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- Volume 63, Issue 1, 2015
Geophysical Prospecting - Volume 63, Issue 1, 2015
Volume 63, Issue 1, 2015
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Prestack exploding reflector modelling and migration for anisotropic media
More LessABSTRACTThe double‐square‐root equation is commonly used to image data by downward continuation using one‐way depth extrapolation methods. A two‐way time extrapolation of the double‐square‐root‐derived phase operator allows for up and downgoing wavefields but suffers from an essential singularity for horizontally travelling waves. This singularity is also associated with an anisotropic version of the double‐square‐root extrapolator. Perturbation theory allows us to separate the isotropic contribution, as well as the singularity, from the anisotropic contribution to the operator. As a result, the anisotropic residual operator is free from such singularities and can be applied as a stand alone operator to correct for anisotropy. We can apply the residual anisotropy operator even if the original prestack wavefield was obtained using, for example, reverse‐time migration. The residual correction is also useful for anisotropic parameter estimation. Applications to synthetic data demonstrate the accuracy of the new prestack modelling and migration approach. It also proves useful in approximately imaging the Vertical Transverse Isotropic Marmousi model.
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Determining finite difference weights for the acoustic wave equation by a new dispersion‐relationship‐preserving method
Authors Wenquan Liang, Yanfei Wang and Changchun YangABSTRACTNumerical simulation of the acoustic wave equation is widely used to theoretically synthesize seismograms and constitutes the basis of reverse‐time migration. With finite‐difference methods, the discretization of temporal and spatial derivatives in wave equations introduces numerical grid dispersion. To reduce the grid dispersion effect, we propose to satisfy the dispersion relation for a number of uniformly distributed wavenumber points within a wavenumber range with the upper limit determined by the maximum source frequency, the grid spacing and the wave velocity. This new dispersion‐relationship‐preserving method relatively uniformly reduces the numerical dispersion over a large‐frequency range. Dispersion analysis and seismic numerical simulations demonstrate the effectiveness of the proposed method.
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Source–receiver two‐way wave extrapolation for prestack exploding‐reflector modelling and migration
Authors Tariq Alkhalifah, Sergey Fomel and Zedong WuABSTRACTMost modern seismic imaging methods separate input data into parts (shot gathers). We develop a formulation that is able to incorporate all available data at once while numerically propagating the recorded multidimensional wavefield forward or backward in time. This approach has the potential for generating accurate images free of artiefacts associated with conventional approaches. We derive novel high‐order partial differential equations in the source–receiver time domain. The fourth‐order nature of the extrapolation in time leads to four solutions, two of which correspond to the incoming and outgoing P‐waves and reduce to the zero‐offset exploding‐reflector solutions when the source coincides with the receiver. A challenge for implementing two‐way time extrapolation is an essential singularity for horizontally travelling waves. This singularity can be avoided by limiting the range of wavenumbers treated in a spectral‐based extrapolation. Using spectral methods based on the low‐rank approximation of the propagation symbol, we extrapolate only the desired solutions in an accurate and efficient manner with reduced dispersion artiefacts. Applications to synthetic data demonstrate the accuracy of the new prestack modelling and migration approach.
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Wavefield tomography based on local image correlations
Authors Francesco Perrone, Paul Sava and Jacopo PanizzardiThe estimation of a velocity model from seismic data is a crucial step for obtaining a high‐quality image of the subsurface. Velocity estimation is usually formulated as an optimization problem where an objective function measures the mismatch between synthetic and recorded wavefields and its gradient is used to update the model. The objective function can be defined in the data‐space (as in full‐waveform inversion) or in the image space (as in migration velocity analysis). In general, the latter leads to smooth objective functions, which are monomodal in a wider basin about the global minimum compared to the objective functions defined in the data‐space. Nonetheless, migration velocity analysis requires construction of common‐image gathers at fixed spatial locations and subsampling of the image in order to assess the consistency between the trial velocity model and the observed data. We present an objective function that extracts the velocity error information directly in the image domain without analysing the information in common‐image gathers. In order to include the full complexity of the wavefield in the velocity estimation algorithm, we consider a two‐way (as opposed to one‐way) wave operator, we do not linearize the imaging operator with respect to the model parameters (as in linearized wave‐equation migration velocity analysis) and compute the gradient of the objective function using the adjoint‐state method. We illustrate our methodology with a few synthetic examples and test it on a real 2D marine streamer data set.
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Burying receivers for improved time‐lapse seismic repeatability: CO2CRC Otway field experiment
ABSTRACT4D seismic is widely used to remotely monitor fluid movement in subsurface reservoirs. This technique is especially effective offshore where high survey repeatability can be achieved. It comes as no surprise that the first 4D seismic that successfully monitored the CO2 sequestration process was recorded offshore in the Sleipner field, North Sea. In the case of land projects, poor repeatability of the land seismic data due to low S/N ratio often obscures the time‐lapse seismic signal. Hence for a successful on shore monitoring program improving seismic repeatability is essential.
Stage 2 of the CO2CRC Otway project involves an injection of a small amount (around 15,000 tonnes) of CO2/CH4 gas mixture into a saline aquifer at a depth of approximately 1.5 km. Previous studies at this site showed that seismic repeatability is relatively low due to variations in weather conditions, near surface geology and farming activities. In order to improve time‐lapse seismic monitoring capabilities, a permanent receiver array can be utilised to improve signal to noise ratio and hence repeatability.
A small‐scale trial of such an array was conducted at the Otway site in June 2012. A set of 25 geophones was installed in 3 m deep boreholes in parallel to the same number of surface geophones. In addition, four geophones were placed into boreholes of 1–12 m depth. In order to assess the gain in the signal‐to‐noise ratio and repeatability, both active and passive seismic surveys were carried out. The surveys were conducted in relatively poor weather conditions, with rain, strong wind and thunderstorms. With such an amplified background noise level, we found that the noise level for buried geophones is on average 20 dB lower compared to the surface geophones.
The levels of repeatability for borehole geophones estimated around direct wave, reflected wave and ground roll are twice as high as for the surface geophones. Both borehole and surface geophones produce the best repeatability in the 30–90 Hz frequency range. The influence of burying depth on S/N ratio and repeatability shows that significant improvement in repeatability can be reached at a depth of 3 m. The level of repeatability remains relatively constant between 3 and 12 m depths.
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Research Note: Sparsity‐Aware Multiple Microseismic Event Localization Blind to the Source Time‐Function
Authors Hadi Jamali‐Rad, Zijian Tang, Xander Campman, Alexander Droujinine and Geert LeusABSTRACTWe consider the problem of simultaneously estimating three parameters of multiple microseimic events, i.e., the hypocenter, moment tensor, and origin time. This problem is of great interest because its solution could provide a better understanding of reservoir behavior and can help to optimize the hydraulic fracturing process. The existing approaches employing spatial source sparsity have advantages over traditional full‐wave inversion‐based schemes; however, their validity and accuracy depend on the knowledge of the source time‐function, which is lacking in practical applications. This becomes even more challenging when multiple microseimic sources appear simultaneously. To cope with this shortcoming, we propose to approach the problem from a frequency‐domain perspective and develop a novel sparsity‐aware framework that is blind to the source time‐function. Through our simulation results with synthetic data, we illustrate that our proposed approach can handle multiple microseismic sources and can estimate their hypocenters with an acceptable accuracy. The results also show that our approach can estimate the normalized amplitude of the moment tensors as a by‐product, which can provide worthwhile information about the nature of the sources.
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Time‐lapse seismic imaging using regularized full‐waveform inversion with a prior model: which strategy?
Authors A. Asnaashari, R. Brossier, S. Garambois, F. Audebert, P. Thore and J. VirieuxABSTRACTFull‐waveform inversion is an appealing technique for time‐lapse imaging, especially when prior model information is included into the inversion workflow. Once the baseline reconstruction is achieved, several strategies can be used to assess the physical parameter changes, such as parallel difference (two separate inversions of baseline and monitor data sets), sequential difference (inversion of the monitor data set starting from the recovered baseline model) and double‐difference (inversion of the difference data starting from the recovered baseline model) strategies. Using synthetic Marmousi data sets, we investigate which strategy should be adopted to obtain more robust and more accurate time‐lapse velocity changes in noise‐free and noisy environments. This synthetic application demonstrates that the double‐difference strategy provides the more robust time‐lapse result. In addition, we propose a target‐oriented time‐lapse imaging using regularized full‐waveform inversion including a prior model and model weighting, if the prior information exists on the location of expected variations. This scheme applies strong prior model constraints outside of the expected areas of time‐lapse changes and relatively less prior constraints in the time‐lapse target zones. In application of this process to the Marmousi model data set, the local resolution analysis performed with spike tests shows that the target‐oriented inversion prevents the occurrence of artefacts outside the target areas, which could contaminate and compromise the reconstruction of the effective time‐lapse changes, especially when using the sequential difference strategy. In a strongly noisy case, the target‐oriented prior model weighting ensures the same behaviour for both time‐lapse strategies, the double‐difference and the sequential difference strategies and leads to a more robust reconstruction of the weak time‐lapse changes. The double‐difference strategy can deliver more accurate time‐lapse variation since it can focus to invert the difference data. However, the double‐difference strategy requires a preprocessing step on data sets such as time‐lapse binning to have a similar source/receiver location between two surveys, while the sequential difference needs less this requirement. If we have prior information about the area of changes, the target‐oriented sequential difference strategy can be an alternative and can provide the same robust result as the double‐difference strategy.
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Implementation aspects of eigendecomposition‐based high‐resolution velocity spectra
Authors Tiago Barros, Renato Lopes and Martin TygelABSTRACTIn this paper, we discuss high‐resolution coherence functions for the estimation of the stacking parameters in seismic signal processing. We focus on the Multiple Signal Classification which uses the eigendecomposition of the seismic data to measure the coherence along stacking curves. This algorithm can outperform the traditional semblance in cases of close or interfering reflections, generating a sharper velocity spectrum. Our main contribution is to propose complexity‐reducing strategies for its implementation to make it a feasible alternative to semblance. First, we show how to compute the multiple signal classification spectrum based on the eigendecomposition of the temporal correlation matrix of the seismic data. This matrix has a lower order than the spatial correlation used by other methods, so computing its eigendecomposition is simpler. Then we show how to compute its coherence measure in terms of the signal subspace of seismic data. This further reduces the computational cost as we now have to compute fewer eigenvectors than those required by the noise subspace currently used in the literature. Furthermore, we show how these eigenvectors can be computed with the low‐complexity power method. As a result of these simplifications, we show that the complexity of computing the multiple signal classification velocity spectrum is only about three times greater than semblance. Also, we propose a new normalization function to deal with the high dynamic range of the velocity spectrum. Numerical examples with synthetic and real seismic data indicate that the proposed approach provides stacking parameters with better resolution than conventional semblance, at an affordable computational cost.
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Scattered ground‐roll attenuation using model‐driven interferometry
Authors David Halliday, Phil Bilsby, Lee West, Ed Kragh and John QuigleyABSTRACTScattered ground roll is a type of noise observed in land seismic data that can be particularly difficult to suppress. Typically, this type of noise cannot be removed using conventional velocity‐based filters. In this paper, we discuss a model‐driven form of seismic interferometry that allows suppression of scattered ground‐roll noise in land seismic data. The conventional cross‐correlate and stack interferometry approach results in scattered noise estimates between two receiver locations (i.e. as if one of the receivers had been replaced by a source). For noise suppression, this requires that each source we wish to attenuate the noise from is co‐located with a receiver. The model‐driven form differs, as the use of a simple model in place of one of the inputs for interferometry allows the scattered noise estimate to be made between a source and a receiver. This allows the method to be more flexible, as co‐location of sources and receivers is not required, and the method can be applied to data sets with a variety of different acquisition geometries. A simple plane‐wave model is used, allowing the method to remain relatively data driven, with weighting factors for the plane waves determined using a least‐squares solution. Using a number of both synthetic and real two‐dimensional (2D) and three‐dimensional (3D) land seismic data sets, we show that this model‐driven approach provides effective results, allowing suppression of scattered ground‐roll noise without having an adverse effect on the underlying signal.
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Characterizing the degree of amplitude‐variation‐with‐offset nonlinearity in seismic physical modelling reflection data
Authors Kristopher A. Innanen and Faranak MahmoudianABSTRACTThe nonlinearity of the seismic amplitude‐variation‐with‐offset response is investigated with physical modelling data. Nonlinearity in amplitude‐variation‐with‐offset becomes important in the presence of large relative changes in acoustic and elastic medium properties. A procedure for pre‐processing physical modelling reflection data is enacted on the reflection from a water‐plexiglas boundary. The resulting picked and processed amplitudes are compared with the exact solutions of the plane‐wave Zoeppritz equations, as well as approximations that are first, second, and third order in , , and . In the low angle range of 0°–20°, the third‐order plane‐wave approximation is sufficient to capture the nonlinearity of the amplitude‐variation‐with‐offset response of a liquid‐solid boundary with , , and ρ contrasts of 1485–2745 m/s, 0–1380 m/s, and 1.00–1.19 gm/cc respectively, to an accuracy value of roughly 1%. This is in contrast to the linear Aki–Richards approximation, which is in error by as much as 25% in the same angle range. Even‐order nonlinear corrective terms are observed to be primarily involved in correcting the angle dependence of , whereas the odd‐order nonlinear terms are involved in determining the absolute amplitude‐variation‐with‐offset magnitudes.
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Frequency‐dependent anisotropy of porous rocks with aligned fractures
Authors Robert J. Galvin and Boris GurevichABSTRACTNaturally fractured reservoirs are becoming increasingly important for oil and gas exploration in many areas of the world. Because fractures may control the permeability of a reservoir, it is important to be able to find and characterize fractured zones. In fractured reservoirs, the wave‐induced fluid flow between pores and fractures can cause significant dispersion and attenuation of seismic waves. For waves propagating normal to the fractures, this effect has been quantified in earlier studies. Here we extend normal incidence results to oblique incidence using known expressions for the stiffness tensors in the low‐ and high‐frequency limits. This allows us to quantify frequency‐dependent anisotropy due to the wave‐induced flow between pores and fractures and gives a simple recipe for computing phase velocities and attenuation factors of quasi‐P and SV waves as functions of frequency and angle. These frequency and angle dependencies are concisely expressed through dimensionless velocity anisotropy and attenuation anisotropy parameters. It is found that, although at low frequencies, the medium is close to elliptical (which is to be expected as a dry medium containing a distribution of penny‐shaped cracks is known to be close to elliptical); at high frequencies, the coupling between P‐wave and SV‐wave results in anisotropy due to the non‐vanishing excess tangential compliance.
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Sensitivity of the elastic anisotropy and seismic reflection amplitude of the Eagle Ford Shale to the presence of kerogen
Authors Colin M. Sayers, Shiguang Guo and Josimar SilvaABSTRACTThe Eagle Ford Shale of Central and South Texas is currently of great interest for oil and gas exploration and production. Laboratory studies show that the Eagle Ford Shale is anisotropic, with a correlation between anisotropy and total organic carbon. Organic materials are usually more compliant than other minerals present in organic‐rich shales, and their shapes and distribution are usually anisotropic. This makes organic materials an important source of anisotropy in organic‐rich shales. Neglecting shale anisotropy may lead to incorrect estimates of rock and fluid properties derived from inversion of amplitude versus offset seismic data. Organic materials have a significant effect on the PP and PS reflection amplitudes from the Austin Chalk/Upper Eagle Ford interface, the Upper Eagle Ford/Lower Eagle Ford interface, and the Lower Eagle Ford/Buda Limestone interface. The higher kerogen content of the Lower Eagle Ford compared with that of the Upper Eagle Ford leads to a negative PP reflection amplitude that dims with offset, whereas the PS reflection coefficient increases in magnitude with increasing offset. The PP and PS reflection coefficients at the Austin Chalk/Upper Eagle Ford interface, the Upper Eagle Ford/Lower Eagle Ford interface, and the Lower Eagle Ford/Buda Limestone interface all increase in magnitude with increasing volume fraction of kerogen.
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Seeing coal‐seam top ahead of the drill bit through seismic‐while‐drilling
Authors Binzhong Zhou, Iain Mason, Stewart Greenhalgh and Shankar SubramaniyanABSTRACTBlast damage to the tops of coal seams due to incorrect blast standoff distances is a serious issue, costing the industry in Australia about one open‐cut mine for every ten operating mines. The current approach for mapping coal‐seam tops is through drilling and pierce‐point logging. To provide appropriate depth control with accuracy of ±0.2 m for blast hole drilling, it is typically necessary to drill deep reconnaissance boreholes on a 50 m x 50 m grid well in advance of overburden removal. Pierce‐point mapping is expensive and can be inaccurate, particularly when the seam is disturbed by rolls, faults, and other obstacles.Numerical modelling and prototype‐field testing are used in this paper to demonstrate the feasibility of two seismic‐while‐drilling‐based approaches for predicting the approach to the top of coal during blast hole drilling: (i) reverse “walk‐away” vertical seismic profiling recording, in which the drill bit vibration provides the source signal and the geophones are planted on the surface near the drill rig, and (ii) in‐seam seismic recording, in which channel waves, driven by the coupling to the coal of the seismic signal emitted by the approaching drill bit, are guided by the seam to geophones located within the seam in nearby or remote boreholes.
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Spatial constrained inverse rock physics modelling
Authors Bernardo Moyano, Erling H. Jensen and Tor Arne JohansenABSTRACTPredicting reservoir parameters, such as porosity, lithology, and saturations, from geophysical parameters is a problem with non‐unique solutions. The variance in solutions can be extensive, especially for saturation and lithology. However, the reservoir parameters will typically vary smoothly within certain zones—in vertical and horizontal directions. In this work, we integrate spatial correlations in the predicted parameters to constrain the range of predicted solutions from a particular type of inverse rock physics modelling method. Our analysis is based on well‐log data from the Glitne field, where vertical correlations with depth are expected. It was found that the reservoir parameters with the shortest depth correlation (lithology and saturation) provided the strongest constraint to the set of solutions. In addition, due to the interdependence between the reservoir parameters, constraining the predictions by the spatial correlation of one parameter also reduced the number of predictions of the other two parameters. Moreover, the use of additional constraints such as measured log data at specific depth locations can further narrow the range of solutions.
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Signal detectability of marine electromagnetic methods in the exploration of resistive targets
Authors Mark Goldman, Vladimir Mogilatov, Amir Haroon, Eldad Levi and Bülent TezkanABSTRACTWe compare selected marine electromagnetic methods for sensitivity to the presence of relatively thin resistive targets (e.g., hydrocarbons, gas hydrates, fresh groundwater, etc.). The study includes the conventional controlled‐source electromagnetic method, the recently introduced transient electromagnetic prospecting with vertical electric lines method, and the novel marine circular electric dipole method, which is still in the stage of theoretical development. The comparison is based on general physical considerations, analytical (mainly asymptotic) analysis, and rigorous one‐dimensional and multidimensional forward modelling. It is shown that transient electromagnetic prospecting with vertical electric lines and marine circular electric dipole methods represent an alternative to the conventional controlled‐source electromagnetic method at shallow sea, where the latter becomes less efficient due to the air‐wave phenomenon. Since both former methods are essentially short‐offset time‐domain techniques, they exhibit a much better lateral resolution than the controlled‐source electromagnetic method in both shallow sea and deep sea. The greatest shortcoming of the transient electromagnetic prospecting with vertical electric lines and marine circular electric dipole methods comes from the difficulties in accurately assembling the transmitter antenna within the marine environment. This makes these methods significantly less practical than the controlled‐source electromagnetic method. Consequently, the controlled‐source electromagnetic method remains the leading marine electromagnetic technique in the exploration of large resistive targets in deep sea. However, exploring laterally small targets in deep sea and both small and large targets in shallow sea might require the use of the less practical transient electromagnetic prospecting with vertical electric lines and/or marine circular electric dipole method as a desirable alternative to the controlled‐source electromagnetic method.
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Interference effects of aircraft on earth's electromagnetic response at very low frequency and low frequency
Authors C. Shan and L. B. PedersenABSTRACTOver the last few decades, very low frequency electromagnetics has been widely and successfully applied in mineral exploration and groundwater exploration. Many radio transmitters with strong signal‐to‐noise ratios are scattered in the very low frequency band and low frequency band. Based on experiences gained from ground measurements with the radio‐magnetotelluric technique operating in the frequency interval 1–250 kHz, broadband magnetometers have been used to cover both very low frequency (3–30 kHz) and low frequency (30–300 kHz) bands to increase the resolution of the near‐surface structure. The metallic aircraft as a conductive body will distort the magnetic signal to some extent, and thus it is important to investigate aircraft interference on the electromagnetic signal. We studied noise caused by rotation of an aircraft and the aircraft itself as a metallic conductive body with three methods: 3D wave polarization, determination of transmitter direction and full tipper estimation. Both very low frequency and low frequency bands were investigated. The results show that the magnetic field is independent of the aircraft at low frequencies in the very low frequency band and part of the low frequency band (below 100 kHz). At high frequencies (above 100 kHz), the signals are more greatly influenced by the aircraft, and the wave polarization directions are more scattered, as observed when the aircraft turned. Some aircraft generated noise mixed with radio transmitter signals, detected as ‘dummy’ signals by the 3D wave polarization method. The estimated scalar magnetic transfer functions are dependent on the aircraft flight directions at high frequencies, because of aircraft interference. The aircraft eigenresponse in the transfer functions (tippers) between vertical and horizontal magnetic field components was compensated for in the real part of the estimated tippers, but some unknown effect was still observed in the imaginary parts.
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Reorientation of three‐component borehole magnetic data
Authors C. Virgil, S. Ehmann, A. Hördt, M. Leven and E. StevelingABSTRACTThree‐component borehole magnetics provide important additional information compared to total field or horizontal and vertical measurements. These data can be used for several tasks such as the localization of ferromagnetic objects, the determination of apparent polar wander curves and the computation of the magnetization of rock units. However, the crucial point in three‐component borehole magnetics is the reorientation of the measured data from the tool's frame to the geographic reference frame North, East and Downwards. For this purpose, our tool, the Göttinger Borehole Magnetometer, comprises three orthogonally aligned fibre optic gyros along with three fluxgate sensors. With these sensors, the vector of the magnetic field along with the tool rotation can be recorded continuously during the measurement. Using the high–precision gyro data, we can compute the vector of the magnetic anomaly with respect to the Earth's reference frame. Based on the comparison of several logs measured in the Outokumpu Deep Drill Hole (OKU R2500, Finland), the repeatability of the magnetic field vector is 0.8° in azimuthal direction, 0.08° in inclination and 71 nT in magnitude.
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Sharp spatially constrained inversion with applications to transient electromagnetic data
ABSTRACTTime‐domain electromagnetic data are conveniently inverted by using smoothly varying 1D models with fixed vertical discretization. The vertical smoothness of the obtained models stems from the application of Occam‐type regularization constraints, which are meant to address the ill‐posedness of the problem. An important side effect of such regularization, however, is that horizontal layer boundaries can no longer be accurately reproduced as the model is required to be smooth. This issue can be overcome by inverting for fewer layers with variable thicknesses; nevertheless, to decide on a particular and constant number of layers for the parameterization of a large survey inversion can be equally problematic.
Here, we present a focusing regularization technique to obtain the best of both methodologies. The new focusing approach allows for accurate reconstruction of resistivity distributions using a fixed vertical discretization while preserving the capability to reproduce horizontal boundaries. The formulation is flexible and can be coupled with traditional lateral/spatial smoothness constraints in order to resolve interfaces in stratified soils with no additional hypothesis about the number of layers. The method relies on minimizing the number of layers of non‐vanishing resistivity gradient, instead of minimizing the norm of the model variation itself. This approach ensures that the results are consistent with the measured data while favouring, at the same time, the retrieval of horizontal abrupt changes. In addition, the focusing regularization can also be applied in the horizontal direction in order to promote the reconstruction of lateral boundaries such as faults.
We present the theoretical framework of our regularization methodology and illustrate its capabilities by means of both synthetic and field data sets. We further demonstrate how the concept has been integrated in our existing spatially constrained inversion formalism and show its application to large‐scale time‐domain electromagnetic data inversions.
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Identifying gravity anomalies caused by granitic intrusions in Nanling mineral district, China: a multifractal perspective
Authors Guoxiong Chen, Qiuming Cheng, Renguang Zuo, Tianyou Liu and Yufei XiABSTRACTSeveral power‐law relationships of geophysical potential fields have been discussed recently with renewed interests, including field value–distance () and power spectrum–wavenumber () models. The singularity mapping technique based on the density/concentration–area (C–A) power‐law model is applied to act as a high‐pass filter for extracting gravity and magnetic anomalies regardless of the background value and to detect the edges of gravity or magnetic sources with the advantage of scale invariance. This is demonstrated on a synthetic example and a case study from the Nanling mineral district, Southern China. Compared with the analytic signal amplitude and total horizontal gradient methods, the singularity mapping technique provides more distinct and less noisy boundaries of granites than traditional methods. Additionally, it is efficient for enhancing and outlining weak anomalies caused by concealed granitic intrusions, indicating that the singularity method based on multifractal analysis is a potential tool to process gravity and magnetic data.
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Volumes & issues
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Volume 72 (2023 - 2024)
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