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- Volume 64, Issue 2, 2016
Geophysical Prospecting - Volume 64, Issue 2, 2016
Volume 64, Issue 2, 2016
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Geophone‐ground coupling with flat bases
Authors José M. Carcione, Hashim S. Almalki and Ayman N. QadrouhABSTRACTSeismic acquisition can be costly and inefficient when using spiked geophones. In most cases, such as the desert, the most practical solution is the use of flat bases, where geophone‐ground coupling is based on an optimal choice of the mass and area of contact between the receiver and the ground. This optimization is necessary since areas covered by sand are loose sediments and poor coupling occurs. Other cases include ground coupling in stiff pavements, for instance urban areas and ocean‐bottom nodes. We consider three different approaches to analyse coupling and model the geophone with a flat base (plate) resting on an elastic half‐space. Two existing models, based on the full‐wave theory, which we refer to as the Wolf and Hoover‐O'Brien models, predict a different behaviour with respect to the novel method introduced in this work. This method is based on the transmission coefficient of upgoing waves impinging in the geophone‐ground contact, where the ground is described as an anelastic half‐space. The boundary conditions at the contact have already been used to model fractures and are shown here to provide the equation of the damped oscillator. This fracture‐contact model depends on the stiffness characteristic of the contact between the geophone base plate and the ground. The transmission coefficient from the ground to the plate increases for increasing weight and decreasing base plate area. The new model predicts that the resonant frequency is independent of the geophone weight and plate radius, while the recorded energy increases with increasing weight and decreasing base plate area (as shown from our own experiments and measurements by Krohn) which is contrary to the theories developed by Wolf and Hoover‐O'Brien. The transient response is obtained by an inverse Fourier transform. Optimal geophone‐ground coupling and energy transmission are required, the first concept meaning that the geophone is following the motion of the ground and the second one that the signal is detectable. As a final example, we simulate seismic acquisition based on the novel theory, showing the differences between optimal and poor ground‐to‐geophone energy transmission.
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Earthquake detection probability within a seismically quiet area: application to the Bruchsal geothermal field
More LessABSTRACTIn applications such as oil and gas production, deep geothermal energy production, underground storage, and mining, it is common practice to implement local seismic networks to monitor and to mitigate induced seismicity. For this purpose, it is crucial to determine the capability of the network to detect a seismic event of predefined magnitude in the target area. The determination of the magnitude of completeness of a network is particularly required to properly interpret seismic monitoring results. We propose a method to compute the detection probability for existing local seismic networks, which (i) strictly follows the applied detection sequence; (ii) estimates the detection capability where seismicity has not yet occurred; and (iii) delivers the results in terms of probabilities. The procedure includes a calibration of a local magnitude scale using regional earthquakes recorded by the network and located outside the monitored area. It involves pre‐processing of the seismograms recorded at each station as performed during the triggering sequence, which is assumed based on amplitude thresholds. Then, the calibrated magnitude–distance–amplitude relations are extrapolated at short distances and combined to reproduce the network detection sequence. This generates a probability to detect a seismic event of a given magnitude at a specified location. This observation‐based approach is an alternative to a fully theoretical detection capability modelling and includes field conditions. Seismic wave attenuation by geometrical spreading and intrinsic attenuation, site effect, and instrumental responses are partly accounted for by the calibration. We apply this procedure on the seismic network deployed in the Bruchsal geothermal field (Germany). Although the system was in good working order, no induced seismicity was identified in the area between June 2010, when monitoring started, and November 2012. The recording of distant seismicity during this time period, however, allowed the application of the proposed procedure. According to the applied network detection parameters, the results indicate that the absence of seismicity can be interpreted as a 95% probability that no seismic event with ML ≥ 0.7 occurred below the network at 2.4‐km depth, i.e., in the geothermal reservoir.
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Fracture characterization using converted waves
Authors Mehdi E. Far and Bob HardageABSTRACTWe present a method for inversion of fracture compliance matrix components from wide‐azimuth noisy synthetic PS reflection data and quantitatively show that reflection amplitude variations with offset and azimuth for converted PS‐waves are more informative than P‐waves for fracture characterization. We consider monoclinic symmetry for fractured reservoir (parameters chosen from Woodford Shale), which can be formed by two or more sets of vertical fractures embedded in a vertically transverse isotropic background.
Components of effective fracture compliance matrices for a medium with monoclinic symmetry are related to the characteristics of the fractured medium. Monte Carlo simulation results show that inversion of PS reflection data is more robust than that of PP reflection data to uncertainties in our a priori knowledge (vertically transverse isotropic parameters of unfractured rock) than PP reflection data. We also show that, while inversion of PP reflections is sensitive to contrasts in elastic properties of upper and lower media, inversion of PS reflections is robust with respect to such contrasts.
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Effect of anelastic patchy saturated sand layers on the reflection and transmission responses of a periodically layered medium
Authors Bastien Dupuy and Alexey StovasABSTRACTBased on analytic relations, we compute the reflection and transmission responses of a periodically layered medium with a stack of elastic shales and partially saturated sands. The sand layers are considered anelastic (using patchy saturation theory) or elastic (with effective velocity). Using the patchy saturation theory, we introduce a velocity dispersion due to mesoscale attenuation in the sand layer. This intrinsic anelasticity is creating frequency dependence, which is added to the one coming from the layering (macroscale). We choose several configurations of the periodically layered medium to enhance more or less the effect of anelasticity. The worst case to see the effect of intrinsic anelasticity is obtained with low dispersion in the sand layer, strong contrast between shales and sands, and a low value of the net‐to‐gross ratio (sand proportion divided by the sand + shale proportion), whereas the best case is constituted by high dispersion, weak contrast, and high net‐to‐gross ratio. We then compare the results to show which dispersion effect is dominating in reflection and transmission responses. In frequency domain, the influence of the intrinsic anelasticity is not negligible compared with the layering effect. Even if the main resonance patterns are the same, the resonance peaks for anelastic cases are shifted towards high frequencies and have a slightly lower amplitude than for elastic cases. These observations are more emphasized when we combine all effects and when the net‐to‐gross ratio increases, whereas the differences between anelastic and elastic results are less affected by the level of intrinsic dispersion and by the contrast between the layers. In the time domain, the amplitude of the responses is significantly lower when we consider intrinsic anelastic layers. Even if the phase response has the same features for elastic and anelastic cases, the anelastic model responses are clearly more attenuated than the elastic ones. We conclude that the frequency dependence due to the layering is not always dominating the responses. The frequency dependence coming from intrinsic visco‐elastic phenomena affects the amplitude of the responses in the frequency and time domains. Considering intrinsic attenuation and velocity dispersion of some layers should be analyzed while looking at seismic and log data in thin layered reservoirs.
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Regularized sparse‐grid geometric sampling for uncertainty analysis in non‐linear inverse problems
Authors Leonardo Azevedo, Michael J. Tompkins and Tapan MukerjiABSTRACTThis paper introduces an efficiency improvement to the sparse‐grid geometric sampling methodology for assessing uncertainty in non‐linear geophysical inverse problems. Traditional sparse‐grid geometric sampling works by sampling in a reduced‐dimension parameter space bounded by a feasible polytope, e.g., a generalization of a polygon to dimension above two. The feasible polytope is approximated by a hypercube. When the polytope is very irregular, the hypercube can be a poor approximation leading to computational inefficiency in sampling. We show how the polytope can be regularized using a rotation and scaling based on principal component analysis. This simple regularization helps to increase the efficiency of the sampling and by extension the computational complexity of the uncertainty solution. We demonstrate this on two synthetic 1D examples related to controlled‐source electromagnetic and amplitude versus offset inversion. The results show an improvement of about 50% in the performance of the proposed methodology when compared with the traditional one. However, as the amplitude versus offset example shows, the differences in the efficiency of the proposed methodology are very likely to be dependent on the shape and complexity of the original polytope. However, it is necessary to pursue further investigations on the regularization of the original polytope in order to fully understand when a simple regularization step based on rotation and scaling is enough.
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Salt body detection from seismic data via sparse representation
Authors Carlos Ramirez, German Larrazabal and Gladys GonzalezABSTRACTIn seismic interpretation and seismic data analysis, it is of critical importance to effectively identify certain geologic formations from very large seismic data sets. In particular, the problem of salt characterization from seismic data can lead to important savings in time during the interpretation process if solved efficiently and in an automatic manner. In this work, we present a novel numerical approach that is able to automatically segmenting or identifying salt structures from a post‐stack seismic data set with a minimum intervention from the interpreter. The proposed methodology is based on the recent theory of sparse representation and consists in three major steps: first, a supervised learning assisted by the user which is performed only once, second a segmentation process via unconstrained ℓ1 optimization, and finally a post‐processing step based on signal separation. Furthermore, since the second step only depends upon local information at each time, the whole process greatly benefits from parallel computing platforms. We conduct numerical experiments in a synthetic 3D seismic data set demonstrating the viability of our method. More specifically, we found that the proposed approach matches up to 98.53% with respect to the corresponding 3D velocity model available in advance. Finally, in appendixes A and B, we present a convergence analysis providing theoretical guarantees for the proposed method.
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Retrieving virtual reflection responses at drill‐bit positions using seismic interferometry with drill‐bit noise
Authors Yi Liu, Deyan Draganov, Kees Wapenaar and Børge ArntsenABSTRACTIn the field of seismic interferometry, researchers have retrieved surface waves and body waves by cross‐correlating recordings of uncorrelated noise sources to extract useful subsurface information. The retrieved wavefields in most applications are between receivers. When the positions of the noise sources are known, inter‐source interferometry can be applied to retrieve the wavefields between sources, thus turning sources into virtual receivers. Previous applications of this form of interferometry assume impulsive point sources or transient sources with similar signatures. We investigate the requirements of applying inter‐source seismic interferometry using non‐transient noise sources with known positions to retrieve reflection responses at those positions and show the results using synthetic drilling noise as source. We show that, if pilot signals (estimates of the drill‐bit signals) are not available, it is required that the drill‐bit signals are the same and that the phases of the virtual reflections at drill‐bit positions can be retrieved by deconvolution interferometry or by cross‐coherence interferometry. Further, for this case, classic interferometry by cross‐correlation can be used if the source power spectrum can be estimated. If pilot signals are available, virtual reflection responses can be obtained by first using standard seismic‐while‐drilling processing techniques such as pilot cross‐correlation and pilot deconvolution to remove the drill‐bit signatures in the data and then applying cross‐correlation interferometry. Therefore, provided that pilot signals are reliable, drill‐bit data can be redatumed from surface to borehole depths using this inter‐source interferometry approach without any velocity information of the medium, and we show that a well‐positioned image below the borehole can be obtained using interferometrically redatumed reflection responses with just a simple velocity model. We discuss some of the practical hurdles that restrict the application of the proposed method offshore.
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Unified multi‐depth‐level field decomposition
ABSTRACTWavefield decomposition forms an important ingredient of various geophysical methods. An example of wavefield decomposition is the decomposition into upgoing and downgoing wavefields and simultaneous decomposition into different wave/field types. The multi‐component field decomposition scheme makes use of the recordings of different field quantities (such as particle velocity and pressure). In practice, different recordings can be obscured by different sensor characteristics, requiring calibration with an unknown calibration factor. Not all field quantities required for multi‐component field decomposition might be available, or they can suffer from different noise levels. The multi‐depth‐level decomposition approach makes use of field quantities recorded at multiple depth levels, e.g., two horizontal boreholes closely separated from each other, a combination of a single receiver array combined with free‐surface boundary conditions, or acquisition geometries with a high‐density of vertical boreholes. We theoretically describe the multi‐depth‐level decomposition approach in a unified form, showing that it can be applied to different kinds of fields in dissipative, inhomogeneous, anisotropic media, e.g., acoustic, electromagnetic, elastodynamic, poroelastic, and seismoelectric fields. We express the one‐way fields at one depth level in terms of the observed fields at multiple depth levels, using extrapolation operators that are dependent on the medium parameters between the two depth levels. Lateral invariance at the depth level of decomposition allows us to carry out the multi‐depth‐level decomposition in the horizontal wavenumber–frequency domain. We illustrate the multi‐depth‐level decomposition scheme using two synthetic elastodynamic examples. The first example uses particle velocity recordings at two depth levels, whereas the second example combines recordings at one depth level with the Dirichlet free‐surface boundary condition of zero traction. Comparison with multi‐component decomposed fields shows a perfect match in both amplitude and phase for both cases. The multi‐depth‐level decomposition scheme is fully customizable to the desired acquisition geometry. The decomposition problem is in principle an inverse problem. Notches may occur at certain frequencies, causing the multi‐depth‐level composition matrix to become uninvertible, requiring additional notch filters. We can add multi‐depth‐level free‐surface boundary conditions as extra equations to the multi‐component composition matrix, thereby overdetermining this inverse problem. The combined multi‐component–multi‐depth‐level decomposition on a land data set clearly shows improvements in the decomposition results, compared with the performance of the multi‐component decomposition scheme.
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Suppression of near‐surface scattered body‐to‐surface waves: a steerable and nonlinear filtering approach
Authors Abdulaziz M. Almuhaidib and M. Nafi ToksözABSTRACTWe present an approach based on local‐slope estimation for the separation of scattered surface waves from reflected body waves. The direct and scattered surface waves contain a significant amount of seismic energy. They present great challenges in land seismic data acquisition and processing, particularly in arid regions with complex near‐surface heterogeneities (e.g., dry river beds, wadis/large escarpments, and karst features). The near‐surface scattered body‐to‐surface waves, which have comparable amplitudes to reflections, can mask the seismic reflections. These difficulties, added to large amplitude direct and back‐scattered surface (Rayleigh) waves, create a major reduction in signal‐to‐noise ratio and degrade the final sub‐surface image quality. Removal of these waves can be difficult using conventional filtering methods, such as an filter, without distorting the reflected signal. The filtering algorithm we present is based on predicting the spatially varying slope of the noise, using steerable filters, and separating the signal and noise components by applying a directional nonlinear filter oriented toward the noise direction to predict the noise and then subtract it from the data. The slope estimation step using steerable filters is very efficient. It requires only a linear combination of a set of basis filters at fixed orientation to synthesize an image filtered at an arbitrary orientation. We apply our filtering approach to simulated data as well as to seismic data recorded in the field to suppress the scattered surface waves from reflected body waves, and we demonstrate its superiority over conventional techniques in signal preservation and noise suppression.
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Deghosting by echo‐deblending
Authors A.J. (Guus) Berkhout and Gerrit BlacquièreABSTRACTA marine source generates both a direct wavefield and a ghost wavefield. This is caused by the strong surface reflectivity, resulting in a blended source array, the blending process being natural. The two unblended response wavefields correspond to the real source at the actual location below the water level and to the ghost source at the mirrored location above the water level. As a consequence, deghosting becomes deblending (‘echo‐deblending’) and can be carried out with a deblending algorithm. In this paper we present source deghosting by an iterative deblending algorithm that properly includes the angle dependence of the ghost: It represents a closed‐loop, non‐causal solution. The proposed echo‐deblending algorithm is also applied to the detector deghosting problem. The detector cable may be slanted, and shot records may be generated by blended source arrays, the blending being created by simultaneous sources. Similar to surface‐related multiple elimination the method is independent of the complexity of the subsurface; only what happens at and near the surface is relevant. This means that the actual sea state may cause the reflection coefficient to become frequency dependent, and the water velocity may not be constant due to temporal and lateral variations in the pressure, temperature, and salinity. As a consequence, we propose that estimation of the actual ghost model should be part of the echo‐deblending algorithm. This is particularly true for source deghosting, where interaction of the source wavefield with the surface may be far from linear. The echo‐deblending theory also shows how multi‐level source acquisition and multi‐level streamer acquisition can be numerically simulated from standard acquisition data. The simulated multi‐level measurements increase the performance of the echo‐deblending process. The output of the echo‐deblending algorithm on the source side consists of two ghost‐free records: one generated by the real source at the actual location below the water level and one generated by the ghost source at the mirrored location above the water level. If we apply our algorithm at the detector side as well, we end up with four ghost‐free shot records. All these records are input to migration. Finally, we demonstrate that the proposed echo‐deblending algorithm is robust for background noise.
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Calendar time interpolation of amplitude maps from 4D seismic data
Authors Anders Fredrik Kiær, Ola Eiken and Martin LandrøABSTRACTA calendar time interpolation method for 2D seismic amplitude maps, done in two steps, is presented. The contour interpolation part is formulated as a quadratic programming problem, whereas the amplitude value interpolation is based on a conditional probability formulation. The method is applied on field data from the Sleipner CO2 storage project. The output is a continuous image (movie) of the CO2 plume. Besides visualization, the output can be used to better couple 4D seismic to other types of data acquired. The interpolation uncertainty increases with the time gap between consecutive seismic surveys and is estimated by leaving a survey out (blind test). Errors from such tests can be used to identify problems in understanding the flow and possibly improve the interpolation scheme for a given case. Field‐life cost of various acquisition systems and repeat frequencies are linked to the time‐lapse interpolation errors. The error in interpolated amplitudes increased by 3%‐4% per year of interpolation gap for the Sleipner case. Interpolation can never fully replace measurements.
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Quantitative estimation of water storage and residence time in the epikarst with time‐lapse refraction seismic
More LessABSTRACTThe hydrodynamic characterization of the epikarst, the shallow part of the unsaturated zone in karstic systems, has always been challenging for geophysical methods. This work investigates the feasibility of coupling time‐lapse refraction seismic data with petrophysical and hydrologic models for the quantitative determination of water storage and residence time at shallow depth in carbonate rocks. The Biot–Gassmann fluid substitution model describing the seismic velocity variations with water saturation at low frequencies needs to be modified for this lithology. I propose to include a saturation‐dependent rock‐frame weakening to take into account water–rock interactions. A Bayesian inversion workflow is presented to estimate the water content from seismic velocities measured at variable saturations. The procedure is tested first with already published laboratory measurements on core samples, and the results show that it is possible to estimate the water content and its uncertainty. The validated procedure is then applied to a time‐lapse seismic study to locate and quantify seasonal water storage at shallow depth along a seismic profile. The residence time of the water in the shallow layers is estimated by coupling the time‐lapse seismic measurements with rainfall chronicles, simple flow equations, and the petrophysical model. The daily water input computed from the chronicles is used to constraint the inversion of seismic velocities for the daily saturation state and the hydrodynamic parameters of the flow model. The workflow is applied to a real monitoring case, and the results show that the average residence time of the water in the epikarst is generally around three months, but it is only 18 days near an infiltration pathway. During the winter season, the residence times are three times shorter in response to the increase in the effective rainfall.
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Analysis of laboratory data on ultrasonic monitoring of permeability reduction due to biopolymer formation in unconsolidated granular media
Authors J.G. Berryman, T.‐H. Kwon, S. Dou, J.B. Ajo‐Franklin and S.S. HubbardABSTRACTWe show how to estimate the fluid permeability changes due to accumulated biopolymer within the pore space of a granular material using laboratory measurements of overall permeability, together with various well‐known quantitative measures (e.g., porosity, specific surface area, and formation factor) of the granular medium microstructure. The main focus of the paper is on mutual validation of existing theory and a synthesis of new experimental results. We find that the theory and data are in good agreement within normal experimental uncertainties. We also establish quantitative empirical relationships between seismic and/or acoustic attenuation and overall permeability for these same systems.
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A regularized Wiener–Hopf filter for inverting models with magnetic susceptibility
Authors Shib Sankar Ganguli, Goutam Kumar Nayak, Nimisha Vedanti and V.P. DimriABSTRACTFor a magnetic target, the spatial magnetic signal can be expressed as a convolutional integral over Green's function of an assumed model with susceptibility as its parameter. A filter can be used to obtain the susceptibility by minimizing the mismatch between observed and the computed magnetic anomalies. In this perspective, we report the development of an advanced digital filter, which is efficient and can be used to map rock susceptibility from the acquired magnetic data. To design the new filter, we modified the space‐domain standard Wiener–Hopf filter by imposing two different constraints: (i) the filter energy constraint; and (ii) normalization of the filter coefficients. These constraints make it capable to characterize source bodies from their produced magnetic anomalies. We assume that the magnetic data are produced by induced magnetization only and interpretation can be as good as the subsurface model.
Our technique is less sensitive to the data noise, which makes it efficient in enhancing the interpretation model. The modified filter demonstrates its applicability over the synthetic data with additive white Gaussian noise. In order to check the efficacy and adaptivity of this tool in a more realistic perspective, it is also tested on the real magnetic data acquired over a kimberlitic district adjoining to the western margin of the Cuddapah Basin in India to identify the source bodies from the anomalies. Our result shows that the modified Wiener–Hopf filter with the constraint for the magnetic data is more stable and efficient than the standard Wiener–Hopf filter.
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The electrical conductivity of Posidonia black shales — from magnetotelluric exploration to rock samples
Authors Filipe Adão, Oliver Ritter and Erik SpangenbergABSTRACTWe carried out a magnetotelluric field campaign in the South–East Lower Saxony Basin, Germany, with the main goal of testing this method for imaging regional Posidonia black shale sediments. Two‐dimensional inversion results of the magnetotelluric data show a series of conductive structures correlating with brine‐saturated sediments but also with deeper, anthracitic Westphalian/Namurian coals. None of these structures can be directly related with the Posidonia black shale, which appears to be generally resistive and therefore difficult to resolve with the magnetotelluric method. This assumption is supported by measurements of electrical resistivity on a set of Posidonia shale samples from the Hils syncline in the Lower Saxony basin. These rock samples were collected in shallow boreholes and show immature (0.53% Ro), oil (0.88% Ro), and gas (1.45% Ro) window thermal maturities. None of the black shale samples showed low electrical resistivity, particularly those with oil window maturity show resistivity exceeding 104 Ωm. Moreover, we could not observe a direct correlation between maturity and electrical resistivity; the Harderode samples showed the highest resistivity, whereas the Haddessen samples showed the lowest. A similar trend has been seen for coals in different states of thermal maturation. Saturation of the samples with distilled and saline water solutions led to decreasing electrical resistivity. Moreover, a positive correlation of electrical resistivity with porosity is observed for the Wickensen and Harderode samples, which suggests that the electrical resistivity of the Posidonia black shale is mainly controlled by porosity.
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Surface nuclear magnetic resonance signals recovery by integration of a non‐linear decomposition method with statistical analysis
Authors Reza Ghanati, Mohammad Kazem Hafizi and Mahdi FallahsafariABSTRACTPresence of noise in the acquisition of surface nuclear magnetic resonance data is inevitable. There are various types of noise, including Gaussian noise, spiky events, and harmonic noise that affect the signal quality of surface nuclear magnetic resonance measurements. In this paper, we describe an application of a two‐step noise suppression approach based on a non‐linear adaptive decomposition technique called complete ensemble empirical mode decomposition in conjunction with a statistical optimization process for enhancing the signal‐to‐noise ratio of the surface nuclear magnetic resonance signal. The filtering procedure starts with applying the complete ensemble empirical mode decomposition method to decompose the noisy surface nuclear magnetic resonance signal into a finite number of intrinsic mode functions. Afterwards, a threshold region based on de‐trended fluctuation analysis is defined to identify the noisy intrinsic mode functions, and then the no‐noise intrinsic mode functions are used to recover the partially de‐noised signal. In the second stage, we applied a statistical method based on the variance criterion to the signal obtained from the initial phase to mitigate the remaining noise. To demonstrate the functionality of the proposed strategy, the method was evaluated on an added‐noise synthetic surface nuclear magnetic resonance signal and on field data. The results show that the proposed procedure allows us to improve the signal‐to‐noise ratio significantly and, consequently, extract the signal parameters (i.e., and V0) from noisy surface nuclear magnetic resonance data efficiently.
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Research Note: Insights into the data dependency on anisotropy: an inversion prospective
More LessABSTRACTWhile velocity contrasts are responsible for most of the events recorded in our data, the long wavelength behavior of the velocity model is responsible for the geometrical shape of these events. For isotropic acoustic materials, the wave dependency on the long (wave propagation) and short (scattering) wavelength velocity components is stationary with the propagation angle. On the other hand, in representing a transversely isotropic with a vertical symmetry axis medium with the normal moveout velocity, the anellepticity parameter η, the vertical scaling parameter δ, and the sensitivity of waves vary with the polar angle for both the long and short wavelength features of the anisotropic dimensionless medium parameters (δ and η). For horizontal reflectors at reasonable depths, the long wavelength features of the η model is reasonably constrained by the long offsets, whereas the short wavelength features produce very week reflections at even reasonable offsets. Thus, for surface acquired seismic data, we could mainly invert for smooth η responsible for the geometrical shape of reflections. On the other hand, while the δ long wavelength components mildly affects the recorded data, its short wavelength variations can produce reflections at even zero offset, with a behavior pattern synonymous to density. The lack of the long wavelength δ information will mildly effect focusing but will cause misplacement of events in depth. With low enough frequencies (very low), we may be able to recover the long wavelength δ using full waveform inversion. However, unlike velocity, the frequencies needed for that should be ultra‐low to produce long‐wavelength scattering‐based model information as δ perturbations do not exert scattering at large offsets. For a combination given by the horizontal velocity, η, and ε, the diving wave influence of η is absorbed by the horizontal velocity, severely limiting the η influence on the data and full waveform inversion. As a result, with a good smooth η estimation, for example, from tomography, we can focus the full waveform inversion to invert for only the horizontal velocity and maybe ε as a parameter to fit the amplitude. This is possibly the most practical parametrization for inversion of surface seismic data in transversely isotropic with vertical symmetry axis media.
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