Migration Velocity Model Research Articles

Multi-azimuth processing — the kinematics and dynamics of the azimuthal anisotropy, resolved by tilted orthorhombic tomography

This paper explains a qualitative and quantitative approach to identify and resolve P-wave TTI and HTI variations in the depth migration velocity model building process. The combination of these effects can be represented by an orthorhombic model with three mutually orthogonal planes of mirror symmetry; the P-waves in each symmetry plane can be described kinematically as an independent TTI model. Orthorhombic velocity model building and imaging tools are required to address both HTI and TTI simultaneously in the subsurface. The orthorhombic anisotropy has been correctly identified and resolved, which has subsequently resulted in a high-resolution velocity model. A combination of the accurate velocity model building and advancement in the pre-processing techniques has shown significant uplift in the image quality on the earlier processing. The reprocessed PreSDM has provided improved coherency, recovered improved bandwidth, enhanced character, and better fault plane definition.

Including and using internal multiples in closed-loop imaging — Field data examples

Nowadays, it is more widely accepted that multiple reflections should not be considered as noise, but as signal that can provide additional illumination of the subsurface. However, one of the challenges in seismic imaging is including all multiples in the migration process for field data in a reliable manner. Although including surface multiples in imaging has been demonstrated already on field data in recent years, the proper imaging of internal multiples is less established. We have determined successful field data applications on imaging that takes all internal multiples into account. This is done via so-called full-wavefield migration (FWM), an inversion-based method in which, given the migration velocity model, the angle-dependent reflectivity is iteratively estimated by minimizing the misfit between the modeled and the measured data. Its forward model is based on a multidimensional version of the so-called Bremmer series, which allows modeling of transmission effects and any type of multiple scattering in the subsurface and, thereby, is able to minimize the data misfit correctly. An application of FWM on deepwater field data from the Norwegian North Sea validates its capabilities to explain and image internal multiples. Furthermore, it is demonstrated on the same field data that the FWM framework can also be used for data interpolation and primary/multiple separation.

Stereotomography of seismic data acquired on undulant topography

Stereotomography is a robust method for building velocity models from seismic reflection data, and it has been applied to offshore seismic data, but there is almost no stereotomographic study with rugged topographic conditions. We study the topographic effects on the slopes of locally coherent events of seismic data and develop an approach to calculate the slopes on an undulant observation surface using the horizontal and vertical components of slowness vectors estimated. Then, we develop an extended stereotomography with undulant observation surface based on the conventional one. Tests on synthetic data validate the extended stereotomography. Application to the field seismic data in a foothill belt in Xinjiang of the West China indicates that the extended stereotomography is an effective tool to build velocity models for prestack depth migration of seismic data acquired on rugged topography.

Computing near-surface velocity models for S-wave static corrections using raypath interferometry

A near-surface velocity model is one of the typical products generated when computing static corrections, particularly in the processing of PP data. Critically refracted waves are the input usually needed for this process. In addition, for the converted PS mode, S-wave near-surface corrections must be applied at the receiver locations. In this case, however, critically refracted S-waves are difficult to identify when using P-wave energy sources. We use the [Formula: see text]-[Formula: see text] representation of the converted-wave data to capture the intercept-time differences between receiver locations. These [Formula: see text]-differences are then used in the inversion of a near-surface S-wave velocity model. Our processing workflow provides not only a set of raypath-dependent S-wave static corrections, but also a velocity model that is based on those corrections. Our computed near-surface S-wave velocity model can be used for building migration velocity models or to initialize elastic full-waveform inversions. Our tests on synthetic and field data provided superior results to those obtained by using a surface-consistent solution.

Three‐Dimensional Passive‐Source Reverse‐Time Migration of Converted Waves: The Method

AbstractAt seismic discontinuities in the crust and mantle, part of the compressional wave energy converts to shear wave, and vice versa. These converted waves have been widely used in receiver function (RF) studies to image discontinuity structures in the Earth. While generally successful, the conventional RF method has its limitations and is suited mostly to flat or gently dipping structures. Among the efforts to overcome the limitations of the conventional RF method is the development of the wave‐theory‐based, passive‐source reverse‐time migration (PS‐RTM) for imaging complex seismic discontinuities and scatters. To date, PS‐RTM has been implemented only in 2D in the Cartesian coordinate for local problems and thus has limited applicability. In this paper, we introduce a 3D PS‐RTM approach in the spherical coordinate, which is better suited for regional and global problems. New computational procedures are developed to reduce artifacts and enhance migrated images, including back‐propagating the main arrival and the coda containing the converted waves separately, using a modified Helmholtz decomposition operator to separate the P and S modes in the back‐propagated wavefields, and applying an imaging condition that maintains a consistent polarity for a given velocity contrast. Our new approach allows us to use migration velocity models with realistic velocity discontinuities, improving accuracy of the migrated images. We present several synthetic experiments to demonstrate the method, using regional and teleseismic sources. The results show that both regional and teleseismic sources can illuminate complex structures and this method is well suited for imaging dipping interfaces and sharp lateral changes in discontinuity structures.

Common-reflection-surface-based prestack diffraction separation and imaging

Diffraction imaging can lead to high-resolution characterization of small-scale subsurface structures. A key step of diffraction imaging and tomography is diffraction separation and enhancement, especially in the full prestack data volume. We have considered point diffractors and developed a robust and fully data-driven workflow for prestack diffraction separation based on wavefront attributes, which are determined using the common-reflection-surface (CRS) method. In the first of two steps, we apply a zero-offset-based extrapolation operator for prestack diffraction separation, which combines the robustness and stability of the zero-offset CRS processing with enhanced resolution and improved illumination of the finite-offset CRS processing. In the second step, when the finite-offset diffracted events are separated, we apply a diffraction-based time migration velocity model building that provides high-quality diffraction velocity spectra. Applications of the new workflow to 2D/3D complex synthetic data confirm the superiority of prestack diffraction separation over the poststack method as well as the high potential of diffractions for improved time imaging.

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.

Cross-correlation least-squares reverse time migration in the pseudo-time domain

The least-squares reverse time migration (LSRTM) method with higher image resolution and amplitude is becoming increasingly popular. However, the LSRTM is not widely used in field land data processing because of its sensitivity to the initial migration velocity model, large computational cost and mismatch of amplitudes between the synthetic and observed data. To overcome the shortcomings of the conventional LSRTM, we propose a cross-correlation least-squares reverse time migration algorithm in pseudo-time domain (PTCLSRTM). Our algorithm not only reduces the depth/velocity ambiguities, but also reduces the effect of velocity error on the imaging results. It relieves the accuracy requirements on the migration velocity model of least-squares migration (LSM). The pseudo-time domain algorithm eliminates the irregular wavelength sampling in the vertical direction, thus it can reduce the vertical grid points and memory requirements used during computation, which makes our method more computationally efficient than the standard implementation. Besides, for field data applications, matching the recorded amplitudes is a very difficult task because of the viscoelastic nature of the Earth and inaccuracies in the estimation of the source wavelet. To relax the requirement for strong amplitude matching of LSM, we extend the normalized cross-correlation objective function to the pseudo-time domain. Our method is only sensitive to the similarity between the predicted and the observed data. Numerical tests on synthetic and land field data confirm the effectiveness of our method and its adaptability for complex models.

Reverse time migration of multiples: Reducing migration artifacts using the wavefield decomposition imaging condition

In the implementation of migration of multiples, reverse time migration (RTM) is superior to other migration algorithms because it can handle steeply dipping structures and offer high-resolution images of the complex subsurface. However, the RTM results using two-way wave equation contain high-amplitude, low-frequency noise and false images generated by improper wave paths in migration velocity model with sharp velocity interfaces or strong velocity gradients. To improve the imaging quality in RTM of multiples, we separate the upgoing and downgoing waves in the propagation of source and receiver wavefields. A complex function involved with the Hilbert transform is used in wavefield decomposition. Our approach is cost effective and avoids the large storage of wavefield snapshots required by the conventional wavefield separation technique. We applied migration of multiples with wavefield decomposition on a simple two-layer model and the Sigsbee 2B synthetic data set. Our results demonstrate that the proposed approach can improve the image generated by migration of multiples significantly.

Traveltime-based reflection full-waveform inversion for elastic medium

The main difficulty of full waveform inversion (FWI) based on local optimization methods is that it tends to trap in local minima or cycle-skipping associated with inaccurate initial models and waveform misfit functions, especially for elastic media. To address this issue, we first discuss the relationship between reverse time migration (RTM) and traditional reflection FWI (RFWI). Then, we present an elastic RFWI (ERFWI) methodology. However, for ERFWI, high nonlinearity still exists in data residuals related misfit function, when true amplitude migration is not adopted. To further mitigate the cycle skipping and avoid the requirements of true amplitude migration, we develop a traveltime-based ERFWI method to update the low-wavenumber components of P- and S-velocity models. The traveltime-based ERFWI only eliminates traveltime residuals along the wave-path of sensitivity kernels to extract the long-wavelength background of the middle and deep parts. Once the traveltime of reflected waves is described correctly, the inversion result using the traveltime-based ERFWI method could be used as a velocity model for prestack depth migration (PSDM) or as an initial model for the conventional FWI to obtain high-resolution velocity model. The final results by combining traveltime-based ERFWI and conventional FWI illustrate that the combined method can obtain an improved result, compared with regular FWI methods.

Architecture and tectono-stratigraphic evolution of the intramontane Baza Basin (Bétics, SE-Spain): Constraints from seismic imaging

The Baza basin is a large Neogene intramontane basin in the Bétic Cordillera of southern Spain that formed during the Tortonian (late Miocene). The Bétic Cordillera was produced by NW–SE oblique convergence between the Eurasian and African Plates. Three seismic reflection lines (each 18km long; vibroseis method) were acquired across the Baza basin to reveal the architecture of the sedimentary infill and faulting during basin formation. We applied rather conventional CDP data processing followed by first arrival P-wave tomography to provide complementary structural information and establish velocity models for the post-stack migration. These images show a highly asymmetric structure for the Basin with sediments thickening westward, reaching a maximum observed thickness of >2200m near the governing Baza Fault zone (BFZ). Three major seismic units (including several subunits) on top of the acoustic basement could be identified. We use stratigraphic information from the uplifted block of the BFZ and other outcrops at the basin edges together with available information from neighboring Bétic basins to tentatively correlate the seismic units to the known stratigraphy in the area. Until new drilling or surface outcrop data is not available, this interpretation is preliminary.The seismic units could be associated to Tortonian marine deposits, and latest Miocene to Pleistocene continental fluvio-lacustrine sediments. Individual strands of the BFZ truncate the basin sediments. Strong fault reflections imaged in two lines are the product of the large impedance contrast between sedimentary fill and basement. In the central part of the Basin several basement faults document strong deformation related to the early stages of basin formation. Some of these faults can be traced up to the shallowest imaged depth levels indicating activity until recent times.

Application of 3D stereotomography to the deep-sea data acquired in the South China Sea: a tomography inversion case

A 3D stereotomography algorithm, which is derived from the 3D Cartesian coordinate, is applied for the first time to the deep-sea data acquired in the LH area, South China Sea, to invert a macro velocity model for pre-stack depth migration. The successful implementation of stereotomography is highly dependent on the correct extraction of slowness components and the proper application of regularization terms. With the help of the structure tensor algorithm, a high-quality 3D stereotomography data space is achieved in a very efficient manner. Then, considering that the horizontal slowness in cross-line direction is usually unavailable for 3D narrow-azimuth data, the regularization terms must be enhanced to guarantee a stable convergence of the presented algorithm. The inverted model serves as a good model for the 3D pre-stack depth migration. The synthetic and real data examples demonstrated the robustness and effectiveness of the presented algorithm and the related schemes.

Elastic least-squares reverse time migration

We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTM solves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional least-squares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTM will produce migration noise stronger than that seen in the RTM images.

Extracting seismic uncertainties from tomographic velocity inversion and their use in reservoir risk analysis

Structural information in subsurface seismic images is critical for reservoir delineation, reserve estimation, and well planning. However, by its very nature, it is also uncertain. One cause of the image uncertainty is the migration velocity model that directly affects the position of migrated events, both laterally and vertically. (The term “velocity” is meant in the broad sense; i.e., it also includes the anisotropy parameters.) We present a method that accounts for uncertainties in a velocity model estimated by tomography and translates them into the migrated domain. Standard-deviation attributes on target horizon positions or layer thicknesses are extracted. The method includes quality controls for validating the estimated uncertainty attributes before integration with other downstream or interpretative information. The method is demonstrated on a North Sea area covered by data from multiple seismic surveys. We observe that uncertainties increase with model complexity or depth and decrease as the illumination diversity increases. The computed uncertainty maps constitute a valuable source of information for hierarchizing (both qualitatively and quantitatively) different areas in the survey. For the purpose of reservoir risk analysis, we combine our technique with other information (e.g., interpretation uncertainties) to map how uncertainties in the depth of the structural spill point impact the gross rock volume (GRV) estimation of a reservoir.

Extracting geologic information directly from high-resolution full-waveform inversion velocity models — A case study from offshore Trinidad

The East Coast Marine Area (ECMA) of Trinidad and Tobago contains producing gas fields where the imaging of seismic data is known to be challenging. This difficulty has been attributed to the combination of the Dolphin Main Fault, with more than 1 km of throw and large velocity contrasts of up to 30% in magnitude across it, and shallow gas and gas clouds causing very high attenuation. These factors lead to difficulties producing reliable and consistent velocity models. Previous velocity models — generated using traveltime tomography — contained inaccuracies that led to poor imaging and structural positioning, resulting in uncertainty when planning exploration and development drilling programs. In an attempt to reduce these uncertainties, a full-waveform inversion (FWI) feasibility study was performed over the most problematic area, with an initial velocity model built from a combination of legacy prestack time and depth migration velocity models and additional first-break refraction tomography. The geologic complexity near the main fault and the associated poor seismic data quality meant this model gave a poor fit between the synthetic and observed data (from a cycle-skipping point of view) at the lowest usable frequency. This led to the idea of applying a diving-wave-driven, offset-stripping workflow across each frequency band in the FWI, going from 3.5 Hz to 7.5 Hz. After successful application on the test area, the workflow was applied to ∼1400 km2 of 3D seismic over the ECMA. The final velocity model is structurally consistent and highly resolved, containing detailed shallow geologic features such as mud volcanoes, well-defined faults, and potential gas anomalies that were not visible on the legacy tomographic model. A blind test of well-pressure data correlates strongly with velocity drops in the FWI model, showing that FWI models can potentially provide very good input to regional pore-pressure-prediction studies.

Diffraction imaging method by Mahalanobis-based amplitude damping

Clarifying and locating small-scale discontinuities or inhomogeneities in the subsurface, such as faults and collapsed columns, plays a vital role in safe coal mining because these discontinuities or inhomogeneities may destroy the continuity of layers and result in dangerous mining accidents. Diffractions carry key information from these objects and therefore can be used for high-resolution imaging. However, diffracted/scattered waves are much weaker than reflected waves and consequently require separation before being imaged. We have developed a Mahalanobis-based diffraction imaging method by modifying the classic Kirchhoff formula with an exponential function to account for the dynamic differences between reflections and diffractions in the shot domain. The imaging method can automatically account for destroying of reflected waves, constructive stacking of diffracted waves, and strengthening of scattered waves. The method can overcome the difficulties in handling Fresnel apertures, and it is suitable for high-resolution imaging because of the consistency of the waveforms in the shot domain. Although the proposed method in principle requires a good migration velocity model for calculating elementary diffraction traveltimes, it is robust to an inaccurate migration velocity model. Two numerical experiments demonstrate the feasibility of the proposed method in removing reflections and highlighting diffractions, and one field application further confirms its efficiency in resolving masked faults and collapsed columns.

Migration velocity analysis using residual diffraction moveout: a real-data example

Unfocused seismic diffraction events carry direct information about errors in the migration-velocity model. The residual-diffraction-moveout (RDM) migration-velocity-analysis (MVA) method is a recent technique that extracts this information by means of adjusting ellipses or hyperbolas to uncollapsed migrated diffractions. In this paper, we apply this method, which has been tested so far only on synthetic data, to a real data set from the Viking Graben. After application of a plane-wave-destruction (PWD) filter to attenuate the reflected energy, the diffractions in the real data become interpretable and can be used for the RDM method. Our analysis demonstrates that the reflections need not be completely removed for this purpose. Beyond the need to identify and select diffraction events in post-stack migrated sections in the depth domain, the method has a very low computational cost and processing time. To reach an acceptable velocity model of comparable quality as one obtained with common-midpoint (CMP) processing, only two iterations were necessary.

Automatic time-domain velocity estimation based on an accelerated clustering method

Time-domain velocity and moveout parameters can be directly obtained from local event slopes, which are estimated on the prestack seismic gathers. In practice, there are always some errors in the estimated local slopes, especially in low signal-to-noise ratio (S/N) situations. Thus, subsurface velocity information may be hidden in the image domain spanned by velocity and other moveout parameters. We have developed an accelerated clustering algorithm to find cluster centers without prior information about the number of clusters. First, plane-wave destruction is implemented to estimate the local event slopes. For every sample in the seismic gathers, we obtain the estimations of velocity and its location in the image domain, according to the local event slopes. These mapped data points in the new domain exhibit the structure of groups. We represent these points by a mixture distribution model. Then, the cluster centers of the mixture distribution model are located, which correspond to maximum likelihood velocities of the main subsurface structures. Approximate velocity uncertainties bounds are used to select centers corresponding to reflections. Finally, interpolation is performed on the clustered unevenly sampled knot velocities to build the effective velocity model on regular grids. With synthetic and field data examples, we have determined that the proposed automatic velocity estimation method can give a stacking velocity model and a time migration velocity model with relatively high accuracy.

Prestack migration velocity analysis based on simplified two-parameter moveout equation

Stacking velocity VC2, vertical velocity ratio γ0, effective velocity ratio γeff, and anisotropic parameter χeff are correlated in the PS-converted-wave (PS-wave) anisotropic prestack Kirchhoff time migration (PKTM) velocity model and are thus difficult to independently determine. We extended the simplified two-parameter (stacking velocity VC2 and anisotropic parameter keff) moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter (stacking velocity VC2, vertical velocity ratio γ0, effective velocity ratio γeff, and anisotropic parameter keff) PS-wave anisotropic PKTM velocity model updating and process flow based on the simplified two-parameter moveout equation. In the proposed method, first, the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters; then, the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration. The vertical velocity ratio γ0 of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration. The initial effective velocity ratio γeff is calculated using the Thomsen (1999) equation in combination with the P-wave velocity analysis; ultimately, the final velocity model of the effective velocity ratio γeff is obtained by percentage scanning migration. This method simplifies the PS-wave parameter estimation in high-quality imaging, reduces the uncertainty of multiparameter estimations, and obtains good imaging results in practice.

Full‐wavefield migration: using surface and internal multiples in imaging

ABSTRACTMultiple scattering is usually ignored in migration algorithms, although it is a genuine part of the physical reflection response. When properly included, multiples can add to the illumination of the subsurface, although their crosstalk effects are removed. Therefore, we introduce full‐wavefield migration. It includes all multiples and transmission effects in deriving an image via an inversion approach. Since it tries to minimize the misfit between modeled and observed data, it may be considered a full waveform inversion process. However, full‐wavefield migration involves a forward modelling process that uses the estimated seismic image (i.e., the reflectivities) to generate the modelled full wavefield response, whereas a smooth migration velocity model can be used to describe the propagation effects. This separation of modelling in terms of scattering and propagation is not easily achievable when finite‐difference or finite‐element modelling is used. By this separation, a more linear inversion problem is obtained. Moreover, during the forward modelling, the wavefields are computed separately in the incident and scattered directions, which allows the implementation of various imaging conditions, such as imaging reflectors from below, and avoids low‐frequency image artefacts, such as typically observed during reverse‐time migration. The full wavefield modelling process also has the flexibility to image directly the total data (i.e., primaries and multiples together) or the primaries and the multiples separately. Based on various numerical data examples for the 2D and 3D cases, the advantages of this methodology are demonstrated.