Zero-offset Time Research Articles

Nonhyperbolic normal moveout stretch correction with deep learning automation

Normal-moveout (NMO) correction is a fundamental step in seismic data processing. It consists of mapping seismic data from recorded traveltimes to corresponding zero-offset times. This process produces wavelet stretching as an undesired by-product. We have addressed the NMO stretching problem with two methods: (1) an exact stretch-free NMO correction that prevents the stretching of primary reflections and (2) an approximate post-NMO stretch correction. Our stretch-free NMO produces parallel moveout trajectories for primary reflections. Our post-NMO stretch correction calculates the moveout of stretched wavelets as a function of offset. Both methods are based on the generalized moveout approximation and are suitable for application in complex anisotropic or heterogeneous environments. We use new moveout equations, modify the original parameter functions to be a constant over the primary reflections, and then interpolate the seismogram amplitudes at the calculated traveltimes. For fast and automatic modification of the parameter functions, we use deep learning. We design a deep neural network (DNN) using convolutional layers and residual blocks. To train the DNN, we generate a set of 40,000 synthetic NMO-corrected common-midpoint gathers and the corresponding desired outputs of the DNN. The data set is generated using different velocity profiles, wavelets, and offset vectors, and it includes multiples, ground roll, and band-limited random noise. The simplicity of the DNN task — a 1D identification of primary reflections — improves the generalization in practice. We use the trained DNN and find successful applications of our stretch-correction method on synthetic and different real data sets.

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.

Continuous estimation of 3-D reflector orientations along 2-D deep seismic reflection profiles

Interpretation of 2-D deep seismic reflection data can be limited by the recording of out-of-plane reflections that cannot be readily distinguished from those originating beneath a seismic line. Here I present a method analogous to semblance velocity analysis that utilizes varying source-receiver azimuths to derive continuous estimates of 3-D reflector orientations along onshore 2-D reflection profiles. For each zero-offset time within a common depth point supergather, the semblance is calculated along 3-D travel time curves, and the dip and strike of the most coherent reflection is determined. Relative errors in these angles are derived from the range of travel time curves that have semblance values greater than a specified fraction, for example 90%, of the maximum. The method is illustrated using a section from line 10GA-YU1 from the Youanmi terrane of the Yilgarn craton in Australia in which the original field data have been replaced with synthetic in-line and cross-line reflections. Reflector orientations are generally well recovered where the range of available source-receiver azimuths is greater than 20o, but the method fails at lower ranges where the seismic line is almost linear, and this behavior is also observed in analysis of the field data. Nevertheless when using a realistic 1-D velocity function the orientation of upper crustal shear zones can be readily determined, and on unmigrated sections subhorizontal sills can be distinguished on the basis of their geometry from the mid-crustal reflectivity. In future surveys, reflector orientations can be determined along the near-linear sections of a seismic profile by deploying additional receivers, perhaps as cross-line recording spreads, to supplement the limited range of azimuths available from the in-line acquisition. The method can in principle be extended to marine reflection surveys, and more complex sub-surface velocity models.

Mapping of moveout attributes using local slopes

Decomposing seismic data in local slopes is the basic idea behind velocity-independent imaging. Using accurate moveout approximations enables computing moveout attributes such as normal moveout velocity and nonhyperbolic parameters as functions of zero-offset travel time. Mapping of moveout attributes is performed from the pre-stack seismic data domain into the time-migrated image domain. The different moveout attributes have different accuracy for a given moveout approximation that depends on the corresponding order of travel-time derivative. The most accurate attribute is the zero-offset travel time, and the nonhyperbolic parameter has the worst accuracy, regardless of the moveout approximation. Typically, the mapping of moveout attributes is performed using a point-to-point procedure, whereas the generalized moveout approximation requires two point-to-point mappings. Testing the attribute mapping on the different models shows that the accuracy of mapped attributes is model dependent, whereas the generalized moveout approximation gives practically exact results.

Analysis of time-lapse travel-time and amplitude changes to assess reservoir compartmentalization

Fluid depletion within a compacting reservoir can lead to significant stress and strain changes and potentially severe geomechanical issues, both inside and outside the reservoir. We extend previous research of time-lapse seismic interpretation by incorporating synthetic near-offset and full-offset common-midpoint reflection data using anisotropic ray tracing to investigate uncertainties in time-lapse seismic observations. The time-lapse seismic simulations use dynamic elasticity models built from hydro-geomechanical simulation output and a stress-dependent rock physics model. The reservoir model is a conceptual two-fault graben reservoir, where we allow the fault fluid-flow transmissibility to vary from high to low to simulate non-compartmentalized and compartmentalized reservoirs, respectively. The results indicate time-lapse seismic amplitude changes and travel-time shifts can be used to qualitatively identify reservoir compartmentalization. Due to the high repeatability and good quality of the time-lapse synthetic dataset, the estimated travel-time shifts and amplitude changes for near-offset data match the true model subsurface changes with minimal errors. A 1D velocity–strain relation was used to estimate the vertical velocity change for the reservoir bottom interface by applying zero-offset time shifts from both the near-offset and full-offset measurements. For near-offset data, the estimated P-wave velocity changes were within 10% of the true value. However, for full-offset data, time-lapse attributes are quantitatively reliable using standard time-lapse seismic methods when an updated velocity model is used rather than the baseline model.

Local stretch zeroing NMO correction

Summary In this paper we present a new method of normal move-out (NMO) correction called local stretch zeroing (LSZ) method that avoids NMO stretch. The method eliminates the theoretical curves that generate interpolated data samples responsible for NMO stretch. Pre-correction time sampling interval is preserved by reassigning and zero padding of true data samples. The optimum mute zone selection feature of the LSZ method eliminates all interfering reflection events at far offsets. The resulted stacked section from the LSZ method contains generally higher frequency components than a normal stack, and preserves most of the shallow reflectors. The LSZ method requires that zero-offset width of the time gate, i.e. zero-offset time difference between two adjacent reflections, be larger than the dominant period. The major shortcoming of the method occurs when CMP data are over- or under-NMO corrected. Real world examples show the efficiency of the LSZ method over the conventional NMO (CNMO) correction.

An accurate ray-based offset-to-angle transform from normal moveout uncorrected multicomponent data in a transversely isotropic medium with vertical symmetry axis

A new ray-based approach for converting multicomponent normal moveout uncorrected offset domain prestack seismic data into angles is presented. From any two-way zero-offset time sample and a given angle of incidence, the exact ray and a few neighboring rays that contribute to the given angle of incidence are traced through the medium to their corresponding source and receiver locations to compute their raypath lengths, traveltimes, and offsets. A polynomial then is fitted locally between these computed offsets and their corresponding traveltimes. Next the traveltimes for the actual offsets on data that lie within these traced rays are computed from this local polynomial fit, and their corresponding time samples are partially stacked and moved to their two-way zero-offset times. Repetition of this procedure for all zero-offset time samples and for all desired angles produces an angle gather. The procedure allows computation of both primary (P-P) and mode-converted (P-SV) angle gathers. Also, by calculating the exact raypath length, an accurate geometric spreading compensation can be computed and applied to these gathers. By using the methodology for a horizontally stratified transversely isotopic medium with a vertical symmetry axis (a VTI medium), it is possible to extract a much more accurate angle-domain response from the ray-based method than is possible from a traditional NMO-based method. Accuracy out to large angles for both primary and mode-converted reflection suggests that this ray-based transform potentially could be used in a multicomponent prestack waveform inversion scheme.

Correction for the influence of velocity lenses on nonhyperbolic moveout inversion for VTI media

Nonhyperbolic moveout analysis plays an increasingly important role in velocity model building because it provides valuable information for anisotropic parameter estimation. However, lateral heterogeneity associated with stratigraphic lenses such as channels and reefs can significantly distort the moveout parameters, even when the structure is relatively simple. We analyze the influence of a low-velocity isotropic lens on nonhyperbolic moveout inversion for horizontally layered VTI (transversely isotropic with a vertical symmetry axis) models. Synthetic tests demonstrate that a lens can cause substantial, laterally varying errors in the normal-moveout velocity [Formula: see text] and the anellipticity parameter [Formula: see text]. The area influenced by the lens can be identified using the residual moveout after the nonhyperbolic moveout correction as well as the dependence of errors in [Formula: see text] and [Formula: see text] on spreadlength. To remove such errors in [Formula: see text] and [Formula: see text], we propose a correction algorithm designed for a lens embedded in a horizontally layered overburden. This algorithm involves estimation of the incidence angle of the ray passing through the lens for each recorded trace. With the assumption that lens-related perturbation of the raypath is negligible, the lens-induced traveltime shifts are computed from the corresponding zero-offset time distortion (i.e., from “pull-up” or “push-down” anomalies). Synthetic tests demonstrate that this algorithm substantially reduces the errors in the effective and interval parameters [Formula: see text] and [Formula: see text]. The corrected traces and reconstructed “background” values of [Formula: see text] and [Formula: see text] are suitable for anisotropic time imaging and producing a high-quality stack.

Generalized nonhyperbolic moveout approximation

Reflection moveout approximations are commonly used for velocity analysis, stacking, and time migration. A novel functional form for approximating the moveout of reflection traveltimes at large offsets is introduced. In comparison with the classic hyperbolic approximation, which uses only two parameters (zero-offset time and moveout velocity), this form involves five parameters that can be determined, in a known medium, from zero-offset computations and from tracing one nonzero-offset ray. It is called a generalized approximation because it reduces to some known three-parameter forms with a particular choice of coefficients. By testing the accuracy of the proposed approximation with analytical and numerical examples, the new approximation is shown to bring an improvement in accuracy of several orders of magnitude compared to known analytical approximations, which makes it as good as exact for many practical purposes.

GPR velocity determination by image-wave remigration

We have studied in detail the theoretical and numerical properties of a finite-difference algorithm for image-wave time-remigration. For a number of synthetic models, numerical experiments have been performed. For these examples, we obtained perfect agreement between the theoretical predictions and numerical results. The examples also prove the computational efficiency of the algorithm. An application to ground-penetrating-radar (GPR) data demonstrates that image-wave remigration can be used to estimate models with laterally varying velocities. The quality of the latter is confirmed by a final zero-offset time migration.

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.

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.

Multifocusing imaging with controlled reflection‐point dispersal

Multifocusing imaging proposed by Gelchinsky (Gelchinsky et al., 1999a, b; Landa et al., 1999) belongs to a group of techniques that can be characterized as macro-model independent imaging methods. These methods, which also include the common-reflection surface method (Mann et al., 1999; Jager et al., 2001), and optical stack (de Bazelaire, 1988), are described in a collection of papers published as a special issue of the Journal of Applied Geophysics (Hubral, 1999). Macro-model independent imaging methods represent a new alternative to the classical processing sequence of NMO, dip moveout (DMO), and stacking. They are based upon a new transformation of 2-D multicoverage prestack data into a simulated zero-offset stack section. This transformation involves stacking large supergathers of seismic traces, each of which can span many common-midpoint (CMP) gathers. Stacking of large supergathers is made possible by the use of a generalized moveout correction. For a given source-receiver pair, this correction depends on three parameters: the wavefront curvatures of the normal wave, the normal incidence point wave (Hubral, 1983), and the emergence angle of the central ray. For each supergather and each zero-offset time, T , these parameters are obtained through a coherence analysis of the moveout corrected supergather.

Processing of pre-critical wide-angle seismic reflection data from the BABEL project

In addition to using the now widely recognised technique of simultaneously acquiring deep reflection profiles at sea and long-range refraction profiles using three-component land stations, the BABEL seismic experiment also recorded P- and S-wave energy from the large airgun array at four linear 38-component land spreads. The pioneering nature of this work led, in hindsight, to several deficiences in design, but also pointed the way towards substantial advances in analysis and interpretation of integrated seismic observations. The multifold nature of the recordings at offsets providing pre-critical reflections from Moho depths resulted in interleaved receiver gathers with trace spacings of 4–5 m, thus providing some of the most densely spaced deep-seismic wide-angle sections to date. With such a trace density, the signal-to-noise ratio was substantially increased by summation of adjacent traces, without degrading spatial resolution. Stacking the land array data using conventional common midpoint (CMP) gather techniques over source-receiver offsets of 7–78 km doubled the depth range constrained by numerically precise stacking velocity analysis. Offsets > 10 km provide normal moveouts > 1 s, although the 1.5 km of differential moveout available here limited velocity discrimination and required additional constraints to define zero-offset traveltimes. For one array, stacking velocity errors of ±200 m s−1 imposed a resulting error in zero-offset time of up to ±400 ms without use of any marine data. With receiver response functions matched, stacked sections using data from geophone arrays exhibit similar features to stacks made using hydrophone arrays at 0–3 km offsets in the same area, but also significant differences. The differences in reflection amplitudes cannot be simply attributed to theoretical amplitude-offset variations and probably represent variation in the reflectivity of the crustal rocks of the Baltic shield.

Suppression of Dipping Noise and Multiples Using 3D Pre-Stack Time Migration

Conventional imaging of seismic data includes an approximate NMO and DMO prior to velocity analysis. The NMO and DMO imaging steps are approximate only in the sense that an approximate (simple) velocity field is used; the algorithms themselves are accurate. After velocity analysis, NMO is re-applied with the more detailed velocity field derived from the analyses. In the constant velocity case, DMO is almost independent of velocity and the iterative procedure described above plus post-stack migration yields an accurate image. The derived velocities may also be used for multiple suppression. Also, DMO itself may change the stacking velocities of dipping noise in such a way as to suppress the noise. An improved approach to velocity estimation and imaging is to apply the conventional approximate NMO and DMO and then also to apply an approximate zero-offset time migration to each common offset dataset prior to velocity analysis (3D MOVES). After velocity analysis, the NMO is re-applied and the data stacked. Post stack, either a residual migration or full diffraction plus full time or depth migration is applied. The pre-stack migration is either a constant velocity or single function v(z) algorithm. This is consistent with the NMO, DMO approach of accurate algorithms in an approximate velocity field. The algorithms are fast and can be inverted post stack to allow depth migration. The technique has been extensively used in 2D and 3D for imaging primaries and yielding accurate velocities. However, as with DMO, the derived velocity field may also be used for multiple suppression and the migration process may itself attenuate noise and multiples. For example, multiple diffractions may be focused and then attenuated in the stack process or with standard de-multiple methods. Alternatively, dipping noise and multiples may be migrated up dip and be located above the NMO mute pattern at middle and far offsets; the subsequent NMO, mute and stack remove the multiples from the data. In these applications, the migration process should be viewed as a transformation rather than an imaging tool, and the velocity used for migration need not be geologically correct, i.e. the velocity is a transformation parameter which is tuned to obtain the optimum noise suppression. Optimal imaging is obtained with residual, post-stack migration.

Seismic profiling of Archean crust: Crustal structure in the Morton block, Minnesota River Valley subprovince

A 58 km seismic reflection profile recorded by the University of Wyoming over the early Archean gneisses (3.6–3.8 Ga) of the Minnesota River Valley subprovince (Superior Province) shows more complicated structure and rock variation with depth than the limited surface geology suggests. Wide-angle data show a high average velocity of 6.8 ± 0.1 km/s and a crustal thickness of 49 ± 1 km from a zero-offset time of 14.2 ± 0.2 s. Upper-crustal (0–10 km) reflections are consistent with the gentle dips from surface folding, while middle-crustal (10–24 km) reflections are interpreted as a 40 km long SE dipping thrust or fold structure, 6 km thick. Lower-crustal (24–48 km) reflections are short and low amplitude, consistent with small reflection coefficients and short reflectors. Modeling suggests that this reflectivity is consistent with small (< 2 km horizontal length) lenticular, boudin-like bodies or heterogeneities within the lower crust, and/or the lower crust may be complexly deformed. At 14 s (49 km) the Moho occurs as a locally layered, 10 km long structure at the depth determined for Moho from the wide-angle data. This vertical-incidence Moho reflection demonstrates the occurrence of lateral changes in Moho structure. The seismic profile suggests a model that incorporates a thrust sheet in the middle crust, emplaced by horizontal tectonics in the Archean, and restite bodies in the deep crust, formed from the production of the presently exposed gneisses.

Quantitative Evaluation of Dynamic Time-Shifts for Correcting Seismic Data

Large lateral velocity changes, particularly those associated with sea-floor topography, can severely distort seismic stack sections, for example, under the submarine canyons in the Gippsland Basin in Bass Strait. Conventional replacement statics partially correct these problems, but are usually inadequate in situations where the sea-floor variation is severe or the water is deep. Dynamic corrections calculated by ray-tracing through the region of strong lateral velocity variation give improved results.Dynamic corrections derived by ray-tracing can be evaluated by analyzing t2 -y2 plots where t is time and y is offset within CMP gathers. This facilitates making the following comparisons: (1) the zero-offset time before and after dynamic correction; (2) the RMS velocities (calculated using zero-offset rays traced in the model) with normalized stacking velocities after dynamics; (3) hyperbolic moveout before and after dynamics. A similar evaluation of conventional replacement statics provides a reference for evaluating the ray-tracing derived ‘replacement dynamics’.Ray-tracing requires a subsurface model which can be difficult to construct in areas of structural complexity. This is often the case near submarine canyons. A simple model using water depth and a single marker horizon or datum when ray-traced to derive replacement dynamics gives significant improvement with respect to the conventional statics solution in submarine canyon areas. Errors in velocity can be reduced by as much as 50% and errors in hyperbolic moveout reduced by about 70%.

Seismic migration in stratified media

A point diffractor is located in a medium where the velocity of sound propagation is linear in the vertical direction. The analysis is based upon the exploding reflector concept of D. Leowenthal et al. (1976), in which reflectors are replaced by seismic sources which explode at time t=0. The point diffractor is activated at time t=0, and the zero-offset time section is migrated with a constant velocity. Kinematic migration is a simple method to track waves through a medium of known velocity. There are two distinct parts of seismic migration: extrapolation and imaging. Extrapolation presupposes that the velocity changes are known, but to obtain an image of the subsurface, an imaging principle must be applied. An unknown velocity gradient and the depth of a point diffractor can be determined by relaxing the imaging condition to allow for an extra time-shift. The extra time-shift must be determined by focusing of the migrated output. The rays and the caustic enveloped by the family of rays stay fixed in space; hence, the present method yields unique results. >

Application of the tau-p transform (slant-stack) in processing seismic reflection data

Abstract The tau-p transform, or slant-stack, converts seismic records (i.e. time versus offset records) into a space in which many seismic events are well separated. In particular, ground-roll transforms to a point at time zero, refractions transform to points at their zero offset intercept times and reflection hyperbolae transform to ellipses. Significantly, the ellipses do not cross one another, even if the reflection hyperbolae do cross each other in record space. The tau-p space has different dimensions than conventional record space. Record space can be thought of as traces with units of time and with each trace representing a given offset x. In the tau-p space, tau (in dimensions of time), actually represents zero offset reflection time. Each trace corresponds to a particular ray parameter, p. This parameter p can be thought of in many different ways: it is a ray parameter sin i/v; it is the dt/dx, or the slope of the arriving event; and it is the horizontal slowness of the event across the recordi...