Tomographic Velocity Analysis Research Articles

Tomographic velocity analysis and wave-equation depth migration in an overthrust terrain: A case study from the Tuha Basin, China

Although the structures associated with overthrust terrains form important targets in many basins, accurately imaging remains challenging. Steep dips and strong lateral velocity variations associated with these complex structures require prestack depth migration instead of simpler time migration. The associated rough topography, coupled with older, more indurated, and thus high-velocity rocks near or outcropping at the surface often lead to seismic data that suffer from severe statics problems, strong head waves, and backscattered energy from the shallow section, giving rise to a low signal-to-noise ratio that increases the difficulties in building an accurate velocity model for subsequent depth migration. We applied a multidomain cascaded noise attenuation workflow to suppress much of the linear noise. Strong lateral velocity variations occur not only at depth but near the surface as well, distorting the reflections and degrading all deeper images. Conventional elevation corrections followed by refraction statics methods fail in these areas due to poor data quality and the absence of a continuous refracting surface. Although a seismically derived tomographic solution provides an improved image, constraining the solution to the near-surface depth-domain interval velocities measured along the surface outcrop data provides further improvement. Although a one-way wave-equation migration algorithm accounts for the strong lateral velocity variations and complicated structures at depth, modifying the algorithm to account for lateral variation in illumination caused by the irregular topography significantly improves the image, preserving the subsurface amplitude variations. We believe that our step-by-step workflow of addressing the data quality, velocity model building, and seismic imaging developed for the Tuha Basin of China can be applied to other overthrust plays in other parts of the world.

Sensitivity-kernel-based tomographic migration velocity analysis using reverse time migration angle-image gathers

Sensitivity-kernel-based tomographic migration velocity analysis (TMVA) provides a means to better update the migration velocity model in complex media. For actual seismic data with finite-frequency bandwidth, migration velocity updated from wave-equation-based tomography is more suitable and robust than ray-based tomography for images obtained from reverse time migration (RTM). Depth residuals in the RTM-extracted angle-image gathers offer a reliable source of velocity information. We have developed cost-effective means of calculating the angle-domain sensitivity kernel and incorporated it into the TMVA approach using RTM angle-image gathers. The angle-domain sensitivity kernels are used to convert the depth residuals from RTM angle-image gathers into velocity perturbations, which were then used to refine the velocity model. We derived an approximate analytical residual moveout function for measuring depth residuals of the RTM angle-image gather in isotropic media and also devised a workflow for sensitivity-kernel-based TMVA. The workflow maintains the simplicity of ray-based tomography by replacing the rays with the more accurate angle-domain sensitivity kernels. We determined the capability of this method in updating migration velocity with the 2D Sigsbee2 model and the 3D SEAM model. Our method significantly improved the quality of the migrated depth image and flattened the RTM angle-image gathers.

Seismic imaging of subsurface structure using tomographic migration velocity analysis: a case study of South China Sea data

Seismic migration algorithms are often used to reveal subsurface structures and can be roughly divided into stacking methods, pre-stack time migration methods and pre-stack depth migration methods. In theory, pre-stack depth migration methods can provide the most accurate subsurface images. However, these methods are sensitive to the accuracy of the migration velocity model, and thus the creation of a precise migration velocity model is one of the most important steps in seismic processing. We applied the tomographic travel-time inversion and the method of pre-stack Kirchhoff depth migration-based migration velocity analysis (MVA) to certain South China Sea data, in which we iteratively inverted the precise, high-resolution migration velocity model. We selected travel-time differences from the offset-domain common image gathers of the pre-stack Kirchhoff depth migration and inverted the travel-time differences for velocity updating. After several iterations, both the precise migration velocity model and the corresponding pre-stack depth migration image were obtained. The comparisons with Normal Move-out stacking and pre-stack Kirchhoff time migration confirm that the tomographic MVA and corresponding pre-stack Kirchhoff depth migration provide the best image quality and highest-resolution subsurface images from the South China Sea data.

Estimation of surface wave Green's functions from correlation of direct waves, coda waves, and ambient noise in SE Tibet

Empirical Green's functions (EGFs) between receivers can be obtained from seismic interferometry through cross-correlation of pairs of ground motion records. Full reconstruction of the Green's function requires diffuse wavefields or a uniform distribution of (noise) sources. In practice, EGFs differ from actual Green's functions because wavefields are not diffuse and the source distribution not uniform. This difference, which may depend on medium heterogeneity, complicates (stochastic) medium characterization as well as imaging and tomographic velocity analysis with EGFs. We investigate how source distribution and scale lengths of medium heterogeneity influence surface wave Green's function reconstruction in the period band of primary microseisms ( T = 10–20 s). With data from a broad-band seismograph array in SE Tibet we analyze the symmetry and travel-time properties of surface wave EGFs from correlation of data in different windows: ambient noise, direct surface waves, and surface wave coda. The EGFs from these different windows show similar dispersion characteristics, which demonstrates that the Green's function can be recovered from direct wavefields (e.g., ambient noise or earthquakes) or from wavefields scattered by heterogeneity on a regional scale. Directional bias and signal-to-noise ratio of EGFs can be understood better with (plane wave) beamforming of the energy contributing to EGF construction. Beamforming also demonstrates that seasonal variations in cross-correlation functions correlate with changes in ocean activity.

Data-driven tomographic velocity analysis in tilted transversely isotropic media: A 3D case history from the Canadian Foothills

We evaluated how velocity and anisotropy model-building strategies affect seismic imaging in the Canadian Foothills Thrust Belt by comparing the results of a model-driven approach with those of a data-driven approach. Two independently run Kirchhoff prestack depth-imaging projects were initiated using different static corrections for near-surface weathering layers and using different velocity and anisotropy model-building strategies. We observed that an isotropic data-driven reflection tomography velocity model-building approach resulted in a significantly better stack image than did a highly interpretive anisotropic model-driven velocity model-building approach. By carefully introducing anisotropy into the former, data-driven approach, we achieved significant improvements in positioning, including more accurate depth ties between the seismic image and well tops and better definition of structural geometries. The differences in the imaging observed at the various stages of this case history illustrate the sensitivity of the final depth images to the treatment of the near-surface velocity field, the macrointerval velocity model-building technique, and the choices of [Formula: see text] and [Formula: see text], which are the Thomsen anisotropy parameters for tilted transverse isotropy. The data-driven approach successfully challenged the historical idea that we must perform a geologic interpretation of the seismic data to derive an accurate depth velocity model in a complex geologic setting.

Velocity and AVO analysis for the investigation of gas hydrate along a profile in the western continental margin of India

The occurrence of gas hydrate has been inferred from the presence of Bottom-Simulating Reflectors (BSRs) along the western continental margin of India. In this paper, we assess the spatial and vertical distribution of gas hydrates by analyzing the interval velocities and Amplitude Versus Offset (AVO) responses obtained from multi-channel seismics (MCSs). The hydrate cements the grains of the host sediment, thereby increasing its velocity, whereas the free gas below the base of hydrate stability zone decreases the interval velocity. Conventionally, velocities are obtained from the semblance analysis on the Common Mid-Point (CMP) gathers. Here, we used wave-equation datuming to remove the effect of the water column before the velocity analysis. We show that the interval velocities obtained in this fashion are more stable than those computed from the conventional semblance analysis. The initial velocity model thus obtained is updated using the tomographic velocity analysis to account for lateral heterogeneity. The resultant interval velocity model shows large lateral velocity variations in the hydrate layer and some low velocity zones associated with free gas at the location of structural traps. The reflection from the base of the gas layer is also visible in the stacked seismic data. Vertical variation in hydrate distribution is assessed by analyzing the AVO response at selected locations. AVO analysis is carried out after applying true amplitude processing. The average amplitudes of BSRs are almost constant with offset, suggesting a fluid expulsion model for hydrate formation. In such a model, the hydrate concentrations are gradational with maxima occurring at the base of hydrate stability zone.

CRP-based seismic migration velocity analysis

A new migration velocity analysis is developed by combining the speed of parsimonious prestack depth migration with velocity adjustments estimated within and across common-reflection-point (CRP) gathers. The proposed approach is much more efficient than conventional tomographic velocity analysis because only the traces that contribute to a series of CRP gathers are depth migrated at each iteration. The local interval-velocity adjustments for each CRP are obtained by maximizing the stack amplitude over the predicted (nonhyperbolic) moveout in each CRP gather; this does not involve retracing rays. At every iteration, the velocity in each pixel is updated by averaging over all the predicted velocity updates. Finally, CRP positions and orientations are updated by parsimonious migration, and rays are retraced to define new CRP gathers for the next iteration; this ensures internal consistency between the updated velocity model and the CRP gather. Because the algorithm has a gridded-model parameterization, no explicit representation or fitting of reflectors is involved. Strong lateral-velocity variations, such as those found at salt flanks, can be handled. Application to synthetic and field data sets show that the proposed algorithm works effectively and efficiently.

Geofluid evidence from analysis of deep crustal seismic data (Southern Tuscany, Italy)

Southern Tuscany is characterized by an extensional tectonic regime, crustal thinning, magmatic intrusions, testifying the presence of fluids at elevated temperature and important geothermal fields. The area was investigated by applying integrated methodologies to deep crustal reflection seismic data: tomographic velocity analysis, amplitude versus offset inversion and theoretical approaches to model overpressure conditions. The seismic transect CROP 18, split in two lines (18-A and 18-B) with a total length of 123 km, has imaged the exceptionally high reflectivity of some markers of the metamorphic-crystalline basement units and of the medium-lower crust. The geometry of the main geological structures was reconstructed performing a pre-stack depth migration. The joint analysis of the available data enabled us to distinguish between the lithologic reflectors and the reflections caused by a predominant fluid effect, such as overpressure conditions. We detected the presence of vertical conduits, responsible for magmatic intrusions rising from the base of the crust, as well as of overpressured reservoirs. Theoretical models are used to quantify the effect of overpressure in terms of porosity increase, and the consequent density decrease in two areas where the main marker characterizing the geothermal fields, called the K horizon, is relatively shallow.

Complex structural velocity model building for depth imaging

The quality of a migration image depends strongly upon the accuracy of the velocity model. For tomographic velocity analysis, which is most popularly used in the seismic industry, pick errors, null space, velocity ambiguity and intrinsic nonlinearity all have a strong effect on the accuracy of the velocity model. The discussion in this paper is based on a post-migration tomography algorithm which can work on either offset domain common-image gathers (CIGs) or angle domain common-image gathers (CAGs). A large number of depth residuals (hyperbolic and non-hyperbolic) and the structural dip field are automatically picked and high-graded based on the event semblance on the CIGs or CAGs and the coherency along the horizon on post-migrated stack volume. In order to further high-grade the picks, a gamma cube is created which is used for QCing and further high-grading the picks. In the solution of the tomographic equations, a few constraints are used, including a preconditioning operator in data space to reduce the influence of extreme picks and a preconditioning operator in model space with a variable-length controlled direction smoother in order to reduce the null space, speed up the convergence and stabilize the solution, and hard constraints that limit the velocity updates within a certain range. The discussion focuses mainly on how to better represent the velocity model, how to automatically pick a large number of events and structural dip field, how to high-grade the picks based on the event semblance, horizon coherency and filtered gamma cube, how to add proper constraints to the solver, and how to further improve the tomographic inverted velocity model by gamma-based inversion. Usually, the tomographic problem is a highly underdetermined problem; even if we pick as many events as possible and add constraints to the tomographic equations, a perfect result is not guaranteed. In some areas, events are still not flat. In order to further improve the velocity model after tomography, a gamma-based inversion is used. Both numerical and real data tests show that our software package for complex structural velocity model building works well and produces encouraging results. Despite many successful applications of tomographic velocity analysis, challenges still remain for this ill-posed problem. The presence of a null space and pick errors guarantees some level of velocity ambiguity. After discussing some of the challenges facing tomographic velocity analysis, we introduce ways to cope with them.

Multiscale traveltime tomography

Nonuniqueness in traveltime tomographic velocity analysis is largely the result of insufficiency in model parameterization. Traditional tomography parameterizes the model with nonoverlapping cells. Such single‐scale tomography (SST) from inverting traveltimes only may produce underdeterminacy at places of insufficient ray coverage. To cope with the poor and uneven ray coverage, a multiscale tomography (MST) method is devised, which is a simultaneous application of many overlapping SSTs with different cell sizes. The MST decomposes velocity anomalies into components in a set of submodels of different cell sizes. At each model location the cells containing higher consistency between data contributions gain more from the inversion. The final MST model is a postinversion superposition of all submodel solutions. The MST method is applicable to the determination of interval velocity and interface geometry using turning rays or reflection rays. In comparison with the SST, superior results of the MST are seen in synthetic examples. The MST method is used to construct the 3D crustal velocities of southern California using the first arrivals from local earthquakes. While the SST and MST models may fit the data equally well, the MST model is smoother and geologically more plausible than the SST model.

Joint inversion of PP and PS reflection data for VTI media: A North Sea case study

Despite the significant advantages of combining PP and PS reflection data in anisotropic parameter estimation, application of this approach has been hindered by the inherent complexity of PS‐wave moveout. To overcome this problem, V. Grechka and I. Tsvankin suggested a model‐independent procedure to construct the traveltimes of pure SS‐wave reflections from PP and PS data. Here, we apply their method and anisotropic multicomponent stacking‐velocity tomography to a 2‐D line acquired over the lower Tertiary Siri reservoir in the North Sea.The computed traveltimes of SS reflections from several horizons are used to estimate the effective SS‐wave normal‐moveout (NMO) velocities, which are combined with the NMO velocities of PP‐waves in the tomographic velocity analysis. Comparison of the vertical and NMO velocities of the PP‐ and SS‐waves provides clear evidence of anisotropy in the section above the reservoir. The interval parameter estimation is performed under the assumption that the section is composed of transversely isotropic layers with a vertical symmetry axis (VTI media). Since the subsurface structure is close to horizontally layered, the reflection data cannot be uniquely inverted for the VTI parameters without additional information (e.g., the vertical velocities found from borehole data).The parameter‐estimation algorithm produces a family of equivalent VTI models that fit the PP and PS (or SS) traveltimes equally well. Although the range of variations in ε and δ for the equivalent models is rather wide, it does not include isotropic media (ε = δ = 0), which implies that accurate matching of both PP and PS data is impossible without accounting for anisotropy. To overcome the nonuniqueness in the inversion of reflection data and build a VTI depth model, we use P‐wave check shots acquired in the only borehole drilled on the processed line. Throughout the section ε > δ, with the largest values of both anisotropic coefficients observed in the depth range 0.7–1.5 km where ε reaches almost 0.25. Time sections of the original PS data computed using the VTI model have a much higher quality than the conventional isotropic sections.

Tomographic velocity estimation with plane‐wave synthesis

In areas with structurally complex geology, tomographic velocity analysis is often required to estimate velocities. In this paper I describe an algorithm for tomographic velocity estimation that uses plane‐wave synthesis imaging as a prestack migration. The classical iterative two‐step process (measures the traveltime errors with the current velocity model and then update the velocity model) is performed as follows. The events are picked in the image space after prestack migration with surface‐oriented plane‐wave synthesis imaging. the traveltime deviations are measured through residual‐moveout (RMO) velocity analysis in common‐surface‐location (CSL) gathers obtained by reflector‐oriented plane‐wave synthesis imaging, and the velocity update is calculated by inverting the traveltime deviations through a conjugate gradient. The results from synthetic data indicate that the tomographic method successfully estimates interval‐velocity models that lead to depth‐migrated images with no residual moveout.

Combining reflection tomography with layer replacement for velocity analysis of near‐surface reefs

Reefs in the Browse Basin on the Australian North West Shelf typically have strong lateral velocity inhomogeneity on the reef flanks and produce an irregular sea‐floor topography. The combination of these two factors reduces the effectiveness of conventional velocity analysis as moveout on common midpoint (CMP) gathers is no longer hyperbolic. Consequently, the velocity structure on the reef flanks cannot be resolved properly. An accurate velocity structure is needed for these reefs if seismic data acquired in the vicinity are to be migrated correctly. Tomographic velocity analysis, using a simultaneous iterative reconstruction technique (SIRT), was found to improve the velocity analysis of the reef when compared to conventional analysis. However, the reef’s profile and rapid internal velocity gradients prevent accurate raypath determination. This technique can be further improved by preconditioning the data with wave‐equation datuming. The water is replaced with an average reef velocity by downward and upward continuation. This effectively removes most of the raypath distortions resulting from ray bending at the sea floor, thus reducing the nonlinearity of the forward modeling and improving the convergence of an iteratively linearized inversion. The velocities obtained from this method give an accurate picture of the reef’s internal velocity structure, as well as the lower portion of the seismic section below the reef.

Linear aspects of tomographic velocity analysis

Prestack velocity analysis in areas of complex structure is a coupled migration and transmission inversion problem that can be analyzed from a tomographic perspective. By making as few a priori assumptions about the solution as possible in parameterizing the inverse problem, generalized tomographic velocity analysis is applicable to a wide range of geologic cases. Constraints modify the method to the unique characteristics of each application. The ray trace/traveltime formulation for tomography, as proposed by Bishop et al. (1985), provides a conceptual tool for presenting features that are important to automated prestack velocity analysis in complex structure, such as (1) the coupling of the velocity field to the reflector positions, (2) the nonuniform coverage of the model by the data, (3) the ability to perform a controlled inversion of large matrices over a wide eigenvalue range, and (4) the implementation of constraints in the inversion. These features may impact other automated prestack velocity analysis methods for reflection seismology.