Dip Moveout Correction Research Articles

Estimating sediment interval velocity using a monostatic sonar from a seabed with tilted layers

Recently, it has been shown that sediment layer interval velocity can be obtained from a multibeam monostatic sonar. In that work, plane-parallel sediment layering was assumed. Since tilted sediment layers are common in the marine environment, the method is expanded to treat them explicitly. The in- and out-of-plane tilted layers affect the travel times in each layer, which complicates interval velocity estimation. This effect is mitigated by applying a dip moveout correction for each sediment layer. Testing is performed using simulated scattering data from rough, tilted, layered seabeds for dip angles up to a few degrees. The interval velocity estimation method is also applied to at-sea data (acquired by the 2–9 kHz SBP29 multibeam sub-bottom profiler) in areas with tilted layers. [Research supported by ONR Coastal Geosciences]

Reprocessing legacy three-dimensional seismic data from the Halfmile Lake and Brunswick No. 6 volcanogenic massive sulphide deposits, New Brunswick, Canada

We reprocessed legacy three-dimensional (3D) seismic data from the Halfmile Lake and Brunswick areas, both of which were acquired for mineral exploration in the Bathurst Mining Camp, New Brunswick. Each 3D seismic survey was acquired over known volcanogenic massive sulphide deposits and covered areas with strong mineral potential. Most improvements resulted from a reduction of coherent and random noise on prestack gathers and from an improved velocity model, combined with re-imaging with dip moveout corrections and poststack migration or prestack time migration. At Halfmile Lake, the new imaging results show the Deep zone and a possible extension of the sulphide mineralization at greater depth. True amplitude processing has shown that this anomaly has strong amplitudes and is offset from the Deep zone by a shallowly dipping fault (<15°). With the clearer geological context provided by our results, this anomaly, which appears as a stand-alone anomaly on an original image obtained by Noranda Exploration Ltd., becomes a defendable exploration target. Nonorthogonal acquisition geometry and receiver patches of the Brunswick No. 6 3D seismic survey generated artefacts after dip moveout processing that reduced the overall quality of the seismic volumes. By using a filtering approach based on the application of a weighted Laplacian-Gaussian filter in the Kx–Ky domain, we reduced the noise and improved the continuity of reflections. We also imaged the short and flat reflections observed previously only in the shallow part of prestack time migrated data. These short reflections appear as diffractions on the filtered stacked section with dip moveout corrections, indicating that they originate from small geological bodies or discontinuities in the subsurface.

Oriented time-domain dip moveout correction for planar reflectors in common-source domain

Oriented time-domain imaging can be orders of magnitude faster than the routine techniques, which rely on velocity analysis. The term “oriented” refers to those techniques that use the information carried by local slopes. Time-domain dip moveout (DMO) correction, which has often been ignored by the seismic imaging community, has been coming back to attention within the last few years. I have developed an oriented time-domain DMO correction workflow that does not face the problematic loop between the dip-dependent and/or dip-independent velocities existing in the classic DMO correction algorithms. Use of the proposed approach is also advantageous over the previous oriented techniques; the proposed technique is independent of the wavefront curvature, and the input seismic data do not need to be sorted in two different domains. The application of the technique is limited to reflectors with a small curvature. The theory of the proposed technique is investigated on a simple synthetic data example and then applied to a 2D marine data set.

Circumventing velocity uncertainty in imaging complex structures

In areas with irregular topography, complex near surface, and complex subsurface, there is much uncertainty in rms velocity estimation for prestack time migration, whereas interval velocity estimation for prestack depth migration is despairingly challenging. We often attribute the velocity uncertainty to various factors, including strong to severe lateral velocity variations, heterogeneity, anisotropy, mode conversion, and three-dimensional behavior of complex structures. Nevertheless, it is not easy to identify the cause of and account for the uncertainty as it often is a combination of the various factors. And the analyst struggles with much difficulty when estimating a velocity field, whether it is for prestack time or depth migration. Velocity uncertainty invariably gives rise to erroneously high or low migration velocities, which then causes two problems with prestack migration: (1) we fail to preserve reflector amplitudes, and (2) we also fail to position the reflectors correctly and focus diffractions to their apexes. We may choose to solve both problems simultaneously as we currently attempt to do with prestack migration workflows, or we may choose to solve them one after the other as we used to do in the 1980s and '90s by workflows that included dip-moveout correction. The quality of image gathers associated with prestack migration may not be adequate for velocity updating and verification and thus may or may not warrant the simultaneous solution. In areas with irregular topography, complex near surface, and complex subsurface, it may not. What then? I propose a workflow, applicable to both 2-D and 3-D seismic data, to solve the two problems with prestack time migration one after the other. The workflow is based on synthesis of a zero-offset wavefield to capture and preserve all reflections and diffractions, followed by zero-offset time migration.

Impact of DMO Processing on 3D Seismic Imaging at Ketzin, Germany

The goal of the dip-moveout correction (DMO) is to eliminate velocity bias when stacking. DMO processing is tested in order to account for variable dips at the Ketzin CO2 storage pilot site. In this study, 3D Squeezing DMO is applied to seismic data to study the impact of DMO on seismic imaging and to investigate if it enhances the CO2 seismic monitoring technique. We compare the data with and without DMO processing by utilizing quantitative and qualitative analysis. Our results indicate its effectiveness with applications to the 3D seismic data at the Ketzin site.

New Insights from Seismic Imaging Over the Youanmi Terrane, Yilgarn Craton,Western Australia

The general crustal structure of the Youanmi Terrane – a tectonic unit within the Neoarchean Yilgarn Craton – and its relationship to ore deposits are of major interest in Western Australia. To image geological structures, the Geological Survey of Western Australia in collaboration with Geoscience Australia acquired three deep crustal 2D seismic profiles over the region in 2010. In this study, we have reprocessed a 120km long section of one of the seismic profiles, line 10GA-YU1. We reprocessed the data with focus on shallow reflections down to 2 s (about 6km depth). A cross-dip analysis was performed to investigate the dip of the reflections in cross-line direction. The cross-dip analysis showed that there is no significant cross-dip influence, confirming that a 2D interpretation is a valid assumption for this dataset. The seismic image of the reflections was improved after applying dip-moveout correction. Finally, the reflections were migrated to their “true” locations in the subsurface. To better understand the physical properties of the subsurface, we also tried First Arrival Travel-Time Tomography. The tomography results show that low velocities correlate with shear zones and that high velocity zones are common where mineral deposits are located close to the surface.

Seismic Imaging of the Geologic Framework and Structures Related to Volcanogenic Massive Sulfide Deposits in the Archean Rouyn-Noranda District, Quebec, Canada

Two seismic reflection profiles acquired by Xstrata Canada in the Noranda mining camp were reprocessed and interpreted with the objective of providing key information on the geologic contacts and structures associated with volcanogenic massive sulfide (VMS) deposits at depth. The Amulet and Ribago seismic profiles run approximately from east to west and cross the volcanic rocks of the Noranda formation, which host most of the ore deposits in this camp. The seismic data interpretation relies strongly on a detailed three-dimensional geologic model built from an extensive number of exploration boreholes available in this area and is further supported by physical rock property measurements from in situ borehole logging data. Some reflections observed on the Amulet and Ribago seismic profiles correlate with rhyolite/andesite or silicified-andesite/andesite contacts that host the prospective exhalites of the Noranda formation. In particular, the silicified-andesite/andesite contact hosting the C-contact exhalite is imaged clearly down to a vertical depth of 1,100 m along the Ribago profile. The processing sequence included dip moveout (DMO) corrections and poststack migration. The seismic data reprocessing allowed the identification of two diffractions that correlate with known sulfide bodies intersected in boreholes located close to the Ribago profile. One of these diffractions, at approximately 1,200-m depth, coincides with the main massive sulfide intersection of the subeconomical Ribago orebody. Diorites cause several reflections observed within the Flavrian pluton. Some diorite units also have sufficient acoustic impedance contrast to produce strong reflections when juxtaposed against volcanic rocks. However, such reflections do not predominate in the Amulet and Ribago profiles, possibly because reflective diorite units are not so significant or have limited lateral continuity in this part of the Noranda formation. The reconciliation of the detailed three-dimensional geologic model and two-dimensional seismic data was not necessarily a straightforward task. A significant complication results from the inherent limitations of two-dimensional seismic imaging techniques in a complex three-dimensional geologic environment. Nevertheless, results presented in this paper indicate that seismic methods can image prospective contacts and deep-seated massive sulfide mineralization and can be a valuable exploration tool in the Noranda mining camp.

Seismic reflection imaging of the mafic-ultramafic Windimurra Igneous Complex, Yilgarn Craton, Western Australia

A deep seismic reflection survey was carried out over the Meso-Neoarchean Youanmi Terrane, Yilgarn Craton in Western Australia, including 3 seismic lines across the Windimurra Igneous Complex. This gabbroic intrusion is the largest exposed single mafic-ultramafic intrusion in Australia, currently mined for magnetite-hosted vanadium in its upper zone. Acquisition was carried out with 3 Hemi 60 vibrators, 80 or 40 m VP interval, 40 m group interval, and a 300 channel symmetric split spread, resulting in 75 to 150 fold high quality data. Key processing steps included refraction and residual automatic statics, spectral equalisation, detailed stacking velocity analysis, dip moveout (DMO) correction and post stack Kirchhoff migration. The Windimurra Igneous Complex exhibits high seismic velocity (approximately 6.5 km/s), both in interval velocity from stacking velocity and bedrock velocity from refraction statics analysis. Seismic attenuation is low, resulting in high frequency and good resolution to the base of the complex, seen at a maximum two way time of around 2.5 seconds. Gross structure on the seismic sections is also consistent with the gravity and magnetic data. An inward dipping conical structure is evident and consistent with surface geological observations. The base of the complex is marked by distinctive high amplitude multi-layered reflectors, which may represent significant thicknesses of ultramafic zone material unexposed at the surface. This zone has been a long sought after target for Cr-PGE exploration. The complex internal structure of the intrusion, possibly including discordant igneous layering features, has been well imaged up to the base of regolith.

3D imaging challenges in steeply dipping mining structures: New lights on acquisition geometry and processing from the Brunswick no. 6 seismic data, Canada

We have analyzed and processed a [Formula: see text] nonorthogonal 3D surface reflection seismic data in the Brunswick no. 6 area to better understand the effect of acquisition geometry on the resultant image and to provide 3D information about the main geologic structures hosting the mineralization. The 3D data were processed using a conventional prestack dip moveout (DMO) and poststack migration algorithm with special focus on refraction static corrections, velocity analysis, and DMO corrections that are important for the data recorded in crystalline environment. However, the nonorthogonal nature of the 3D data combined with its narrow-azimuth, irregular offset distributions, and 2D nature of midpoint distribution in common depth point bins resulted in a lower quality seismic image than those observed on a series of 2D seismic profiles collected in the area prior to the 3D data acquisition. 2D wavenumber spectrum of the data suggests acquisition footprint associated with the data. Most of the noise associated with the acquisition footprint manifested itself as short-length, high-amplitude shallow reflections but largely were attenuated using a dip filter running in the wavenumber domain. Various bin size and geometries were tested, and the best result was obtained using rectangular bins aligned in the orientation of the shot lines. The processing results indicated that the highly prospective and mineralized Brunswick horizon is part of a continuous reflective package that could guide future deep mineral exploration in this mining camp.

Detailed images of the shallow Alpine Fault Zone, New Zealand, determined from narrow-azimuth 3D seismic reflection data

Previous high-resolution seismic reflection investigations of active faults have been based on 2D profiles. Unfortunately, 2D data may be contaminated by out-of-the-plane reflections and diffractions that may be difficult to identify and eliminate. Although full 3D seismic reflection methods allow out-of-the-plane events to be recognized and provide superior resolution to 2D methods, they are only rarely applied in environmental and engineering studies because of high costs. A narrow-azimuth 3D acquisition and processing strategy is introduced to produce a high-resolution seismic reflection volume centered on the Alpine Fault Zone (New Zealand). The shallow 3D images reveal late Quaternary deformation structures associated with this major transpressional plate-boundary fault. The relatively inexpensive narrow-azimuth 3D acquisition pattern consisting of inline source and receiver lines was easily implemented in the field to provide 2- by [Formula: see text] CMP coverage over an approximately 500- by [Formula: see text] area.The narrow-azimuth acquisition strategy was well suited for resolving complex structures within the fault zone. Challenges in processing the data were amplified by the effects of strong velocity heterogeneity in the near surface and the presence of complex dipping, diffracted, and truncated events. A carefully tailored processing scheme including surface-consistent deconvolution, refraction static corrections, noise reduction, dip moveout (DMO) corrections, and 3D depth migration greatly improved the appearance of the final stacks. The 3D images reveal strong reflections from the faulted and folded late Pleistocene erosional basement surface. A steeply dipping planar main (dominant) fault strand can be inferred from the geometry and truncations of the overlying postglacial sediments. The 3D images reveal that the average apparent vertical displacement [Formula: see text] of the basement surface across the dominant fault strand at this location is somewhat less than that estimated from a pilot 2D seismic reflection profile, suggesting that the provisional dip-slip rate based on the 2D data is a maximum.

Prestack and poststack migration of crooked-line seismic reflection data: A case study from the South Portuguese Zone fold belt, southwestern Iberia

Crooked-line 2D seismic reflection survey geometries violate underlying assumptions of 2D imaging routines, affecting our ability to resolve the subsurface reliably. We compare three crooked-line imaging schemes involving prestack and poststack time migration using the 2D IBERSEIS deep seismic reflection profile running over the South Portuguese Zone thrust-and-fold belt to obtain crisp high-resolution images of the shallow crust. The crust is characterized by a complex subsurface geometry with conflicting dips of up to [Formula: see text]. In summary, the three schemes are (1) normal-moveout (NMO) corrections, dip-moveout (DMO) corrections, common-midpoint (CMP) stacking, CMP projection, and poststack time migration; (2) NMO corrections, DMO corrections, CMP projection, zero-offset time migration of the common-offset gathers, and CMP stacking; (3) CMP projection, prestack time migration in the common-offset domain, and CMP stacking. An essential element of all three schemes is a CMP projection routine, projecting the CMPs first binned along individual segments for preprocessing onto one straight line, which is parallel to the general dip direction of the subsurface structures. After CMP projection, the data satisfy the straight-line assumption of 2D imaging routines more closely. We observe that the prestack time-migration scheme yields comparable or more coherent synthetic and field-data images than the other two DMO-based schemes along the parts of the profile where the acquisition overall follows a straight line. However, the schemes involving DMO corrections are less plagued by migration artifacts than the prestack time-migration scheme along profile parts where the acquisition line is crooked. In particular, prominent migration artifacts on the prestack migrated synthetic data can be related to significant variations in source-receiver azimuths for which 2D prestack migration cannot account. Thus, the processing scheme including DMO corrections, CMP projection, and zero-offset migration of common-offset gathers offers a reliable and effective alternative to prestack migration for crooked-line 2D seismic reflection processing.

An exact solution of the conversion point for the converted waves from a dipping reflector with homogeneous (isotropic) overburden

For converted waves, stacking traces with a common reflection point, forming gathers, and performing dip moveout (DMO) all require accurately calculating the location of conversion points. Because of the asymmetrical paths of converted waves, even for horizontally layered media, the calculation of a conversion point for converted waves is complicated. Previous authors have obtained analytic solutions for the conversion point for converted waves in a horizontally layered media. We extend those results to the more general case of converted waves from a dipping reflector with a homogeneous, isotropic overburden. By using Snell's law, we derive a quartic equation and solve it uniquely for the conversion point. The resultant analytic expression is a function of offset, compressional-, and shear-wave velocities; normal reflector depth; and dip angle at the conversion point. This solution can be readily used to generate accurate synthetic seismic responses for converted waves based on ray theory. It also can be extended to operators for stacking converted waves and applying DMO correction.

Imaging zero-offset sections using multipath summation

The main goal of reflection seismology is to obtain a reliable image of the subsurface. The method widely used to accomplish this task is NMO and CMP stacking. In areas with relatively simple geological structures this robust technique produces a reasonably good image of a zero-offset time section. However, in areas with complex geology, the central problem of reflection data processing becomes to produce a reliable image of zero-offset section, i.e. to obtain a stacked time section which is as close as possible to the true zero-offset section. This image should include all the reflected events that may be related to different geological features. The reflections may come from various depths and have various dips. In complex geological media, more than one dipping reflector can exist at the same reflection time. The NMO-based CMP stacking fails to resolve conflicting dips, because it acts as a dip filter selecting one predominant dip, thus deteriorating the quality of the stacked section. The usual way to overcome the problem is to apply dip moveout (DMO) correction (Hale, 1984; Deregowski, 1986; Yilmaz, 2001). The DMO is able to preserve all the dips existing in the data and thus to produce a much better image of zero-offset section. The DMO is usually implemented as a part of a processing sequence including velocity analysis, NMO, DMO, inverse NMO, velocity analysis, and NMO with new velocities and stack. However, applying the DMO sequence can be time-consuming and not always effective. We propose an alternative way for imaging zero-offset sections. We show that using the multipath summation approach implemented as a single, simple, quick and efficient process (Keydar, 2004; Shtivelman and Keydar, 2004; Landa, 2004), one can achieve the results equivalent to those obtained by the above DMO sequence. The proposed method does not require information on velocities, since the multipath summation is performed for all possible velocity values within a wide specified range. Furthermore, the method is stretch free, since no explicit dynamic correction is involved. An additional feature of the method is that it preserves the signature of the waves for which the summation is performed. Application of the method is illustrated by a synthetic example. The example demonstrates that the section obtained by the multipath summation is very close to the true zero-offset section.

Improved imaging of 3D marine seismic data from offshore Costa Rica with CRS processing

G. Gierse, J. Pruessmann, E. Laggiard, C. Boennemann, and H. Meyer show how the Common Reflection Surface (CRS) imaging technique developed by German research and commercial organizations can be successfully applied to a 3D dataset, in this case from a seismic survey off Costa Rica. The macro model independent Common Reflection Surface (CRS) imaging technique has proved to produce superior images in various 2D seismic case studies. A 3D marine dataset application demonstrates similar capabilities of the CRS technique for 3D data. The signal-to-noise ratio is strongly increased and dipping features are better resolved. The marine dataset is selected from the active continental margin offshore Costa Rica. The CRS processing aims at enhancing the image of the slope sediments and deeper crustal structures. The resolution of complex subsurface structures in 2D and 3D still represents a major challenge to seismic exploration. Up to now, continuous efforts have been made throughout the oil and gas industry to improve the imaging of complex structures with the main focus on prestack depth imaging. The seismic wavefront that travels through the complex subsurface is likely to deviate from a spherical shape having passed all sorts of inhomogeneities. Prestack depth migration has the advantage of not assuming a spherical wavefront like conventional techniques, since it calculates the actual deformations of the wavefront from a more or less coarse model of the subsurface. The derivation of the model, however, is a crucial step where prestack depth migration might fail. A very low signal-to-noise ratio in the seismic data often prevents the definition of a reliable basic model and the identification of the main horizons in the prestack data. Likewise, model building can fail in areas of complex tectonics, such as overthrust areas. Thus the strength of the model-based imaging cannot be exploited. For such cases, recent advances in time domain imaging with the CRS technique can be an alternative. CRS processing strongly increases the signal-to-noise ratio, and produces a significant improvement of imaging results. Poststack depth migration allows the transfer of the improved resolution from time domain to depth. In general, time processing has seen fewer efforts to improve the imaging techniques compared with depth processing. In many exploration projects, the conventional NMO / DMO processing flow for producing the zero-offset stack still dominates seismic processing in the time domain. This standard technique has prevailed nearly unchanged throughout the seismic industry during the last two decades. NMO / DMO processing uses a type of a macro model given by the stacking velocity field, which is derived from Common Midpoint (CMP) gathers. The velocity field describes the CMP reflection time curves, which are assumed to be hyperbolic. This assumption corresponds to undisturbed wavefronts from reflection points in a subsurface with plane horizontal layering. In case of dipping layers, the one dimensional subsurface model in the NMO approach leads to reflection point smearing, and requires a partial migration via the Dip Moveout (DMO) correction. Time domain imaging approaches, that were considered alternatives to the established NMO / DMO technique with its simplified subsurface model, have frequently been proposed. At the end of the 80s, de Bazelaire (1986, 1988) and Gelchinsky (1988, 1989) proposed new strategies for a zero-offset imaging. In contrast to the NMO/DMO technique, as well as prestack depth migration, these strategies do not require a macro model, but estimate the imaging parameters directly from the prestack data.

Seismic imaging of steep dips with low fold data: Case studies for Broken Hill and the Lachlan Fold Belt

In hard rock regions, a large range of stacking velocities is required to correctly stack reflectors of different dips. Typically, horizontal reflectors stack at 6000 m/s, whereas reflectors with dips of 60° stack at 12,000 m/s. For high fold (vibrator) data, correct stack of conflicting dips can be achieved by dip moveout (DMO) correction. However, for lower fold (dynamite) data, the sparse offset distribution complicates application of DMO. An alternative technique involves producing stacks with different stacking velocities and stacking these stacks. This technique was applied to two seismic reflection data sets, low fold dynamite data from Broken Hill and high fold vibrator data from the Lachlan Fold Belt. The Lachlan data set was used as both full 60/120 fold and reduced 10/20 fold. Velocity analysis, both analytical and empirical, was carried out to determine the range of stacking velocities. Stacking velocity increases with dip angle (cos-1q), but the velocity range across which an event stacks coherently increases more rapidly (approximately cos-3q for velocities typical of hard rock). The most critical area for analysis is the first two seconds of data, due to greater sensitivity of NMO to stacking velocity. The optimum number of stacks is an important consideration, based on the number of stacks in which an event contributes coherently to the sum The Broken Hill stack data showed simultaneous imaging of horizontal and dipping events. For the Lachlan reduced fold data set, horizontal and moderate to steeply dipping events were stacked successfully, although not as well as the post-DMO stack of the full fold data. The technique has some problems at the shallowest levels, where the stack can be degraded due to time shifts of events in the individual stacks, but is a useful tool for low fold seismic data typical of older regional profiles.

What is DMO coverage?

‘Coverage’ or ‘fold’ is defined as the multiplicity of common-midpoint (CMP) data. For CMP stacking the coverage is consistent with the number of traces sharing a common reflection point on flat subsurface reflectors. This relationship is not true for dipping reflectors. The deficiencies of CMP stacking with respect to imaging dipping events have long been overcome by the introduction of the dip-moveout (DMO) correction. However, the concept of coverage has not yet satisfactorily been updated to a ‘DMO coverage’ consistent with DMO stacking. A definition of constant-velocity DMO coverage will be proposed here. A subsurface reflector will be illuminated from a given source and receiver location if the time difference between the reflector zero-offset traveltime and the NMO- and DMO-corrected traveltime of the reflection event is less than half a dominant wavelength. Due to the fact that a subsurface reflector location is determined by its zero-offset traveltime, its strike and its dip, the DMO coverage also depends on these three parameters. For every surface location, the proposed DMO coverage consists of a 3D fold distribution over reflector strike, dip and zero-offset traveltime.

Seismic and potential‐field imaging of the Guichon Creek batholith, British Columbia, Canada, to delineate structures hosting porphyry copper deposits

The Guichon Creek batholith (GCB), located in south‐central British Columbia, contains several large, low‐grade copper deposits of considerable economic importance. The surface geology of the Guichon batholith and its surrounding region have been well mapped; however, little information about subsurface features is available. The batholith consists of four major phases, emplaced radially outward, which can be separated on the basis of their texture and composition. Previous interpretation of gravity data suggests a mushroom‐shaped structure for the batholith. Data from Lithoprobe seismic reflection line 88-11, acquired across the batholith in 1988, reveal weakly coherent east‐dipping reflections on the west side and west‐dipping reflections on the east in the upper 10 km. To determine if these are related to structures associated with the batholith, we reprocessed the upper 6 s with particular emphasis on applications of signal enhancement techniques (e.g., pattern recognition methods, refraction statics, dip moveout corrections) and correlation of the improved subsurface images with the geological environment associated with porphyry copper deposits. Low near‐surface velocities correlate well with the phases of the batholith hosting the major copper deposits, which structurally lie in faulted and brecciated regions. Although the top 1.5 km cannot be imaged by the regional‐scale seismic reflection data, the reprocessed seismic section helps define the edges of the batholith, its various concentric phases, and the stem in the depth range of 1.5 to 10 km. The seismic results are complemented by 2.5-D (profile sense) modeling and 3-D inversion of regional‐scale gravity and high‐resolution aeromagnetic data. These show a low‐density and low‐magnetic‐susceptibility region associated with the batholith that extends to more than 10 km depth. The region of active mining interest lies above a circular low‐susceptibility area at 2 km depth and a low‐velocity region. Integrated interpretation of geophysical results and geological observations indicates the GCB is a funnel‐shaped feature in which mineralization is located above the stem of the batholith.

Explicit analytic expression for normal moveout from horizontal and dipping reflectors in weakly anisotropic media of arbitrary symmetry type

When processing and inverting seismic reflection data, the NMO velocity must be correctly described, taking into account realistic situations such as the presence of anisotropy and dipping reflectors. Some dip‐moveout (DMO) algorithms have been developed, such as Tsvankin’s analytic formula. It describes the anisotropy‐induced distortions in the classical isotropic cosine of dip dependence of the NMO velocity. However, it is restricted to the vertical symmetry planes of anisotropic media, so the technique is unsuitable for the azimuthal inspection of sedimentary rocks, either with horizontal bedding and vertical fractures or with dipping bedding but no fractures. However, under the weak anisotropy approximation the deviations of the rays from a vertical plane can be neglected for the traveltimes computation, and the equation can still be applicable. Based on this approach, an explicit analytic expression for the P-wave NMO velocity in the presence of horizontal or dipping reflectors in media exhibiting the most general symmetry type (triclinic) is obtained in this work. If the medium exhibits a horizontal symmetry plane, the concise DMO equations are formally identical to Tsvankin’s except that the parameters δ and ε are not constant but depend on the azimuth ψ Physically, δ(ψ) is the deviation from the vertical P-wave velocity of the P-wave NMO velocity for a horizontal reflector normalized by the vertical P-wave velocity for the azimuth ψ. The function ε(ψ) has the same definition as δ(ψ) except that the P-wave NMO velocity is replaced by the horizontal P-wave velocity. Both depend linearly on (1) new dimensionless anisotropy parameters and (2) generalizing to arbitrary symmetry the transversely isotropic parameters δ and ε. In the most general symmetry case (triclinic), an additional term to the DMO formula is necessary. The numerical examples, based on experimental data in rocks, show two things. First, the magnitude of the DMO errors induced by anisotropy depends primarily on the absolute value of ε(ψ) − δ(ψ) and not on the individual values of ε(ψ) and δ(ψ), which is a direct consequence of the similarity between Tsvankin’s equation and the equation presented here. Second, the anisotropy‐induced DMO correction can be significant even in the presence of moderate anisotropy and can exhibit complex azimuthal dependence.

The common reflecting element (CRE) method revisited

The common reflecting element (CRE) method is an interesting alternative to the familiar methods of common midpoint (CMP) stack or migration to zero offset (MZO). Like these two methods, the CRE method aims at constructing a stacked zero‐offset section from a set of constant‐offset sections. However, it requires no more knowledge about the generally laterally inhomogeneous subsurface model than the near‐surface values of the velocity field. In addition to being a tool to construct a stacked zero‐offset section, the CRE method simultaneously obtains information about the laterally inhomogeneous macrovelocity model. An important feature of the CRE method is that it does not suffer from pulse stretch. Moreover, it gives an alternative solution for conflicting dip problems. In the 1-D case, CRE is closely related to the optical stack. For the price of having to search for two data‐derived parameters instead of one, the CRE method provides important advantages over the conventional CMP stack. Its results are similar to those of the MZO process, which is commonly implemented as an NMO correction followed by a dip moveout (DMO) correction applied to the original constant‐offset section. The CRE method is based on 2-D kinematic considerations only and is not an amplitude‐preserving process.

Dip‐moveout processing by Fourier transform in anisotropic media

Conventional dip‐moveout (DMO) processing is designed for isotropic media and cannot handle angle‐dependent velocity. We show that Hale's isotropic DMO algorithm remains valid for elliptical anisotropy but may lead to serious errors for nonelliptical models, even if velocity anisotropy is moderate. Here, Hale's constant‐velocity DMO method is extended to anisotropic media. The DMO operator, to be applied to common‐offset data corrected for normal moveout (NMO), is based on the analytic expression for dip‐dependent NMO velocity given by Tsvankin. Since DMO correction in anisotropic media requires knowledge of the velocity field, it should be preceded by an inversion procedure designed to obtain the normal‐moveout velocity as a function of ray parameter. For transversely isotropic models with a vertical symmetry axis (VTI media), P‐wave NMO velocity depends on a single anisotropic coefficient (η) that can be determined from surface reflection data. Impulse responses and synthetic examples for typical VTI media demonstrate the accuracy and efficiency of this DMO technique. Once the inversion step has been completed, the NMO-DMO sequence does not take any more computing time than the genetic Hale method in isotropic media. Our DMO operator is not limited to vertical transverse isotropy as it can be applied in the same fashion in symmetry planes of more complicated anisotropic models such as orthorhombic.