been proposed to formulate the imaging principle as a minimization problem. The resulting process yields angle-dependent reflectivity and is referred to as recursive full wavefield migration (WFM). The full waveform inversion process for velocity estimation can be extended to a recursive, optionally blended, anisotropic multiple-scattering algorithm. The resulting process yields angle-dependent velocity and is referred to as recursive full waveform inversion (WFI). The mathematical equations of WFM and WFI have an identical structure, but the physical meaning behind the expressions is fundamentally different. In WFM the reflection process is central, and the aim is to estimate reflection operators of the subsurface, using the up- and downgoing incident wavefields (including the codas) in each gridpoint. In WFI, however, the propagation process is central and the aim is to estimate velocity operators of the subsurface, using the total incident wavefield (sum of up- and downgoing) in each gridpoint. Angle-dependent reflectivity in WFM corresponds with angle-dependent velocity (anisotropy) in WFI. The algorithms of WFM and WFI could be joined into one automated joint migration-inversion process. In the resulting hybrid algorithm, being referred to as recursive joint migration inversion (JMI), the elaborate volume integral solution was replaced by an efficient alternative: WFM and WFI are alternately applied at each depth level, where WFM extrapolates the incident wavefields and WFI updates the velocities without any user interaction. The output of the JMI process offers an integrated picture of the subsurface in terms of angle-dependent reflectivity as well as anisotropic velocity. This two-fold output, reflectivity image and velocity model, offers new opportunities to extract accurate rock and pore properties at a fine reservoir scale.
TL;DR: In this article, the angle-domain partial images are calculated by cross-correlating every possible combination of the incident and scattered plane P- and S-waves and then organized them into P-P and P-S local image matrices.
Abstract: An angle-domain imaging condition is recommended for multicomponent elastic reverse time migration. The local slant stack method is used to separate source and receiver waves into P- and S-waves and simultaneously decompose them into local plane waves along different propagation directions. We calculated the angle-domain partial images by crosscorrelating every possible combination of the incident and scattered plane P- and S-waves and then organized them into P-P and P-S local image matrices. Local image matrix preserves all the angle information related to the seismic events. Thus, by working in the image matrix, it is convenient to perform different angle-domain operations (e.g., filtering artifacts, correcting polarity, or conducting illumination and acquisition aperture compensations). Because local image matrix is localized in space, these operations can be designed to be highly flexible, e.g., target-oriented, dip-angle-dependent or reflection-angle-dependent. After performing angle-domain ...
TL;DR: In this article, the authors developed a practical methodology to perform full 3D inversions of entire time- or frequency-domain airborne electromagnetic (AEM) surveys, based on the concept of a moving footprint that reduces the computation requirements by several orders of magnitude.
Abstract: Time-domain airborne surveys gather hundreds of thousands of multichannel, multicomponent samples. The volume of data and other complications have made 1D inversions and transforms the only viable method to interpret these data, in spite of their limitations. We have developed a practical methodology to perform full 3D inversions of entire time- or frequency-domain airborne electromagnetic (AEM) surveys. Our methodology is based on the concept of a moving footprint that reduces the computation requirements by several orders of magnitude. The 3D AEM responses and sensitivities are computed using a frequency-domain total field integral equation technique. For time-domain AEM responses and sensitivities, the frequency-domain responses and sensitivities are transformed to the time domain via a cosine transform and convolution with the system waveform. We demonstrate the efficiency of our methodology with a model study relevant to the Abitibi greenstone belt and a case study from the Reid-Mahaffy test ...
TL;DR: In this article, a tracer test monitored with surface electrical resistivity tomography (ERT) could help by delineating such preferential flow paths and estimating dynamic properties of the aquifer, but the lower resolution of surface ERT compared with crosshole ERT, the finite time that is needed to complete an entire data acquisition, and the strong dilution effects.
Abstract: In hard-rock aquifers, fractured zones constitute adequate drinking water exploitation areas but also potential contamination paths. One critical issue in hydrogeological research is to identify, characterize, and monitor such fractured zones at a representative scale. A tracer test monitored with surface electrical resistivity tomography (ERT) could help by delineating such preferential flow paths and estimating dynamic properties of the aquifer. However, multiple challenges exist including the lower resolution of surface ERT compared with crosshole ERT, the finite time that is needed to complete an entire data acquisition, and the strong dilution effects. We conducted a natural gradient salt tracer test in fractured limestones. To account for the high transport velocity, we injected the salt tracer continuously for four hours at a depth of 18 m. We monitored its propagation with two parallel ERT profiles perpendicular to the groundwater flow direction. Concerning the data acquisition, we always focused ...
TL;DR: In this paper, a joint inversion approach for the direct estimation of in situ reservoir petrophysical parameters such as porosity and fluid saturations by jointly inverting electromagnetic and full-waveform seismic measurements was developed.
Abstract: Accurate determination of reservoir petrophysical parameters is of great importance for reservoir monitoring and characterization. We developed a joint inversion approach for the direct estimation of in situ reservoir petrophysical parameters such as porosity and fluid saturations by jointly inverting electromagnetic and full-waveform seismic measurements. Full-waveform seismic inversions allow the exploitation of the full content of the data so that a more accurate geophysical model can be inferred. Electromagnetic data are linked to porosity and fluid saturations through Archie’s equations, whereas seismic data are linked to them through rock-physics fluid-substitution equations. For seismic modeling, we used an acoustic approximation. Sensitivity studies combined with inversion tests show that seismic data are mainly sensitive to porosity distribution, whereas electromagnetic data are more sensitive to fluid-saturation distribution. The separate inversion of electromagnetic or seismic data is h...
TL;DR: In this article, a 3D frequency-domain solution of the Maxwell's equations for a horizontally layered subsurface was developed for ground-penetrating radar (GPR) data, where the permittivity and conductivity were updated with the phase and amplitude of the source wavelet with a gradient-free optimization approach.
Abstract: Conventional ray-based techniques for analyzing commonmidpoint (CMP) ground-penetrating radar (GPR) data use part of the measured data and simplified approximations of the reality to return qualitative results with limited spatial resolution. Whereas these methods can give reliable values for the permittivity of the subsurface by employing only the phase information, the far-field approximations used to estimate the conductivity of the ground are not valid for near-surface on-ground GPR, such that the estimated conductivity values are not representative for the area of investigation. Full-waveform inversion overcomes these limitations by using an accurate forward modeling and inverts significant parts of the measured data to return reliable quantitative estimates of permittivity and conductivity. Here, we developed a full-waveform inversion scheme that uses a 3D frequency-domain solution of Maxwell’s equations for a horizontally layered subsurface. Although a straight forward full-waveform inversion is relatively independent of the permittivity starting model, inaccuracies in the conductivity starting model result in erroneous effective wavelet amplitudes and therefore in erroneous inversion results, because the conductivity and wavelet amplitudes are coupled. Therefore, the permittivity and conductivity are updated together with the phase and the amplitude of the source wavelet with a gradient-free optimization approach. This novel full-waveform inversion is applied to synthetic and measured CMP data. In the case of synthetic single layered and waveguide data, where the starting model differs significantly from the true model parameter, we were able to reconstruct the obtained model properties and the effective source wavelet. For measured waveguide data, different starting values returned the same wavelet and quantitative permittivities and conductivities. This novel approach enables the quantitative estimation of permittivity and conductivity for the same sensing volume and enables an improved characterization for a wide range of applications.
TL;DR: In this paper, a permanent electrode array has been deployed in three wells to image CO2 injected at the pilot storage Ketzin, Germany, and the results showed that the lateral extent of the related resistivity signature indicated a preferential CO2 migration toward the northwest.
Abstract: Surface-downhole electrical resistivity tomography (SD-ERT) surveys were repeatedly carried out to image CO2 injected at the pilot storage Ketzin, Germany. The experimental setup combines surface with downhole measurements by using a permanent electrode array that has been deployed in three wells. Two baseline experiments were performed during the site startup and three repeat experiments were performed during the first year of CO2 injection. By the time of the third repeat, approximately 13,500 tons of CO2 had been injected into the reservoir sandstones at about 650 m depth. Field data and inverted resistivity models showed a resistivity increase over time at the CO2 injector. The lateral extent of the related resistivity signature indicated a preferential CO2 migration toward the northwest. Using an experimental resistivity-saturation relationship, we mapped CO2 saturations by means of the resistivity index method. For the latest repeat, CO2 saturations show values of up to 70% near the injectio...
TL;DR: In this article, a new methodology for seismic reservoir characterization was proposed that combined advanced geostatistical methods with traditional geophysical models to provide fine-scale reservoir models of facies and reservoir properties, such as porosity and net-to-gross.
Abstract: We presented a new methodology for seismic reservoir characterization that combined advanced geostatistical methods with traditional geophysical models to provide fine-scale reservoir models of facies and reservoir properties, such as porosity and net-to-gross. The methodology we proposed was a stochastic inversion where we simultaneously obtained earth models of facies, rock properties, and elastic attributes. It is based on an iterative process where we generated a set of models of reservoir properties by using sequential simulations, calculated the corresponding elastic attributes through rock-physics relations, computed synthetic seismograms and, finally, compared these synthetic results with the real seismic amplitudes. The optimization is a stochastic technique, the probability perturbation method, that perturbs the probability distribution of the initial realization and allows obtaining a facies model consistent with all available data through a relatively small number of iterations. The pr...
TL;DR: In this article, an analytical computation of the full gravity tensor from a polyhedral source of homogeneous density is presented, with emphasis on its algorithmic implementation, based on the subsequent transition of the general expressions from volume to surface and from surface to line integrals, defined along the closed polygons building each polyhedral face.
Abstract: The analytical computation of the full gravity tensor from a polyhedral source of homogeneous density is presented, with emphasis on its algorithmic implementation. The theoretical development is based on the subsequent transition of the general expressions from volume to surface and from surface to line integrals, defined along the closed polygons building each polyhedral face. However, the accurate numerical computation of the obtained transcendental expressions is linked with the relative position of the computation point and its corresponding projections on the plane of each face and on the line of each segment with respect to the polygons defining each face. Depending on this geometric setup, the application of the divergence theorem of Gauss leads to the appearance of additional correction terms, valid only for these boundary conditions and crucial for the correct numerical evaluation of the polyhedral-related gravity quantities at those locations of the computation point. A program in Fortran is su...
TL;DR: A modeling scheme for 3D CSEM modeling in the frequency domain was developed and the solution to the linear system of equations was obtained using a massive parallel multifrontal solver, because such solvers are robust for indefinite and ill-conditioned linear systems.
Abstract: There has been a recent increase in the use of controlled-source electromagnetic (CSEM) surveys in the exploration for oil and gas. We developed a modeling scheme for 3D CSEM modeling in the frequency domain. The electric field was decomposed in primary and secondary components to eliminate the singularity originated by the source term. The primary field was calculated using a closed form solution, and the secondary field was computed discretizing a second-order partial differential equation for the electric field with the edge finite element. The solution to the linear system of equations was obtained using a massive parallel multifrontal solver, because such solvers are robust for indefinite and ill-conditioned linear systems. Recent trends in parallel computing were investigated for their use in mitigating the computational overburden associated with the use of a direct solver, and of its feasibility for 3D CSEM forward modeling with the edge finite element. The computation of the primary field was par...
TL;DR: The optimal trade-off between memory usage and recomputation can be further improved under the assumption that the information needed to do temporal crosscorrelation is smaller than the information required to restart a simulation from a given time step.
Abstract: Time-domain seismic simulation can form the basis of reverse time depth migration and full-waveform inversion. These applications need to temporally crosscorrelate a forward simulation state with an adjoint simulation state and therefore need to be able to access each time step of a forward simulation in time-reverse order. This requires saving all forward states for all times (which can require more memory than is typically available on a computer system for many problems of interest), or the ability to checkpoint information and rapidly recompute forward simulation states as needed. Prior work has suggested how to do the latter by optimally choosing which forward simulation time steps to checkpoint, thereby enabling the most efficient reuse of memory buffers and minimizing recomputation. The optimal trade-off between memory usage and recomputation can be further improved under the assumption that the information needed to do temporal crosscorrelation is smaller than the information required to restart a simulation from a given time step. This assumption is true for many geophysical problems of interest. The modification can yield a reduction in the memory requirement and recomputation time. The tested examples applied to isotropic elastic reverse time migration and anisotropic viscoelastic full-waveform inversion.
TL;DR: In this paper, the authors used data points enclosed by a square window centered at maxima of the normalized source strength (NSS) for simultaneously estimating the source location and structural index.
Abstract: For a number of widely used models, normalized source strength (NSS) can be derived from eigenvalues of the magnetic gradient tensor. The NSS is proportional to a constant q normalized by the nth power of the distance between observation and integration points where q is a shape factor depending upon geometry of the model and n is the structural index. The NSS is independent of magnetization direction, and its amplitude is only affected by the magnitude of magnetization. The NSS is also a homogenous function and satisfies Euler’s homogeneity equation. Therefore, Euler deconvolution of the NSS can be used to estimate source location. In our algorithm, we use data points enclosed by a square window centered at maxima of the NSS for simultaneously estimating the source location and structural index. The window size is increased until it exceeds a predefined limit. Then the most reliable solution is chosen based on some statistical analysis (minimum uncertainty). One of the advantages of the presented...
TL;DR: In this paper, a truncated convolutional version of the pseudospectral method is used to derive finite-difference operators with different dispersion properties, and these scaled binomial windows can also be used to obtain optimized finite difference operators with enhanced dispersion.
Abstract: The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties.