Showing papers in "Geophysics in 2015"

Random noise attenuation using local signal-and-noise orthogonalization

Abstract: We have developed a novel approach to attenuate random noise based on local signal-and-noise orthogonalization. In this approach, we first removed from a seismic section using one of the conventional denoising operators and then applied a weighting operator to the initially denoised section to predict the signal-leakage energy, as well as retrieve it from the initial noise section. The weighting operator was obtained by solving a least-squares minimization problem via shaping regularization with a smoothness constraint. Next, the initially denoised section and the retrieved signal were combined to form the final denoised section. The proposed denoising approach corresponded to orthogonalizing the initially denoised signal and noise in a local manner. We evaluated the denoising performance using local similarity. To test the orthogonalization property of the estimated signal and noise, we calculated the local similarity map between the denoised signal section and removed noise section. Low values o...

A stable and practical implementation of least-squares reverse time migration

Abstract: By adapting reverse time migration (RTM) and demigration as the migration and modeling operators to maximize the crosscorrelation between the simulated and the acquired seismic data, we introduced a new practical least-squares RTM (LSRTM) scheme and derived a steepest descent method in seeking the optimal image. Through synthetic and real data experiments, we determined that the proposed LSRTM provided high-quality images with balanced amplitudes, improved focusing, and enhanced resolution. The method was also capable of removing free surface ghosts caused by towed streamer acquisition, filling the structures and reducing crosstalk noise associated with simultaneous shooting.

Induced seismicity of the Groningen gas field: History and recent developments

Abstract: Induced seismicity of the Groningen gas field is caused by the production of gas. Because of the large areal extent of the reservoir, the long history of depletion, and the available data sets (which exist as a result of consequences and public unrest caused by induced seismicity), the field presents a valuable case for studying the relationships among geologic, flow-dynamic, geomechanical, and seismological models. Gas production from the Groningen field started in 1963. Induced seismicity of the field first was recorded in 1991 (ML 2.4). During the subsequent 10 years, induced seismicity stayed at a rate of about five events (ML ≥ 1.5) per year. Starting in 2003, the number of events and magnitudes started to increase. In 2012, the largest event (ML 3.6) occurred, which caused the most damage to date. As a consequence, studies carried out in 2013 have fundamentally changed the way to look at the relationship between induced seismicity and gas depletion. There appears to be a close link between ...

Frequencies of the Ricker wavelet

Abstract: The Ricker wavelet is theoretically a solution of the Stokes differential equation, which takes into account the effect of Newtonian viscosity, and is applicable to seismic waves propagated through viscoelastic homogeneous media. In this paper, we defined the time-domain breadth and the frequency-domain bandwidth of the Ricker wavelet and developed quantities analytically in terms of the Lambert W function. We determined that the central frequency, the geometric center of the frequency band, is close to the mean frequency statistically evaluated using the power spectrum, rather than the amplitude spectrum used in some of the published literature. We also proved that the standard deviation from the mean frequency is not, as suggested by the literature, the half-bandwidth of the frequency spectrum of the Ricker wavelet. Moreover, we established mathematically the relationships between the theoretical frequencies (the central frequency and the half-bandwidth) and the numerical measurements (the mean frequency and its standard deviation) and produced each of these frequency quantities analytically in terms of the peak frequency of the Ricker wavelet.

Simultaneous multitrace impedance inversion with transform-domain sparsity promotion

Abstract: The impedance inversion technique plays a crucial role in seismic reservoir properties prediction. However, most existing impedance inversion methods often suffer from spatial discontinuities and instability because each vertical profile is processed independently in the inversion. We tested a transform-domain sparsity promotion simultaneous multitrace impedance inversion method to address this issue. The approach was implemented through minimizing a data misfit term and a transform-domain sparsity constraint term that incorporates the (2D or 3D) structural information into the inversion processing. A 2D synthetic data example was applied to mainly explain the roles of the transform-domain sparsity constraint. We determined that the transform-domain sparsity constraint can help in stabilizing the inversion, reducing the influence of high-wavenumber noise on the inverted result, and exploring spatial continuities of structures. Furthermore, a 3D field data example was used to examine the effectiven...

Microseismic and seismic denoising via ensemble empirical mode decomposition and adaptive thresholding

Abstract: Random and coherent noise exists in microseismic and seismic data, and suppressing noise is a crucial step in seismic processing. We have developed a novel seismic denoising method, based on ensemble empirical mode decomposition (EEMD) combined with adaptive thresholding. A signal was decomposed into individual components called intrinsic mode functions (IMFs). Each decomposed signal was then compared with those IMFs resulting from a white-noise realization to determine if the original signal contained structural features or white noise only. A thresholding scheme then removed all nonstructured portions. Our scheme is very flexible, and it is applicable in a variety of domains or in a diverse set of data. For instance, it can serve as an alternative for random noise removal by band-pass filtering in the time domain or spatial prediction filtering in the frequency-offset domain to enhance the lateral coherence of seismic sections. We have determined its potential for microseismic and reflection seismic denoising by comparing its performance on synthetic and field data using a variety of methods including band-pass filtering, basis pursuit denoising, frequency-offset deconvolution, and frequency-offset empirical mode decomposition.

Interpolation and denoising of high-dimensional seismic data by learning a tight frame

Abstract: Sparse transforms play an important role in seismic signal processing steps, such as prestack noise attenuation and data reconstruction. Analytic sparse transforms (so-called implicit dictionaries), such as the Fourier, Radon, and curvelet transforms, are often used to represent seismic data. There are situations, however, in which the complexity of the data requires adaptive sparse transform methods, whose basis functions are determined via learning methods. We studied an application of the data-driven tight frame (DDTF) method to noise suppression and interpolation of high-dimensional seismic data. Rather than choosing a model beforehand (for example, a family of lines, parabolas, or curvelets) to fit the data, the DDTF derives the model from the data itself in an optimum manner. The process of estimating the basis function from the data can be summarized as follows: First, the input data are divided into small blocks to form training sets. Then, the DDTF algorithm is applied on the training set...

Vector-based elastic reverse time migration

Abstract: Prestack elastic reverse time migration (RTM) of multicomponent seismic data requires separating PP and PS reflections before, or as part of, applying the image condition, and using image conditions that preserve the angle and amplitude information. Both of these requirements are best achieved when all operations are on vectors. We have created a new 2D migration context for isotropic, elastic RTM, which included decomposition of the elastic source and receiver wavefields into P- and S-wave vectors by decoupled elastodynamic extrapolation, which retained the same stress and particle velocity components as the input data. Then, the propagation directions of the incident and reflected P- and S-waves were calculated directly from the stress and particle velocity definitions of the P- and S-wave Poynting vectors. An excitation-amplitude image condition that scaled the receiver wavelet by the source vector magnitude produced angle-dependent images of PP and PS reflection coefficients with the correct p...

Nonlinear multichannel impedance inversion by total-variation regularization

Abstract: The analysis of acoustic impedance (AI) allows for the mapping of seismic reflection data to lithology, and hence it plays an important role in the interpretation of poststack seismic data. The AI is obtainable from the inversion of the earth reflectivity series. Efficient deconvolution methods have been developed for recovering the reflectivity series from band-limited poststack data, which are multiple free, zero offset, and migrated. However, calculation of the AI from the reflectivity, when considering the spatial correlation of the impedance parameters, demands the solution of a constrained nonlinear inverse problem. Two efficient algorithms are proposed for solving the nonlinear impedance problem in multichannel form with the total-variation (TV) constraint to recover impedance maps with blocky structures. The first uses the continuous earth model for reflectivity, which allows linearizing the problem in the logarithm domain. The second uses the discrete (layered) earth model for reflectivit...

Bulk modulus dispersion and attenuation in sandstones

Abstract: We report experimental data on the frequency dependence of bulk elastic modulus in porous sandstones. A new methodology was developed to investigate the dispersion/attenuation phenomena on a rock’s bulk modulus K for varying confining pressures in the range of 1–50 MPa and fluids of varying viscosities (i.e., air, glycerin, and water). This methodology combined (1) ultrasonic (i.e., f∼0.5 MHz) P- and S-wave velocity measurements, leading to the high-frequency (HF) KHF, (2) stress-strain measurements from forced periodic oscillations of confining pressure at low-frequency (LF) ranges (i.e., f∈[4 10-3;4 10-1] Hz), leading to KLF and QK−1, and (3) pore-pressure measurement to document the induced fluid-flow in the LF range (i.e., f∈[4 10-3;4 10-1] Hz). The stress-strain method was first checked using three standard samples: glass, gypsum, and Plexiglas samples. Over the frequency and pressure range of the apparatus KLF was stable and accurate and the lowest measurable LF attenuation was QK−1∼0...

Induced polarization response of porous media with metallic particles — Part 1: A theory for disseminated semiconductors

Abstract: A model is proposed regarding the polarization of dispersed metallic conductors (e.g., pyrite and magnetite) in porous media free of redox-active ionic species in the pore water. We studied two cases corresponding to having a background material with or without chargeability. The model was based on the polarization mechanism of a single particle using well-established bounds for the reflection coefficient entering the definition of the dipole moment of the metallic grains. We used the Maxwell-Clausius-Mossotti mixing equation to obtain the complex conductivity of the mixture of dispersed metallic particles in the background porous material composed of the pore water and the insulating grains coated by an electric double-layer. This equation can be generalized to a mixture of various types of metallic particles (with their own properties) dispersed in the background porous material. Our model led to a very simple linear relationship between the chargeability and the volume content of metallic parti...

Simultaneous inversion of the background velocity and the perturbation in full-waveform inversion

Abstract: The gradient of standard full-waveform inversion (FWI) attempts to map the residuals in the data to perturbations in the model. Such perturbations may include smooth background updates from the transmission components and high wavenumber updates from the reflection components. However, if we fix the reflection components using imaging, the gradient of what is referred to as reflected-waveform inversion (RWI) admits mainly transmission background-type updates. The drawback of existing RWI methods is that they lack an optimal image capable of producing reflections within the convex region of the optimization. Because the influence of velocity on the data was given mainly by its background (propagator) and perturbed (reflectivity) components, we have optimized both components simultaneously using a modified objective function. Specifically, we used an objective function that combined the data generated from a source using the background velocity, and that by the perturbed velocity through Born modeli...

Multidomain petrophysically constrained inversion and geology differentiation using guided fuzzy c-means clustering

Abstract: Geophysical inversion methods are used as part of an interpretation process that seeks to differentiate geologic units. To improve the reliability of geologic differentiation based on recovered images from geophysical inversions, we have developed a multidomain clustering inversion algorithm that can incorporate statistical petrophysical data into a deterministic geophysical inversion framework through the use of the fuzzy c-means clustering technique. Petrophysical data are treated in the parameter domain in the same way that geophysical data are treated in the spatial domain, and these two different types of data are simultaneously inverted in their respective domains through the minimization of a single common objective function. The resulting physical property model honors the geophysical and petrophysical data and therefore can represent the earth better than geophysical inversion models that solely honor the geophysical data. Geophysical inversion and geology differentiation are generally tr...

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

Abstract: We have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, large conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily ef...

Robust reduced-rank filtering for erratic seismic noise attenuation

Abstract: Singular spectrum analysis (SSA) or Cadzow reduced-rank filtering is an efficient method for random noise attenuation. SSA starts by embedding the seismic data into a Hankel matrix. Rank reduction of this Hankel matrix followed by antidiagonal averaging is utilized to estimate an enhanced seismic signal. Rank reduction is often implemented via the singular value decomposition (SVD). The SVD is a nonrobust matrix factorization technique that leads to suboptimal results when the seismic data are contaminated by erratic noise. The term erratic noise designates non-Gaussian noise that consists of large isolated events with known or unknown distribution. We adopted a robust low-rank factorization that permitted use of the SSA filter in situations in which the data were contaminated by erratic noise. In our robust SSA method, we replaced the quadratic error criterion function that yielded the truncated SVD solution by a bisquare function. The Hankel matrix was then approximated by the product of two low...

Correlation-based reflection full-waveform inversion

Abstract: Because modeling for full-waveform inversion (FWI) cannot produce reflections unless the velocity model has the scattering potential (high wavenumbers), using a migration/demigration process to generate modeling data, which is a key step in what is now known as reflection FWI (RFWI), is a credible alternative to tackle the reflection nonlinearity associated with FWI. However, because RFWI depends on a conventional data residual or zero-lag correlation objective function, high nonlinearity can still exist when the true amplitude migration is not used, as well as at far offsets due to cycle skipping. To avoid the cycle skipping and the need for a true amplitude migration, we have developed a correlation-based reflection full-waveform inversion method to update the low-wavenumber components of the velocity model. The success of this method relies on a sensitivity kernel decomposition and a correlation-based objective function. The sensitivity kernel decomposition makes it possible to separate out the contributions of different subkernels and to smear the reflected wave residuals along the “rabbit-ear” wavepath to obtain middle and deep background model estimates. The correlation-based objective function measures differences in kinematic information and behaves in a more linear way than the traditional waveform residual misfit. Moreover, our approach is less sensitive to the frequency content and amplitude information of the seismic data, enabling reliable background velocity estimates to be obtained without the need for low frequencies and full-physics modeling. Because the kinematic features of reflected waves are described correctly, the inversion result of the proposed method can be used as a migration model or an initial model for conventional FWI to achieve a correct high-wavenumber model update.

Five ways to avoid storing source wavefield snapshots in 2D elastic prestack reverse time migration

Abstract: Five alternative algorithms were evaluated to circumvent the excessive storage requirement imposed by saving source wavefield snapshots used for the crosscorrelation image condition in 2D prestack elastic reverse time migration. We compared the algorithms on the basis of their ability, either to accurately reconstruct (not save) the source wavefield or to use an alternate image condition so that neither saving nor reconstruction of full wavefields was involved. The comparisons were facilitated by using the same (velocity-stress) extrapolator in all the algorithms, and running them all on the same hardware. We assumed that there was enough memory in a node to do an extrapolation, and that all input data were stored on disk rather than residing in random-access memory. This should provide a fair and balanced comparison. Reconstruction of the source wavefield from boundary and/or initial values reduced the required storage to a very small fraction of that needed to store source wavefield snapshots fo...

Scalar imaging condition for elastic reverse time migration

Abstract: Polarity changes in converted-wave images constructed by elastic reverse time migration cause destructive interference after stacking over the experiments of a seismic survey. This polarity reversal is due to PS and SP reflectivities reversing sign at certain incidence angles, e.g., at normal incidence in isotropic media. Many of the available polarity correction methods are complex and require costly transformations, e.g., to the angle domain. We derive a simple imaging condition for converted waves to correct the image polarity and reveal the conversion strength from one wave mode to another. Our imaging condition exploits pure P- and S-modes obtained by Helmholtz decomposition. Instead of correlating Cartesian components of the vector S-mode with the P-mode, we exploit all three components of the S wavefield at once to produce a unique image. We generate PS and SP images using geometric relationships among the propagation directions for the P- and S-wavefields, the reflector orientation, and th...

Determination of nuclear magnetic resonance T2 cutoff value based on multifractal theory — An application in sandstone with complex pore structure

Abstract: The cutoff value of nuclear magnetic resonance (NMR) transversal relaxation time T2 is vital for pore structure characterization, permeability prediction, and irreducible water saturation calculation. Conventional default values often lead to inaccurate results for rocks with complex pore structure. Based on NMR experiments and multifractal theory, we have developed an effective statistical method to predict T2 cutoff values without other petrophysical information. The method is based on multifractal theory to analyze the NMR T2 spectrum with the assumption that the T2 spectrum is an indicator of pore size distribution. Multifractal parameters, such as multifractal dimension, singularity strength, and mass exponent, are calculated to investigate the multifractal behavior of T2 spectrum via NMR experiments and a dyadic scaling-down algorithm. To obtain the optimal T2 cutoff value, the rotation speed and time of centrifugation are enlarged increasingly to optimal centrifugal state. A predicating mod...

Increasing seismicity in the U. S. midcontinent: Implications for earthquake hazard

Abstract: Earthquake activity in parts of the central United States has increased dramatically in recent years. The space-time distribution of the increased seismicity, as well as numerous published case studies, indicates that the increase is of anthropogenic origin, principally driven by injection of wastewater coproduced with oil and gas from tight formations. Enhanced oil recovery and long-term production also contribute to seismicity at a few locations. Preliminary hazard models indicate that areas experiencing the highest rate of earthquakes in 2014 have a short-term (one-year) hazard comparable to or higher than the hazard in the source region of tectonic earthquakes in the New Madrid and Charleston seismic zones.

Viscoacoustic modeling and imaging using low-rank approximation

Abstract: A constant-Q wave equation involving fractional Laplacians was recently introduced for viscoacoustic modeling and imaging. This fractional wave equation has a convenient mixed-domain space-wavenumber formulation, which involves the fractional-Laplacian operators with a spatially varying power. We have applied the low-rank approximation to the mixed-domain symbol, which enables a space-variable attenuation specified by the variable fractional power of the Laplacians. Using the proposed approximation scheme, we formulated the framework of the Q-compensated reverse time migration (Q-RTM) for attenuation compensation. Numerical examples using synthetic data demonstrated the improved accuracy of using low-rank wave extrapolation with a constant-Q fractional-Laplacian wave equation for seismic modeling and migration in attenuating media. Low-rank Q-RTM applied to viscoacoustic data is capable of producing images comparable in quality with those produced by conventional RTM from acoustic data.

Multitrace impedance inversion with lateral constraints

Abstract: We have developed a lateral constraint to the inversion of 1D seismic impedance models to suppress the effect of data noise and improve the fidelity of formation boundaries in 2D models for situations with dips of less than 20°. Typical inversion frameworks rely on a 1D forward model with each 1D trace being inverted independently. Adjacent inversion models are combined together to form a 2D impedance model. Adding a lateral constraint improves the fidelity of the 2D impedance models while retaining much of the advantage of the low-computational cost associated with typical 1D inversion schemes. Solving the 1D lateral constraint inversion (1D-LCI) problem involves the simultaneous inversion of multiple 1D traces producing layered sections with lateral smoothed transition. In addition to enforcing lateral continuity in the inversion model, this algorithm allows for the inclusion of a priori knowledge from boreholes. We determined the effectiveness of this algorithm on two synthetic models, as well ...

Removing false images in reverse time migration: The concept of de-primary

Abstract: Primary reflections, like multiples, can generate false images when reverse time migration (RTM) algorithms are used. The false images are formed by the zero-lag correlation of the source wavefields and primary reflections, which are propagated by the migration algorithm along nonphysical paths. These paths are generated by strong velocity gradients or reflection interfaces when the two-way wave equation is used. Conceptually, this type of artifact can be removed by separating up- and downgoing waves, but such separation may be impractical because it often requires storing the entire wavefields at all time steps. We have developed a de-primary RTM method in which such separation can be accomplished without saving the wavefields. The computational cost of the proposed method was only approximately 33% higher than that of conventional RTM algorithms. Using field and synthetic data sets, we have demonstrated the existence of this endemic RTM problem and verified the effectiveness of the de-primary RT...

Marchenko imaging: Imaging with primaries, internal multiples, and free-surface multiples

Abstract: Recent work on retrieving the Green’s function with the Marchenko equation shows how these functions for a virtual source in the subsurface can be obtained from reflection data. The response to the virtual source is the Green’s function from the location of the virtual source to the surface. The Green’s function is retrieved using only the reflection response of the medium and an estimate of the first arrival at the surface from the virtual source. Current techniques, however, only include primaries and internal multiples. Therefore, all surface-related multiples must be removed from the reflection response prior to Green’s function retrieval. We have extended the Marchenko equation to retrieve the Green’s function that includes primaries, internal multiples, and free-surface multiples. In other words, we have retrieved the Green’s function in the presence of a free surface. The information needed for the retrieval is the same as the current techniques, with the only difference being that the reflection response now also includes free-surface multiples. The inclusion of these multiples makes it possible to include them in the imaging operator, and it obviates the need for surface-related multiple elimination. This type of imaging with Green’s functions is called Marchenko imaging.

An approximate inverse to the extended Born modeling operator

Abstract: Given a correct (data-consistent) velocity model, reverse time migration (RTM) correctly positions reflectors but generally with incorrect amplitudes and wavelets Iterative least-squares migration (LSM) corrects the amplitude and wavelet by fitting data in the sense of Born modeling, that is, replacing migration by Born inversion However, LSM also requires a correct velocity model, and it may require many migration/demigration cycles We modified RTM in the subsurface offset domain to create an asymptotic (high-frequency) approximation to extended LSM This extended Born inversion operator outputs extended reflectors (depending on the subsurface offset and position in the earth) with correct amplitude and phase, in the sense that similarly extended Born modeling reproduces the data to good accuracy Although the theoretical justification of the inversion property relies on ray tracing and stationary phase, application of the weight operators does not require any computational ray tracing The co

Multiscale adjoint waveform tomography for surface and body waves

Abstract: We have developed a wavelet-multiscale adjoint scheme for the elastic full-waveform inversion of seismic data, including body waves (BWs) and surface waves (SWs). We start the inversion on the SW portion of the seismograms. To avoid cycle skipping and reduce the dependence on the initial model of these dispersive waves, we commence by minimizing an envelope-based misfit function. Subsequently, we proceed to the minimization of a waveform-difference (WD) metric applied to the SWs only. After that, we fit BWs and SWs indiscriminately using a WD misfit metric. In each of these three steps, we guide the iterative inversion through a sequence of nested subspace projections in a wavelet basis. SW analysis preserves a wealth of near-surface features that would be lost in conventional BW tomography. We used a toy model to illustrate the dispersive and cycle-skipping behavior of the SWs, and to introduce the two ways by which we combat the nonlinearity of waveform inversions involving SWs. The first is the...

Horizon volumes with interpreted constraints

Abstract: Horizons are geologically significant surfaces that can be extracted from seismic images. Color coding of horizons based on amplitude or other attributes can help reveal ancient sedimentary environments and structural features. Extracted horizons are also used for building structure models and stratigraphic interpretations. We propose two methods for constructing seismic horizons aligned with reflectors in a 3D seismic image. The first method generates horizons one at a time; the second method generates an entire volume of horizons at once by first computing a relative geologic time volume from seismic normal vectors. Rather than gradually building a horizon by extending one or more seed points to a surface along seismic reflectors, both of our methods generate whole horizons at once by solving partial differential equations derived from seismic normal vectors. The most significant new aspect of both methods is the ability to specify, perhaps interactively during interpretation, a small number of ...

Seismic data denoising through multiscale and sparsity-promoting dictionary learning

Abstract: Seismic data comprise many traces that provide a spatiotemporal sampling of the reflected wavefield. However, such information maysuffer from ambient and random noise during acquisition, which could possibly limit the use of seismic data in reservoir locating. Traditionally, fixed transforms are used to separate the noise from the data by exploiting their different characteristics in a transform domain. However, their performance may not be satisfactory due to their lack of adaptability to changing data structures. We have developed a novel seismic data denoising method based on a parametric dictionary learning scheme. Unlike previous dictionary learning methods that had to learn unconstrained atoms, our method exploits the underlying sparse structure of the learned atoms over a base dictionary and significantly reduces the dictionary elements that need to be learned. By combining the advantages of multiscale representations with the power of dictionary learning, more degrees of freedom could be provided to the sparse representation, and therefore the characteristics of seismic data could be efficiently captured in sparse coefficients for denoising. The dictionary learning and denoising were processed from all overlapping patches of the given noisy seismic data, which maintained low complexity. Numerical experiments on synthetic seismic data indicated that our scheme achieved the best denoising performance in terms of peak signal-to-noise ratio and minimizes visual distortion.

Separation and reconstruction of simultaneous source data via iterative rank reduction

Abstract: We have developed a rank-reduction algorithm based on singular spectrum analysis (SSA) that is capable of suppressing the interferences generated by simultaneous source acquisition. We evaluated an inversion scheme that minimizes the misfit between predicted and observed blended data in t‐x domain subject to a low-rank constraint that is applied to data in the f‐x domain. In particular, we developed an iterative algorithm by adopting the projected gradient method with the SSA filter acting as the projection operator. This method entails extracting small patches of data from a common receiver gather and organizing the spatial data at a given monochromatic frequency into a Hankel matrix. For the ideal unblended data, Hankel matrices extracted from the data are of low rank. The incoherent interferences in common-receiver domain caused by simultaneously fired shots increase the rank of the aforementioned Hankel matrices. Therefore, rank-reduction filtering is an effective way to annihilate source inte...

Transient-electromagnetic finite-difference time-domain earth modeling over steel infrastructure

Abstract: Including highly conductive steel infrastructure into electromagnetic (EM) earth modeling is motivated by the fact that long metal-cased boreholes have the potential to be used as boosting antennas that enable larger source dipole moments and greater signal penetration depths. Unfortunately, geophysical algorithms designed to simulate EM responses over rather regional scales are complicated by material property contrasts and structure geometries that are more typical for EM engineering applications. Hence, the great majority of earth-modeling algorithms that consider EM responses from steel-cased boreholes use integral-equation methods. To be able to model complex casing scenarios, we revisited the finite-difference time-domain (FDTD) method to advance the modeling of transient-EM field responses from steel-cased boreholes. A time-dependent function that allows for larger FDTD time steps in the DuFort-Frankel method was developed, alleviating the generally large computational overhead. We compared our method against three different kinds of benchmark solutions to demonstrate the reliability of the FDTD field solutions. These test cases were carried out to check the feasibility of a final hydraulic fracturing study. Images of the electric current distribution in a sheetlike rock fracture were calculated for the cases with and without the presence of a connecting borehole casing, demonstrating the casing’s potential of illuminating deep target zones.