Igor Ravve

Full-azimuth subsurface angle domain wavefield decomposition and imaging Part I: Directional and reflection image gathers

We present a new subsurface angle-domain seismic imaging systemforgeneratingandextractinghigh-resolutioninformation about subsurface angle-dependent reflectivity. The system enables geophysicists to use all recorded seismic data in a continuousfashiondirectlyinthesubsurfacelocalangledomainLAD, resulting in two complementary, full-azimuth, common-imageangle gather systems: directional and reflection. The complete setofinformationfrombothtypesofanglegathersleadstoaccurate, high-resolution, reliable velocity model determination and reservoir characterization. The directional angle decomposition enables the implementation of specular and diffraction imaging in real 3D isotropic/anisotropic geological models, leading to simultaneous emphasis on continuous structural surfaces and discontinuous objects such as faults and small-scale fractures. Structural attributes at each subsurface point, e.g., dip, azimuth andcontinuity,canbederiveddirectlyfromthedirectionalangle gathers. The reflection-angle gathers display reflectivity as a function of the opening angle and opening azimuth. These gathers are most meaningful in the vicinity of actual local reflecting surfaces,wherethereflectionanglesaremeasuredwithrespectto the derived background specular direction. The reflection-angle gathers are used for automatic picking of full-azimuth angle-domainresidualmoveoutsRMOwhich,togetherwiththederived background orientations of the subsurface reflection horizons, provide a complete set of input data to isotropic/anisotropic tomography. The full-azimuth, angle-dependent amplitude variations are used for reliable and accurate amplitude versus angle andazimuthAVAZanalysisandreservoircharacterization.The proposed system is most effective for imaging and analysis below complex structures, such as subsalt and subbasalt, high-velocity carbonate rocks, shallow low-velocity gas pockets, and others. In addition, it enables accurate azimuthal anisotropic imaging and analysis, providing optimal solutions for fracture detectionandreservoircharacterization.

Full-Azimuth Angle Domain Imaging

This work presents a new seismic imaging system for generating and extracting high-resolution information about subsurface angle dependent reflectivity, with simultaneous emphasis on both continuous structural surfaces and discontinuous objects, such as faults and small-scale fractures. The system enables full-azimuth, angledependent seismic imaging using reflection data recorded through seismic acquisition surveys, especially wideazimuth and long offset data. Geometrical attributes, such as dip-azimuth and continuity of the local reflecting surfaces, can be automatically extracted directly from the full-azimuth angle gathers. Azimuthal anisotropy can be detected, leading to an accurate anisotropy model representation.

Full-azimuth subsurface angle domain wavefield decomposition and imaging: Part 2 — Local angle domain

We have developed an angle-based system, which defines the interaction between incident and reflected waves at a specific image point. We provide details about the technique used for angle-domain decomposition and imaging; in particular, the creation of two types of 3D subsurface angle gathers, as discussed in Part 1. The system, referred to as local angle domain (LAD) consists of two subsystems: directional and reflection. In the directional subsystem, the orientation of the ray-pair normal is represented by dip and azimuth. The reflection angle system is defined by the opening angle between the phase velocities of the incident and reflected rays, and by the opening azimuth, which describes the orientation of the ray-pair incidence plane measured in the ray-pair reflection plane. The directional angles are defined in a rotated local frame, and the opening azimuth is defined in the ray-pair reflection plane. The vertical axis of the local frame is collinear with a preset background normal to the physical ...

Constrained Dix inversion

We propose a stable inversion method to create geologically constrained instantaneous velocities from a set of sparse, irregularly picked stacking- or rms-velocity functions in vertical time. The method is primarily designed for building initial velocity models for curved-ray time migration and initial macromodels for depth migration and tomography. It is mainly applicable in regions containing compacted sediments, in which the velocity gradually increases with depth and can be laterally varying. Inversion is done in four stages: establishing a global initial background-velocity trend, applying an explicit unconstrained inversion, performing a constrained least-squares inversion, and finally, fine gridding. The method can be applied to create a new velocity field (create mode) or to update an existing one (update mode). In the create mode, initially, the velocity trend is assumed an exponential, asymptotically bounded function, defined locally by three parameters at each lateral node and calculated from a reference datum surface. Velocity picks related to nonsediment rocks, such as salt flanks or basalt boundaries, require different trend functions and therefore are treated differently. In the update mode, the velocity trend is a background-velocity field, normally used for time or depth imaging. The unconstrained inversion results in a piecewise-constant, residual instantaneous velocity with respect to the velocity trend and is mainly used for regularizing the input data. The constrained inversion is performed individually for each rms-velocity function in vertical time, and the lateral and vertical continuities are controlled by the global velocity-trend function. A special damping technique suppresses vertical oscillations of the results. Finally, smoothing and gridding (interpolation) are done for the resulting instantaneous velocity to generate a regular, fine grid in space and time. This method leads to a stable and geologically plausible velocity model, even in cases of noisy input rms-velocity or residual rms-velocity data.

Exponential asymptotically bounded velocity model: Part I — Effective models and velocity transformations

A new compacted-sediment, vertical-velocity model that represents the effect of gradually increasing velocities with depth is proposed. An asymptotically bounded, exponential velocity model is defined by three intuitive parameters. For a given layer, the parameters are 1) the velocity, 2) its vertical gradient at the top interface, and 3) an upper-limit velocity value. Time-depth relations, velocity transformations, hyperbolic, and nonhyperbolic moveouts are derived. The entire vertical velocity profile is composed of a set of layers, where the velocity function for each layer is defined by the proposed model. This method provides a basis for describing the subsurface using a smaller number of thick layers rather than using the classical, linear velocity model.

Anisotropic local tomography

Local tomography is interactive, ray-based, residual-interval-parameter analysis for updating background anisotropic velocity parameters. The method operates directly on image gathers generated by anisotropic curved-ray Kirchhoff time migration. A locally 1D, spatially varying, vertical transversely isotropic model is assumed. The background anisotropy parameters are the instantaneous (interval) vertical compression velocity VP and the two Thomsen anisotropy parameters, δ and e . The interval velocity δ is updated from short-offset reflection events, and e is updated from available long-offset data. The medium parameters are updated from the top down both vertically and by layers, one parameter at a time. The picked residual-anisotropy parameters correspond to the residual-moveout (RMO) curves that best fit the migrated reflection events. The method is based on splitting the contribution to the computed RMO at a given point into two parts: from overburden residual parameters and from the actual picked res...

Discussion and Reply

Sava and Fomel (2003) present an original approach for the generation of angle-domain common-image gathers (CIGs) by wave-equation migration. Their procedure consists of two steps. First, local-offset gathers are created during the migration. Second, depth-migrated angle gathers are generated by applying a slant stack to the local-offset gathers. Angle-domain gathers are very important for velocity analysis and amplitude versus offset (AVO) studies. Unfortunately, we believe that the procedure outlined in the article does not yield correct angle gathers when there are velocity errors. In the following, this is demonstrated for the simplest example of a single horizontal reflector embedded in a uniform-velocity medium.

Normal moveout velocity for pure‐mode and converted waves in layered orthorhombic medium

We study the azimuthally dependent hyperbolic moveout approximation for small angles (or offsets) for quasi-compressional, quasi-shear, and converted waves in onedimensional multi-layer orthorhombic media. The vertical orthorhombic axis is the same for all layers, but the azimuthal orientation of the horizontal orthorhombic axes at each layer may be different. By starting with the known equation for normal moveout velocity with respect to the surface-offset azimuth and applying our derived relationship between the surface-offset azimuth and phase-velocity azimuth, we obtain the normal moveout velocity versus the phase-velocity azimuth. As the surface offset/azimuth moveout dependence is required for analysing azimuthally dependent moveout parameters directly from time-domain rich azimuth gathers, our phase angle/azimuth formulas are required for analysing azimuthally dependent residual moveout along the migrated local-angle-domain common image gathers. The angle and azimuth parameters of the local-angle-domain gathers represent the opening angle between the incidence and reflection slowness vectors and the azimuth of the phase velocity ψphs at the image points in the specular direction. Our derivation of the effective velocity parameters for a multi-layer structure is based on the fact that, for a one-dimensional model assumption, the horizontal slowness ph and the azimuth of the phase velocity ψphs remain constant along the entire ray (wave) path. We introduce a special set of auxiliary parameters that allow us to establish equivalent effective model parameters in a simple summation manner. We then transform this set of parameters into three widely used effective parameters: fast and slow normal moveout velocities and azimuth of the slow one. For completeness, we show that these three effective normal moveout velocity parameters can be equivalently obtained in both surface-offset azimuth and phase-velocity azimuth domains.

Specular/diffraction imaging by full azimuth subsurface angle domain decomposition

This work presents a new seismic imaging system for generating amplitude preserved, three-dimensional directional gathers. The proposed method is based on directional angle decomposition that enables the implementation of both specular and diffraction imaging in real 3D isotropic/anisotropic geological models, leading to simultaneous emphasis on both continuous structural surfaces and discontinuous objects, such as faults and small-scale fractures. Structural attributes at each subsurface point, e.g., dip, azimuth and continuity, can be derived directly from the directional angle gathers. The proposed approach is most effective for imaging and analysis below complex structures, such as subsalt and subbasalt, high-velocity carbonate rocks, shallow velocity anomalies, and others.

Fourth-order normal moveout velocity in elastic layered orthorhombic media — Part 1: Slowness-azimuth domain

Considering all types of pure-mode and converted waves, we derive the azimuthally dependent, fourth-order normal moveout (NMO) velocity functions, and hence the corresponding effective anellipticity functions, for horizontally layered orthorhombic media. We emphasize that this paper does not suggest a new nonhyperbolic traveltime approximation; rather, it provides exact expressions of the NMO series coefficients, computed for normal-incidence rays, which can then be further used within known azimuthally dependent traveltime approximations for short to moderate offsets. We do not assume weak anisotropy or acoustic approximation for P-waves. At each layer, the elastic parameters, thickness, and azimuth of the orthorhombic vertical symmetry planes are considered to be different. We distinguish between two different azimuths: slowness azimuth (part 1 of this paper) and offset azimuth (part 2 of this paper). In part 1, the slownessazimuth domain NMO is approximated as a series of either infinitesimal horizontal slowness (slowness-azimuth/slowness domain) or infinitesimal offsets (slowness-azimuth/offset domain). Similarly, in part 2, we distinguish between two offset-azimuth domains: offset-azimuth/slowness and offset-azimuth/offset. Note that the azimuthally dependent NMO velocity functions of each of the four cases are different. The validity of the method is tested by introducing our derived azimuthally dependent, fourth-order effective anellipticity, into the well-known azimuthally dependent, asymptotic nonhyperbolic traveltime approximation, in which we compare the traveltime approximation versus exact numerical ray tracing for short to moderate offsets. It is clearly shown that for these types of azimuthally anisotropic layered models, the fourth-order terms are essential even for relatively small horizontal-slowness values or short offsets.