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1.
A robust approach to time‐to‐depth conversion and interval velocity estimation from time migration in the presence of lateral velocity variations 
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下载免费PDF全文 Sergey Fomel 《Geophysical Prospecting》2015,63(2):315-337
The problem of conversion from time‐migration velocity to an interval velocity in depth in the presence of lateral velocity variations can be reduced to solving a system of partial differential equations. In this paper, we formulate the problem as a non‐linear least‐squares optimization for seismic interval velocity and seek its solution iteratively. The input for the inversion is the Dix velocity, which also serves as an initial guess. The inversion gradually updates the interval velocity in order to account for lateral velocity variations that are neglected in the Dix inversion. The algorithm has a moderate cost thanks to regularization that speeds up convergence while ensuring a smooth output. The proposed method should be numerically robust compared to the previous approaches, which amount to extrapolation in depth monotonically. For a successful time‐to‐depth conversion, image‐ray caustics should be either nonexistent or excluded from the computational domain. The resulting velocity can be used in subsequent depth‐imaging model building. Both synthetic and field data examples demonstrate the applicability of the proposed approach. 相似文献
2.
Survey sinking migration downward continues the entire surface observed multi‐shot data to the subsurface step by step recursively. Reflected energy from reflectors at current depth appear at zero time and zero offset in the extrapolated wavefield. The data (seismic records) of t > 0 at this depth are equivalent to the data acquired by a survey system deployed at this depth. This is the reason to name the process ‘survey sinking’. The records of negative time need not to be further propagated since they carry no information to image structures beneath the new survey system. In this paper, we combine survey sinking with dreamlet migration. The dreamlet migration method decomposes the seismic wavefield and one‐way wave propagator by complete time‐space localized bases. The localization on time gives flexibility on time‐varying operations during depth extrapolation. In dreamlet survey sinking migration, it only keeps the data for imaging the structures beneath the sunk survey system and gets rid of the data already used to image structures above it. The deeper the depth is, the shorter is the valid time records of the remaining data and less computation is needed for one depth step continuation. For data decomposition, in addition to time axis, dreamlet survey sinking also decomposes the data for source and receiver gathers, which is a fully localized decomposition of prestack seismic data. A three‐scatter model is first used to demonstrate the computational feature and principle of this method. Tests on the two‐dimensional SEG/EAGE salt model show that with reduced data sets the proposed method can still obtain good imaging quality on complex geology structures and a strong velocity contrast environment. 相似文献
3.
Surface‐wave inversion for a P‐velocity profile with a constant depth gradient of the squared slowness 下载免费PDF全文
下载免费PDF全文 Surface waves are often used to estimate a near‐surface shear‐velocity profile. The inverse problem is solved for the locally one‐dimensional problem of a set of homogeneous horizontal elastic layers. The result is a set of shear velocities, one for each layer. To obtain a P‐wave velocity profile, the P‐guided waves should be included in the inversion scheme. As an alternative to a multi‐layered model, we consider a simple smooth acoustic constant‐density velocity model, which has a negative constant vertical depth gradient of the squared P‐wave slowness and is bounded by a free surface at the top and a homogeneous half‐space at the bottom. The exact solution involves Airy functions and provides an analytical expression for the dispersion equation. If the ratio is sufficiently small, the dispersion curves can be picked from the seismic data and inverted for the continuous P‐wave velocity profile. The potential advantages of our model are its low computational cost and the fact that the result can serve as a smooth starting model for full‐waveform inversion. For the latter, a smooth initial model is often preferred over a rough one. We test the inversion approach on synthetic elastic data computed for a single‐layer P‐wave model and on field data, both with a small ratio. We find that a single‐layer model can recover either the shallow or deeper part of the profile but not both, when compared with the result of a multi‐layer inversion that we use as a reference. An extension of our analytic model to two layers above a homogeneous half‐space, each with a constant vertical gradient of the squared P‐wave slowness and connected in a continuous manner, improves the fit of the picked dispersion curves. The resulting profile resembles a smooth approximation of the multi‐layered one but contains, of course, less detail. As it turns out, our method does not degrade as gracefully as, for instance, diving‐wave tomography, and we can only hope to fit a subset of the dispersion curves. Therefore, the applicability of the method is limited to cases where the ratio is small and the profile is sufficiently simple. A further extension of the two‐layer model to more layers, each with a constant depth gradient of the squared slowness, might improve the fit of the modal structure but at an increased cost. 相似文献
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Interval velocity analysis using post‐stack data has always been a desire, mainly for 3D data sets. In this study we present a method that uses the unique characteristics of migrated diffractions to enable interval velocity analysis from three‐dimensional zero‐offset time data. The idea is to perform a standard three‐dimensional prestack depth migration on stack cubes and generate three‐dimensional common image gathers that show great sensitivity to velocity errors. An efficient ‘top‐down’ scheme for updating the velocity is used to build the model. The effectiveness of the method is related to the incorporation of wave equation based post‐stack datuming in the model building process. The proposed method relies on the ability to identify diffractions along redatumed zero‐offset data and to analyse their flatness in the migrated local angle domain. The method can be considered as an additional tool for a complete, prestack depth migration based interval velocity analysis. 相似文献
6.
Shear-wave velocity of the near-surface ground is an important soil property in earthquake and civil engineering. Using the data from 643 boreholes from the KiK-net in Japan and 135 boreholes from California where the shear-wave velocity profile reaches at least 30 m, firstly, we classify sites by building code, then build site-dependent relationships between travel time and depth by regression utilizing the logarithmic model and power-law model, lastly, we get shear-wave velocity equations versus depth based on the mathematical relationship between travel time and velocity. The results show that: (1) the travel time is strongly correlated with depth, and the Pearson correlation coefficients range between 0.867 and 0.978. (2) there is a certain difference between linear velocity equations and power-law velocity equations, and the power-lower equations are generally more close to measured data than linear equations except for class E in Japan and class D in California. (3) the velocities are similar at the sites of each class for different regions but that the gradient of velocity with depth vary between different regions. 相似文献
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The exponential decline in saturated hydraulic conductivity with depth: a novel method for exploring its effect on water flow paths and transit time distribution 下载免费PDF全文
下载免费PDF全文 The strong vertical gradient in soil and subsoil saturated hydraulic conductivity is characteristic feature of the hydrology of catchments. Despite the potential importance of these strong gradients, they have proven difficult to model using robust physically based schemes. This has hampered the testing of hypotheses about the implications of such vertical gradients for subsurface flow paths, residence times and transit time distribution. Here we present a general semi‐analytical solution for the simulation of 2D steady‐state saturated‐unsaturated flow in hillslopes with saturated hydraulic conductivity that declines exponentially with depth. The grid‐free solution satisfies mass balance exactly over the entire saturated and unsaturated zones. The new method provides continuous solutions for head, flow and velocity in both saturated and unsaturated zones without any interpolation process as is common in discrete numerical schemes. This solution efficiently generates flow pathlines and transit time distributions in hillslopes with the assumption of depth‐varying saturated hydraulic conductivity. The model outputs reveal the pronounced effect that changing the strength of the exponential decline in saturated hydraulic conductivity has on the flow pathlines, residence time and transit time distribution. This new steady‐state model may be useful to others for posing hypotheses about how different depth functions for hydraulic conductivity influence catchment hydrological response. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
为利用sPn与Pn波的走时差测定震源深度,进一步提高地震震源深度的测定精度,推导多层介质下sPn与Pn波的走时差与震源深度的关系,发现走时差与震中距无关,只与震源深度及区域地壳速度模型有关。震源在同一层中,走时差曲线的斜率不变,而当震源位于不同层中时,sPn-Pn走时差曲线的斜率不同,并呈分段直线的走时差曲线形态。地壳速度结构纵向越不均匀,多层和单层介质下利用sPn-Pn走时差计算的震源深度误差就越大,走时曲线的各分段直线斜率相差越大;探讨地壳中sPn与Pn波传播路径相同但波速不同的单层地壳速度模型,发现单层介质下波速越大,测定的震源深度越大;对于同一地区相同的地壳分层结构,测得的震源深度随着泊松比的增大而减小。基于前人给出的中国五个典型块体多层平均地壳模型,给出sPn-Pn走时差与震源深度计算公式速查表。 相似文献
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Soazig Le Bégat Hervé Chauris † Vincent Devaux Sylvain Nguyen Mark Noble 《Geophysical Prospecting》2004,52(5):427-438
The estimation of velocity models is still crucial in seismic reflection imaging as it controls the quality of the depth‐migrated image, which is the basis of geological interpretation. Among the numerous existing methods for velocity determination, tomographic methods are very attractive for their efficiency and ability to retrieve heterogeneities of the medium. We present three tomographic methods in order to estimate heterogeneous velocity models from 2D prestack PP reflection data: a traveltime tomography in the time‐migrated domain, a traveltime and slope tomography in the non‐migrated time domain, and a slope tomography in the depth‐migrated domain. The first method (traveltime tomography in the time domain) is based on continuous picked events, whereas the two slope tomographic methods, one in the time domain and the other in the depth domain, are based on locally coherent events, with no assumptions about reflector geometry or the unknown velocity field. The purpose of this paper is not to describe in detail the theoretical basis and implementation of the methods, but to apply and compare their output using the same marine real data set. Based on the estimated velocity models, the migrated images and the common‐image gathers from the three processing routes, the relative strengths and weaknesses of the methods are discussed. Finally, similarities are indicated and potential alternative approaches are proposed. 相似文献
10.
An automated cross‐validation method to assess seismic time‐to‐depth conversion accuracy: a case study on the Cooper and Eromanga basins,Australia 下载免费PDF全文
下载免费PDF全文 Selecting a seismic time‐to‐depth conversion method can be a subjective choice that is made by geophysicists, and is particularly difficult if the accuracy of these methods is unknown. This study presents an automated statistical approach for assessing seismic time‐to‐depth conversion accuracy by integrating the cross‐validation method with four commonly used seismic time‐to‐depth conversion methods. To showcase this automated approach, we use a regional dataset from the Cooper and Eromanga basins, Australia, consisting of 13 three‐dimensional (3D) seismic surveys, 73 two‐way‐time surface grids and 729 wells. Approximately 10,000 error values (predicted depth vs. measured well depth) and associated variables were calculated. The average velocity method was the most accurate overall (7.6 m mean error); however, the most accurate method and the expected error changed by several metres depending on the combination and value of the most significant variables. Cluster analysis tested the significance of the associated variables to find that the seismic survey location (potentially related to local geology (i.e. sedimentology, structural geology, cementation, pore pressure, etc.), processing workflow, or seismic vintage), formation (potentially associated with reduced signal‐to‐noise with increasing depth or the changes in lithology), distance to the nearest well control, and the spatial location of the predicted well relative to the existing well data envelope had the largest impact on accuracy. Importantly, the effect of these significant variables on accuracy were found to be more important than choosing between the four methods, highlighting the importance of better understanding seismic time‐to‐depth conversions, which can be achieved by applying this automated cross‐validation method. 相似文献
11.
Tariq Alkhalifah 《Geophysical Prospecting》2005,53(5):643-653
Imaging pre‐salt reflections for data acquired from the coastal region of the Red Sea is a task that requires prestack migration velocity analysis. Conventional post‐stack time processing lacks the lateral inhomogeneity capability, necessary for such a problem. Prestack migration velocity analysis in the vertical time domain reduces the velocity–depth ambiguity that usually hampers the performance of prestack depth‐migration velocity analysis. In prestack τ‐migration velocity analysis, the interval velocity model and the output images are defined in τ (i.e. vertical time). As a result, we avoid placing reflectors at erroneous depths during the velocity analysis process and thus avoid inaccurately altering the shape of the velocity model, which in turn speeds up the convergence to the true model. Using a 1D velocity update scheme, the prestack τ‐migration velocity analysis produces good images of data from the Midyan region of the Red Sea. For the first seismic line from this region, only three prestack τ‐migration velocity analysis iterations were required to focus pre‐salt reflections in τ. However, the second line, which crosses the first line, is slightly more complicated and thus required five iterations to reach the final, reasonably focused, τ‐image. After mapping the images for the two crossing lines to depth, using the final velocity models, the placements of reflectors in the two 2D lines were consistent at their crossing point. Some errors occurred due to the influence of out‐of‐plane reflections on 2D imaging. However, such errors are identifiable and are generally small. 相似文献
12.
In this study we present the workflow and results of 2D frequency domain waveform tomography applied to the global‐offset seismic data acquired in central Poland along a 50‐km long profile during the GRUNDY 2003 experiment. The waveform tomography method allows full exploitation of the wide‐aperture content of these data and produces in a semi‐automatic way both the detailed P‐wave velocity model and the structural image (i.e., perturbations in respect to the starting model). Thirteen frequencies ranging from 4 to 16 Hz were inverted sequentially, gradually introducing higher wavenumbers and more details into the velocity models. Although the data were characterised by relatively large shot spacings (1.5 km), we obtained clear images both of the Mesozoic and Permian sedimentary cover. Velocity patterns indicated facies changes within the Jurassic and Zechstein strata. A high velocity layer (ca. 5500 m/s) was found near the base of Triassic (Scythian), which made the imaging of a deeper layer difficult. Nevertheless, we were able to delineate the base of the Permian (i.e., base of the Rotliegend), which was not possible to derive from conventional common‐depth‐point processing, as well as some deeper events, attributed to the Carboniferous. The sub‐Permian events formed a syn‐form which favoured our previous interpretation of a depression filled with Upper Carboniferous molasse. The validity of the waveform tomography‐derived model was confirmed by well‐log data. Forward ray‐tracing modelling and synthetic seismograms calculations provided another justification for the key structures present in the waveform tomography model. 相似文献
13.
Wave‐equation migration velocity analysis is a technique designed to extract and update velocity information from migrated images. The velocity model is updated through the process of optimizing the coherence of images migrated with the known background velocity model. The capacity for handling multi‐pathing of the technique makes it appropriate in complex subsurface regions characterized by strong velocity variation. Wave‐equation migration velocity analysis operates by establishing a linear relation between a slowness perturbation and a corresponding image perturbation. The linear relationship and the corresponding linearized operator are derived from conventional extrapolation operators and the linearized operator inherits the main properties of frequency‐domain wavefield extrapolation. A key step in the implementation is to design an appropriate procedure for constructing an image perturbation relative to a reference image that represents the difference between the current image and a true, or more correct image of the subsurface geology. The target of the inversion is to minimize such an image perturbation by optimizing the velocity model. Using time‐shift common‐image gathers, one can characterize the imperfections of migrated images by defining the focusing error as the shift of the focus of reflections along the time‐shift axis. The focusing error is then transformed into an image perturbation by focusing analysis under the linear approximation. As the focusing error is caused by the incorrect velocity model, the resulting image perturbation can be considered as a mapping of the velocity model error in the image space. Such an approach for constructing the image perturbation is computationally efficient and simple to implement. The technique also provides a new alternative for using focusing information in wavefield‐based velocity model building. Synthetic examples demonstrate the successful application of our method to a layered model and a subsalt velocity update problem. 相似文献
14.
Igor Ravve 《Geophysical Prospecting》2016,64(3):517-542
We suggest a new method to determine the piecewise‐continuous vertical distribution of instantaneous velocities within sediment layers, using different order time‐domain effective velocities on their top and bottom points. We demonstrate our method using a synthetic model that consists of different compacted sediment layers characterized by monotonously increasing velocity, combined with hard rock layers, such as salt or basalt, characterized by constant fast velocities, and low velocity layers, such as gas pockets. We first show that, by using only the root‐mean‐square velocities and the corresponding vertical travel times (computed from the original instantaneous velocity in depth) as input for a Dix‐type inversion, many different vertical distributions of the instantaneous velocities can be obtained (inverted). Some geological constraints, such as limiting the values of the inverted vertical velocity gradients, should be applied in order to obtain more geologically plausible velocity profiles. In order to limit the non‐uniqueness of the inverted velocities, additional information should be added. We have derived three different inversion solutions that yield the correct instantaneous velocity, avoiding any a priori geological constraints. The additional data at the interface points contain either the average velocities (or depths) or the fourth‐order average velocities, or both. Practically, average velocities can be obtained from nearby wells, whereas the fourth‐order average velocity can be estimated from the quartic moveout term during velocity analysis. Along with the three different types of input, we consider two types of vertical velocity models within each interval: distribution with a constant velocity gradient and an exponential asymptotically bounded velocity model, which is in particular important for modelling thick layers. It has been shown that, in the case of thin intervals, both models lead to similar results. The method allows us to establish the instantaneous velocities at the top and bottom interfaces, where the velocity profile inside the intervals is given by either the linear or the exponential asymptotically bounded velocity models. Since the velocity parameters of each interval are independently inverted, discontinuities of the instantaneous velocity at the interfaces occur naturally. The improved accuracy of the inverted instantaneous velocities is particularly important for accurate time‐to‐depth conversion. 相似文献
15.
The image‐wave equation for depth remigration is a partial differential equation that is similar to the acoustic wave equation. In this work, we study its finite‐difference solution and possible applications. The conditions for stability, dispersion and dissipation exhibit a strong wavenumber dependence. Where higher horizontal than vertical wavenumbers are present in the data to be remigrated, stability may be difficult to achieve. Grid dispersion and dissipation can only be reduced to acceptable levels by the choice of very small grid intervals. Numerical tests demonstrate that, upon reaching the true medium velocity, remigrated images of curved reflectors propagate to the correct depth and those of diffractions collapse to single points. The latter property points towards the method's potential for use as a tool for migration velocity analysis. A first application to inhomogeneous media shows that in a horizontally layered medium, the reflector images reach their true depth when the remigration velocity equals the inverse of the mean medium slowness. 相似文献
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Wavefield‐based migration velocity analysis using the semblance principle requires computation of images in an extended space in which we can evaluate the imaging consistency as a function of overlapping experiments. Usual industry practice is to assemble those seismic images in common‐image gathers that represent reflectivity as a function of depth and extensions, e.g., reflection angles. We introduce extended common‐image point (CIP) gathers constructed only as a function of the space‐ and time‐lag extensions at sparse and irregularly distributed points in the image. Semblance analysis using CIP's constructed by this procedure is advantageous because we do not need to compute gathers at regular surface locations and we do not need to compute extensions at all depth levels. The CIP's also give us the flexibility to distribute them in the image at irregular locations aligned with the geologic structure. Furthermore, the CIP's remove the depth bias of common‐image gathers constructed as a function of the depth axis. An interpretation of the CIP's using the scattering theory shows that they are scattered wavefields associated with sources and receivers inside the subsurface. Thus, when the surface wavefields are correctly reconstructed, the extended CIP's are characterized by focused energy at the origin of the space‐ and time‐lag axes. Otherwise, the energy defocuses from the origin of the lag axes proportionally with the cumulative velocity error in the overburden. This information can be used for wavefield‐based tomographic updates of the velocity model, and if the velocity used for imaging is correct, the coordinate‐independent CIP's can be a decomposed as a function of the angles of incidence. 相似文献
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用解析分析、时域有限差分、时-频分析的方法,以地面中心回线装置和阶跃脉冲激励源为例,分析讨论了瞬变电磁测深法的勘探深度问题,以便为野外勘探工作设计提供依据,达到预期的探测目的.解析计算证实了瞬变场在地下以有限速度传播,数值模拟表示出了准静态条件下瞬变场的反射.研究结果表明,由于时间域电磁场遵循因果律,瞬变电磁法的探测深度主要由观测时间决定. 瞬变电磁场的初始传播速度与大地电阻率无关,继后在大地色散作用下,阶跃脉冲前沿逐渐变得平缓,各频率分量的传播速度与电阻率有关,在低阻地层中探测同样的深度需要较长的观测时间. 最大探测深度是在给定时间内电磁波往返地下某一深度的单程距离,最小探测深度受仪器性能的限制,但是埋藏较浅的异常体也有可能在晚时段被观测到.从时-频密度谱中可得到瞬变电磁场信号时间与频率的关系. 相似文献
18.
A 2D reflection tomographic method is described, for the purpose of estimating an improved macrovelocity field for prestack depth migration. An event-oriented local approach of the ‘layer-stripping’ type has been developed, where each input event is defined by its traveltime and a traveltime derivative, taken with respect to one of four coordinates in the source/receiver and midpoint half-offset systems. Recent work has shown that the results of reflection tomography may be improved by performing event picking in a prestack depth domain. We adopt this approach and allow events to be picked either before or after prestack depth migration. Hence, if events have been picked in a depth domain, such as the common-shot depth domain or the common-offset depth domain, then a depth-time transformation is required before velocity estimation. The event transformation may, for example, be done by conventional kinematic ray tracingr and with respect to the original depth-migration velocity field. By this means, we expect the input events for velocity updating to become less sensitive to migration velocity errors. For the purpose of velocity estimation, events are subdivided into two categories; reference horizon events and individual events. The reference horizon events correspond to a fixed offset in order to provide basic information about reflector geometry, whereas individual events, corresponding to any offset, are supposed to provide the additional information needed for velocity estimation. An iterative updating approach is used, based on calculation of derivatives of event reflection points with respect to velocity. The event reflection points are obtained by ray-theoretical depth conversion, and reflection-point derivatives are calculated accurately and efficiently from information pertaining to single rays. A number of reference horizon events and a single individual event constitute the minimum information required to update the velocity locally, and the iterations proceed until the individual event reflection point is consistent with those of the reference horizon events. Normally, three to four iterations are sufficient to attain convergence. As a by-product of the process, we obtain so-called uncertainty amplification factors, which relate a picking error to the corresponding error in the estimated velocity or depth horizon position. The vector formulation of the updating relationship makes it applicable to smooth horizons having arbitrary dips and by applying velocity updating in combination with a flexible model-builder, very general macro-model structures can be obtained. As a first step in the evaluation of the new method, error-free traveltime events were generated by applying forward ray tracing within given macrovelocity models. When using such ‘perfect’ observations, the velocity estimation algorithm gave consistent reconstructions of macro-models containing interfaces with differential dip and curvature, a low-velocity layer and a layer with a laterally varying velocity function. 相似文献
19.
Martin Tygel Bjørn Ursin Einar Iversen Maarten V. de Hoop 《Geophysical Prospecting》2012,60(2):201-216
Starting from a given time‐migrated zero‐offset data volume and time‐migration velocity, recent literature has shown that it is possible to simultaneously trace image rays in depth and reconstruct the depth‐velocity model along them. This, in turn, allows image‐ray migration, namely to map time‐migrated reflections into depth by tracing the image ray until half of the reflection time is consumed. As known since the 1980s, image‐ray migration can be made more complete if, besides reflection time, also estimates of its first and second derivatives with respect to the time‐migration datum coordinates are available. Such information provides, in addition to the location and dip of the reflectors in depth, also an estimation of their curvature. The expressions explicitly relate geological dip and curvature to first and second derivatives of reflection time with respect to time‐migration datum coordinates. Such quantitative relationships can provide useful constraints for improved construction of reflectors at depth in the presence of uncertainty. Furthermore, the results of image‐ray migration can be used to verify and improve time‐migration algorithms and can therefore be considered complementary to those of normal‐ray migration. So far, image‐ray migration algorithms have been restricted to layered models with isotropic smooth velocities within the layers. Using the methodology of surface‐to‐surface paraxial matrices, we obtain a natural extension to smooth or layered anisotropic media. 相似文献
20.
Single‐component towed‐streamer marine data acquisition records the pressure variations of the upgoing compressional waves followed by the polarity‐reversed pressure variations of downgoing waves, creating sea‐surface ghost events in the data. The sea‐surface ghost for constant‐depth towed‐streamer marine data acquisition is usually characterised by a ghost operator acting on the upgoing waves, which can be formulated as a filtering process in the frequency–wavenumber domain. The deghosting operation, usually via the application of the inverse Wiener filter related to the ghost operator, acts on the signal as well as the noise. The noise power transfer into the deghosted data is proportional to the power spectrum of the inverse Wiener filter and is amplifying the noise strongly at the notch wavenumbers and frequencies of the ghost operator. For variable‐depth streamer acquisition, the sea‐surface ghost cannot be described any longer as a wavenumber–frequency operator but as a linear relationship between the wavenumber–frequency representation of the upgoing waves at the sea surface and the data in the space–frequency domain. In this article, we investigate how the application of the inverse process acts on noise. It turns out that the noise magnification is less severe with variable‐depth streamer data, as opposed to constant depth, and is inversely proportional to the local slant of the streamer. We support this statement via application of the deghosting process to real and numerical random noise. We also propose a more general concept of a wavenumber–frequency ghost power transfer function, applicable for variable‐depth streamer acquisition, and demonstrate that the inverse of the proposed variable‐depth ghost power transfer function can be used to approximately quantify the action of the variable‐depth streamer deghosting process on noise. 相似文献