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- Volume 65, Issue 6, 2017
Geophysical Prospecting - Volume 65, Issue 6, 2017
Volume 65, Issue 6, 2017
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Review paper: Virtual sources and their responses, Part I: time‐reversal acoustics and seismic interferometry
Authors Kees Wapenaar and Jan ThorbeckeABSTRACTA focusing acoustic wave field, emitted into a medium from its boundary, converges to a focal spot around the designated focal point. Subsequently, the focused field acts as a virtual source that emits a field propagating away from the focal point, mimicking the response to a real source at the position of the focal point. In this first part of a two‐part review paper on virtual sources and their responses, we define the focusing wave field as the time reversal of an observed point‐source response. This approach underlies time‐reversal acoustics and seismic interferometry. We analyse the propagation of a time‐reversed point‐source response through an inhomogeneous medium, paying particular attention to the effect of internal multiples. We investigate the differences between emitting the focusing field from a closed boundary and from an open boundary, and we analyse in detail the properties of the virtual source. Whereas emitting the time‐reversed field from a closed boundary yields an accurate isotropic virtual source, emitting the field from an open boundary leads to a highly directional virtual source and significant artefacts related to multiple scattering. The latter problems are addressed in Part II, where we define the focusing wave field as an inverse filter that accounts for primaries and multiples.
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Review paper: Virtual sources and their responses, Part II: data‐driven single‐sided focusing
Authors Kees Wapenaar, Jan Thorbecke, Joost van der Neut, Evert Slob and Roel SniederABSTRACTIn Part I of this paper, we defined a focusing wave field as the time reversal of an observed point‐source response. We showed that emitting a time‐reversed field from a closed boundary yields a focal spot that acts as an isotropic virtual source. However, when emitting the field from an open boundary, the virtual source is highly directional and significant artefacts occur related to multiple scattering. The aim of this paper is to discuss a focusing wave field, which, when emitted into the medium from an open boundary, yields an isotropic virtual source and does not give rise to artefacts. We start the discussion from a horizontally layered medium and introduce the single‐sided focusing wave field in an intuitive way as an inverse filter. Next, we discuss single‐sided focusing in two‐dimensional and three‐dimensional inhomogeneous media and support the discussion with mathematical derivations. The focusing functions needed for single‐sided focusing can be retrieved from the single‐sided reflection response and an estimate of the direct arrivals between the focal point and the accessible boundary. The focal spot, obtained with this single‐sided data‐driven focusing method, acts as an isotropic virtual source, similar to that obtained by emitting a time‐reversed point‐source response from a closed boundary.
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Parsimonious wave‐equation travel‐time inversion for refraction waves
Authors Lei Fu, Sherif M. Hanafy and Gerard T. SchusterABSTRACTWe present a parsimonious wave‐equation travel‐time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2N refraction travel times, which can be spawned into refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for wave‐equation travel‐time inversion. Numerical results show that the parsimonious wave‐equation travel‐time tomogram has about the same accuracy as the tomogram computed by standard wave‐equation travel‐time inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.
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Prestack amplitude versus angle inversion for Young's modulus and Poisson's ratio based on the exact Zoeppritz equations
Authors Lin Zhou, Jingye Li, Xiaohong Chen, Xingye Liu and Li ChenABSTRACTElastic parameters such as Young's modulus, Poisson's ratio, and density are very important characteristic parameters that are required to properly characterise shale gas reservoir rock brittleness, evaluate gas characteristics of reservoirs, and directly interpret lithology and oil‐bearing properties. Therefore, it is significant to obtain accurate information of these elastic parameters. Conventionally, they are indirectly calculated by the rock physics method or estimated by approximate formula inversion. The cumulative errors caused by the indirect calculation and low calculation accuracy of the approximate Zoeppritz equations make accurate estimation of Young's modulus, Poisson's ratio, and density difficult in the conventional method. In this paper, based on the assumption of isotropy, we perform several substitutions to convert the Zoeppritz equations from the classical form to a new form containing the chosen elastic constants of Young's modulus, Poisson's ratio, and density. The inversion objective function is then constructed by utilising Bayesian theory. Meanwhile, the Cauchy distribution is introduced as a priori information. We then combine the idea of generalised linear inversion with an iterative reweighed least squares algorithm in order to solve the problem. Finally, we obtain the iterative updating formula of the three elastic parameters and achieve the direct inversion of these elastic parameters based on the exact Zoeppritz equations. Both synthetic and field data examples show that the new method is not only able to obtain the two elastic parameters of Young's modulus and Poisson's ratio stably and reasonably from prestack seismic data but also able to provide an accurate estimation of density information, which demonstrates the feasibility and effectiveness of the proposed method. The proposed method offers an efficient seismic method to identify a “sweet spot” within a shale gas reservoir.
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Three‐term inversion of prestack seismic data using a weighted l2, 1 mixed norm
Authors Daniel O. Pérez, Danilo R. Velis and Mauricio D. SacchiABSTRACTWe present a new inversion method to estimate, from prestack seismic data, blocky P‐ and S‐wave velocity and density images and the associated sparse reflectivity levels. The method uses the three‐term Aki and Richards approximation to linearise the seismic inversion problem. To this end, we adopt a weighted mixed l2, 1‐norm that promotes structured forms of sparsity, thus leading to blocky solutions in time. In addition, our algorithm incorporates a covariance or scale matrix to simultaneously constrain P‐ and S‐wave velocities and density. This a priori information is obtained by nearby well‐log data. We also include a term containing a low‐frequency background model. The l2, 1 mixed norm leads to a convex objective function that can be minimised using proximal algorithms. In particular, we use the fast iterative shrinkage‐thresholding algorithm. A key advantage of this algorithm is that it only requires matrix–vector multiplications and no direct matrix inversion. The latter makes our algorithm numerically stable, easy to apply, and economical in terms of computational cost. Tests on synthetic and field data show that the proposed method, contrarily to conventional l2‐ or l1‐norm regularised solutions, is able to provide consistent blocky and/or sparse estimators of P‐ and S‐wave velocities and density from a noisy and limited number of observations.
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Microseismic events enhancement and detection in sensor arrays using autocorrelation‐based filtering
ABSTRACTPassive microseismic data are commonly buried in noise, which presents a significant challenge for signal detection and recovery. For recordings from a surface sensor array where each trace contains a time‐delayed arrival from the event, we propose an autocorrelation‐based stacking method that designs a denoising filter from all the traces, as well as a multi‐channel detection scheme. This approach circumvents the issue of time aligning the traces prior to stacking because every trace's autocorrelation is centred at zero in the lag domain. The effect of white noise is concentrated near zero lag; thus, the filter design requires a predictable adjustment of the zero‐lag value. Truncation of the autocorrelation is employed to smooth the impulse response of the denoising filter. In order to extend the applicability of the algorithm, we also propose a noise prewhitening scheme that addresses cases with coloured noise. The simplicity and robustness of this method are validated with synthetic and real seismic traces.
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Determination of moment tensor and location of microseismic events under conditions of highly correlated noise based on the maximum likelihood method
Authors E.V. Birialtsev, D.E. Demidov and E.V. MokshinABSTRACTWe examine the problem of localization of a single microseismic event and determination of its seismic moment tensor in the presence of strongly correlated noise. This is a typical problem occurring in monitoring of microseismic events from a daylight surface during producing or surface monitoring of hydraulic fracturing. We propose a solution to this problem based on the method of maximum likelihood. We discuss mathematical aspects of the problem, some features and weak points of the proposed approach, estimate the required computing resources, and present the results of numerical experiments. We show that the proposed approach is much more resistant to correlated noises than diffraction stacking methods and time reverse modeling.
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3D seismic residual statics solutions derived from refraction interferometry
More LessABSTRACTWe apply interferometric theory to solve a three‐dimensional seismic residual statics problem to improve reflection imaging. The approach calculates the static solutions without picking the first arrivals from the shot or receiver gathers. The static correction accuracy can be significantly improved by utilising stacked virtual refraction gathers in the calculations. Shots and receivers may be placed at any position in a three‐dimensional seismic land survey. Therefore, it is difficult to determine stationary shots and receivers to form the virtual refraction traces that have identical arrival times, as in a two‐dimensional scenario. To overcome this problem, we use a three‐dimensional super‐virtual interferometry method for residual static calculations. The virtual refraction for a stationary shot/receiver pair is obtained via an integral along the receiver/shot lines, which does not require knowledge of the stationary locations. We pick the maximum energy times on the interferometric stacks and solve a set of linear equations to derive reliable residual static solutions. We further apply the approach to both synthetic and real data.
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Double plane‐wave reverse‐time migration
Authors Zeyu Zhao, Mrinal K. Sen and Paul L. StoffaABSTRACTWe develop a new time‐domain reverse‐time migration method called double plane‐wave reverse‐time migration that uses plane‐wave transformed gathers. Original shot gathers with appropriate data acquisition geometry are double slant stacked into the double plane‐wave domain with minimal slant stacking artefacts. The range of plane‐wave components needed for migration can be determined by estimating the maximum time dips present in shot gathers. This reduces the total number of input traces for migration and increases migration efficiency. Unlike the pre‐stack shot‐profile reverse‐time migration where the number of forward propagations is proportional to the number of shots, the number of forward propagations needed for the proposed method remains constant and is relatively small even for large seismic datasets. Therefore, the proposed method can improve the efficiency of the migration and be suitable for migrating large datasets. Double plane‐wave reverse‐time migration can be performed for selected plane‐wave components to obtain subsurface interfaces with different dips, which makes the migration method target oriented. This feature also makes the method a useful tool for migration velocity analysis. For example, we are able to promptly obtain trial images with nearly horizontal interfaces and adjust velocity models according to common image gathers. Seismic signal coming from steeply dipping interfaces can be included into the migration to build images with more detailed structures and higher spatial resolution as better velocity models become available. Illumination compensation imaging conditions for the proposed method are also introduced to obtain images with balanced amplitudes.
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Traveltime approximation in vertical transversely isotropic layered media
Authors Igor Ravve and Zvi KorenABSTRACTThe well‐known asymptotic fractional four‐parameter traveltime approximation and the five‐parameter generalised traveltime approximation in stratified multi‐layer transversely isotropic elastic media with a vertical axis of symmetry have been widely used for pure‐mode and converted waves. The first three parameters of these traveltime expansions are zero‐offset traveltime, normal moveout velocity, and quartic coefficient, ensuring high accuracy of traveltimes at short offsets. The additional parameter within the four‐parameter approximation is an effective horizontal velocity accounting for large offsets, which is important to avoid traveltime divergence at large offsets. The two additional parameters in the above‐mentioned five‐parameter approximation ensure higher accuracy up to a given large finite offset with an exact match at this offset. In this paper, we propose two alternative five‐parameter traveltime approximations, which can be considered extensions of the four‐parameter approximation and an alternative to the five‐parameter approximation previously mentioned. The first three short‐offset parameters are the same as before, but the two additional long‐offset parameters are different and have specific physical meaning. One of them describes the propagation in the high‐velocity layer of the overburden (nearly horizontal propagation in the case of very large offsets), and the other characterises the intercept time corresponding to the critical slowness that includes contributions of the lower velocity layers only. Unlike the above‐mentioned approximations, both of the proposed traveltime approximations converge to the theoretical (asymptotic) linear traveltime at the limit case of very large (“infinite”) offsets. Their accuracy for moderate to very large offsets, for quasi‐compressional waves, converted waves, and shear waves polarised in the horizontal plane, is extremely high in cases where the overburden model contains at least one layer with a dominant higher velocity compared with the other layers. We consider the implementation of the proposed traveltime approximations in all classes of problems in which the above‐mentioned approximations are used, such as reflection and diffraction analysis and imaging.
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Using beamforming to maximise the detection capability of small, sparse seismometer arrays deployed to monitor oil field activities
Authors James P. Verdon, J.‐Michael Kendall, Stephen P. Hicks and Philip HillABSTRACTLike most other industrial activities that affect the subsurface, hydraulic fracturing carries the risk of reactivating pre‐existing faults and thereby causing induced seismicity. In some regions, regulators have responded to this risk by imposing traffic light scheme‐type regulations, where fracture stimulation programs must be amended or shut down if events larger than a given magnitude are induced. Some sites may be monitored with downhole arrays and/or dense near‐surface arrays, capable of detecting very small microseismic events. However, such monitoring arrangements will not be logistically or economically feasible at all sites. Instead, operators are using small, sparse arrays of surface seismometers to meet their monitoring obligations.
The challenge we address in this paper is to maximise the detection thresholds of such small, sparse, surface arrays so that they are capable of robustly identifying small‐magnitude events whose signal‐to‐noise ratios may be close to 1. To do this, we develop a beamforming‐and‐stacking approach, computing running short‐term/long‐term average functions for each component of each recorded trace (P, SH, and SV), time‐shifting these functions by the expected travel times for a given location, and performing a stack.
We assess the effectiveness of this approach with a case study using data from a small surface array that recorded a multi‐well, multi‐stage hydraulic fracture stimulation in Oklahoma over a period of 8 days. As a comparison, we initially used a conventional event‐detection algorithm to identify events, finding a total of 17 events. In contrast, the beamforming‐and‐stacking approach identified a total of 155 events during this period (including the 17 events detected by the conventional method). The events that were not detected by the conventional algorithm had low‐signal‐to‐noise ratios to the extent that, in some cases, they would be unlikely to be identified even by manual analysis of the seismograms. We conclude that this approach is capable of improving the detection thresholds of small, sparse arrays and thus can be used to maximise the information generated when deployed to monitor industrial sites.
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Predicting the elastic response of organic‐rich shale using nanoscale measurements and homogenisation methods
Authors M. Goodarzi, M. Rouainia, A.C. Aplin, P. Cubillas and M. de BlockABSTRACTDetermination of the mechanical response of shales through experimental procedures is a practical challenge due to their heterogeneity and the practical difficulties of retrieving good‐quality core samples. Here, we investigate the possibility of using multi‐scale homogenisation techniques to predict the macroscopic mechanical response of shales based on quantitative mineralogical descriptions. We use the novel PeakForce Quantitative Nanomechanical Mapping technique to generate high‐resolution mechanical images of shales, allowing the response of porous clay, organic matter, and mineral inclusions to be measured at the nanoscale. These observations support some of the assumptions previously made in the use of homogenisation methods to estimate the elastic properties of shale and also earlier estimates of the mechanical properties of organic matter. We evaluate the applicability of homogenisation techniques against measured elastic responses of organic‐rich shales, partly from published data and also from new indentation tests carried out in this work. Comparison of experimental values of the elastic constants of shale samples with those predicted by homogenisation methods showed that almost all predictions were within the standard deviation of experimental data. This suggests that the homogenisation approach is a useful way of estimating the elastic and mechanical properties of shales in situations where conventional rock mechanics test data cannot be measured.
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How does water near clay mineral surfaces influence the rock physics of shales?
Authors Rune M. Holt and Morten I. KolstøABSTRACTClays and clay‐bearing rocks like shale are extremely water sensitive. This is partly due to the interaction between water and mineral surfaces, strengthened by the presence of nanometer‐size pores and related large specific surface areas. Molecular‐scale numerical simulations, using a discrete‐element model, show that shear rigidity can be associated with structurally ordered (bound or adsorbed) water near charged surfaces. Building on these and other molecular dynamics simulations plus nanoscale experiments from the literature, the water monolayer adjacent to hydrophilic solid surfaces appears to be characterised by shear stiffness and/or enhanced viscosity. In both cases, elastic wave propagation will be affected by the bound or adsorbed water. Using a simple rock physics model, bound water properties were adjusted to match laboratory measured P‐ and S‐wave velocities on pure water‐saturated kaolinite and smectite. To fit the measured stress sensitivity, particularly for kaolinite, the contribution from solid‐grain contact stiffness needs to be added. The model predicts, particularly for S‐waves, that viscoelastic bound water could be a source of dispersion in clay and clay‐rich rocks. The bound‐water‐based rock physics model is found to represent a lower bound to laboratory‐measured velocities obtained with shales of different mineralogy and porosity levels.
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Frequency‐ and angle‐dependent poroelastic seismic analysis for highly attenuating reservoirs
Authors Luanxiao Zhao, Qiuliang Yao, De‐hua Han, Rui Zhou, Jianhua Geng and Hui LiABSTRACTWe extend the frequency‐ and angle‐dependent poroelastic reflectivity to systematically analyse the characteristic of seismic waveforms for highly attenuating reservoir rocks. It is found that the mesoscopic fluid pressure diffusion can significantly affect the root‐mean‐square amplitude, frequency content, and phase signatures of seismic waveforms. We loosely group the seismic amplitude‐versus‐angle and ‐frequency characteristics into three classes under different geological circumstances: (i) for Class‐I amplitude‐versus‐angle and ‐frequency, which corresponds to well‐compacted reservoirs having Class‐I amplitude‐versus‐offset characteristic, the root‐mean‐square amplitude at near offset is boosted at high frequency, whereas seismic energy at far offset is concentrated at low frequency; (ii) for Class‐II amplitude‐versus‐angle and ‐frequency, which corresponds to moderately compacted reservoirs having Class‐II amplitude‐versus‐offset characteristic, the weak seismic amplitude might exhibit a phase‐reversal trend, hence distorting both the seismic waveform and energy distribution; (iii) for Class‐III amplitude‐versus‐angle and ‐frequency, which corresponds to unconsolidated reservoir having Class‐III amplitude‐versus‐offset characteristic, the mesoscopic fluid flow does not exercise an appreciable effect on the seismic waveforms, but there exists a non‐negligible amplitude decay compared with the elastic seismic responses based on the Zoeppritz equation.
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Effect of fracture fill on frequency‐dependent anisotropy of fractured porous rocks
Authors Liyun Kong, Boris Gurevich, Yan Zhang and Yibo WangABSTRACTIn fractured reservoirs, seismic wave velocity and amplitude depend on frequency and incidence angle. Frequency dependence is believed to be principally caused by the wave‐induced flow of pore fluid at the mesoscopic scale. In recent years, two particular phenomena, i.e., patchy saturation and flow between fractures and pores, have been identified as significant mechanisms of wave‐induced flow. However, these two phenomena are studied separately. Recently, a unified model has been proposed for a porous rock with a set of aligned fractures, with pores and fractures filled with two different fluids. Existing models treat waves propagating perpendicular to the fractures. In this paper, we extend the model to all propagation angles by assuming that the flow direction is perpendicular to the layering plane and is independent of the loading direction. We first consider the limiting cases through poroelastic Backus averaging, and then we obtain the five complex and frequency‐dependent stiffness values of the equivalent transversely isotropic medium as a function of the frequency. The numerical results show that, when the bulk modulus of the fracture‐filling fluid is relatively large, the dispersion and attenuation of P‐waves are mainly caused by fractures, and the values decrease as angles increase, almost vanishing when the incidence angle is 90° (propagation parallel to the fracture plane). While the bulk modulus of fluid in fractures is much smaller than that of matrix pores, the attenuation due to the “partial saturation” mechanism makes the fluid flow from pores into fractures, which is almost independent of the incidence angle.
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Using constrained inversion of gravity and magnetic field to produce a 3D litho‐prediction model
Authors Omid Mahmoodi, Richard S. Smith and Bill SpicerABSTRACTGeologically constrained inversion of gravity and magnetic field data of the Victoria property (located in Sudbury, Canada) was undertaken in order to update the present three‐dimensional geological model. The initial and reference model was constructed based on geological information from over 950 drillholes to constrain the inversion. In addition, downhole density and magnetic susceptibility measured in six holes were statistically analysed to derive lower and upper bounds on the physical properties attributed to the lithological units in the reference model. Constrained inversion of the ground gravity and the airborne magnetic data collected at the Victoria property were performed using GRAV3D and MAG3D, respectively. A neural network was trained to predict lithological units from the physical properties measured in six holes. Then, the trained network was applied on the three‐dimensional distribution of physical properties derived from the inversion models to produce a three‐dimensional litho‐prediction model. Some of the features evident in the lithological model are remnants of the constraints, where the data did not demand a significant change in the model from the initial constraining model (e.g., the thin pair of diabase dykes). However, some important changes away from the initial model are evident; for example, a larger body was predicted for quartz diorite, which may be related to the prospective offset dykes; a new zone was predicted as sulfide, which may represent potential mineralisation; and a geophysical subcategory of metabasalt was identified with high magnetic susceptibility and high density. The litho‐prediction model agrees with the geological expectation for the three‐dimensional structure at Victoria and is consistent with the geophysical data, which results in a more holistic understanding of the subsurface lithology.
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Research Note: A simple method of image solution for a sphere of constant electrical potential in a conducting half‐space: implications for the applied potential method
By S.L. ButlerABSTRACTThe applied potential, or mise‐à‐la‐masse, method is used in mineral exploration and environmental applications to constrain the shape and extent of conductive anomalies. However, few simple calculations exist to help gain understanding and intuition regarding the pattern of measured electrical potential at the ground surface. While it makes intuitive sense that the conductor must come close to the ground surface in order for the lateral extent of the potential anomaly to be affected by the dimensions of the conductor rather than simply by the depth, no simple calculation exists to quantify this effect. In this contribution, a simple method of images solution for the case of a sphere of constant electrical potential in a conducting half‐space is presented. The solution consists of an infinite series where the first term is the same as the method of images solution for a point current source in an infinite half‐space. The higher order terms result from the interaction of the constant potential sphere with the no‐flux boundary condition representing the ground surface and cause the change in the shape of the potential anomaly that is of interest in the applied potential method. The calculation is relevant to applied potentials when the conductive anomaly is limited in all three space dimensions and is highly conductive. Using the derived formula, it is shown that, while the electrical potential at the ground surface caused by the sphere is affected even when the sphere is quite deep, the ratio of the potential to the current, a quantity that is more relevant to the applied potential method, is not affected until the centre of the sphere is within two radii of the ground surface. An expression for the contact resistance of the sphere as a function of depth is also given, and the contact resistance is shown to increase by roughly 45% as the sphere is moved from great depth to the ground surface.
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An alternative approach in establishing relation between vertical and horizontal gradients of 2D potential field
More LessABSTRACTThe relation in which the vertical and horizontal gradients of potential field data measured along a profile across a two‐dimensional source are a Hilbert transform pair is re‐established using complex domain mathematics. In addition, a relation between the measured field and its vertical gradient in terms of a closed‐form formula is also established. The formula is based on hypersingular or Hadamard's finite‐part integral. To estimate the vertical gradient directly from the field data, Linz's algorithm of computing Hadamard's finite‐part integral is implemented. Numerical experiments are conducted on synthetically generated total magnetic intensity data with a mild level of noise contamination. A model of a magnetically polarised vertical thin sheet buried at a finite depth within a non‐magnetic half‐space was considered in generating the synthetic response. The results from numerical experiments on the mildly noise‐contaminated synthetic response are compared with those from using classical Fourier and robust regularised Hilbert transform‐based techniques.
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Research Note: Near‐surface layer replacement for sparse data: is interpolation needed?
Authors Yimin Sun, Eric Verschuur and Yi LuoABSTRACTNear‐surface problem is a common challenge faced by land seismic data processing, where often, due to near‐surface anomalies, events of interest are obscured. One method to handle this challenge is near‐surface layer replacement, which is a wavefield reconstruction process based on downward wavefield extrapolation with the near‐surface velocity model and upward wavefield extrapolation with a replacement velocity model. This requires, in theory, that the original wavefield should be densely sampled. In reality, data acquisition is always sparse due to economic reasons, and as a result in the near‐surface layer replacement data interpolation should be resorted to. For datasets with near‐surface challenges, because of the complex event behaviour, a suitable interpolation scheme by itself is a challenging problem, and this, in turn, makes it difficult to carry out the near‐surface layer replacement. In this research note, we first point out that the final objective of the near‐surface layer replacement is not to obtain a newly reconstructed wavefield but to obtain a better final image. Next, based upon this finding, we propose a new thinking, interpolation‐free near‐surface layer replacement, which can handle complex datasets without any interpolation. Data volume expansion is the key idea, and with its help, the interpolation‐free near‐surface layer replacement is capable of preserving the valuable information of areas of interest in the original dataset. Two datasets, i.e., a two‐dimensional synthetic dataset and a three‐dimensional field dataset, are used to demonstrate this idea. One conclusion that can be drawn is that an attempt to interpolate data before layer replacement may deteriorate the final image after layer replacement, whereas interpolation‐free near‐surface layer replacement preserves all image details in the subsurface.
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