Amélia Novais

A comparison of imaging conditions for wave-equation shot-profile migration

The application of a deconvolution imaging condition in wave-equation shot-profile migration is important to provide illumination compensation and amplitude recovery. Particularly if the aim is to successfully recover a measure of the medium reflectivity, an imaging condition that destroys amplitudes is unacceptable. We study a set of imaging conditions with illumination compensation. The imaging conditions are evaluated by the quality of the output amplitudes and artifacts produced. In numerical experiments using a vertically inhomogeneous velocity model, the best of all imaging conditions we tested is the one that divides the crosscorrelation of upgoing and downgoing wavefields by the autocorrelation of the downgoing wavefield, also known as the illumination map. In an application to Marmousi data, unconditional division by autocorrelation turned out to be unstable. Effective stabilization was achieved by smoothing the illumination map.

Obliquity-correction imaging condition for reverse time migration

The quality of seismic images obtained by reverse time migration (RTM) strongly depends on the imaging condition. We propose a new imaging condition that is motivated by stationary phase analysis of the classical crosscorrelation imaging condition. Its implementation requires the Poynting vector of the source and receiver wavefields at the imaging point. An obliquity correction is added to compensate for the reflector dip effect on amplitudes of RTM. Numerical experiments show that using an imaging condition with obliquity compensation improves reverse time migration by reducing backscattering artifacts and improving illumination compensation.

Time-migration velocity analysis by image-wave propagation of common-image gathers

Image-wave propagation or velocity continuation describes the variation of the migrated position of a seismic event as a function of migration velocity. Image-wave propagation in the common-image gather (CIG) domain can be combined with residual-moveout analysis for iterative migration velocity analysis (MVA). Velocity continuation of CIGs leads to a detection of those velocities in which events flatten. Although image-wave continuation is based on the assumption of a constant migration velocity, the procedure can be applied in inhomogeneous media. For this purpose, CIGs obtained by migration with an inhomogeneous macrovelocity model are continued starting from a constant reference velocity. The interpretation of continued CIGs, as if they were obtained from residual migrations, leads to a correction formula that translates residual flattening velocities into absolute time-migration velocities. In this way, the migration velocity model can be improved iteratively until a satisfactory result is reached. Wi...

Offset continuation (OCO) ray tracing using OCO trajectories

Offset continuation (OCO) is a seismic configuration transform designed to simulate a seismic section as if obtained with a certain source-receiver offset using the data measured with another offset. Since OCO is dependent on the velocity model used in the process, comparison of the simulated section to an acquired section allows for the extraction of velocity information. An algorithm for such a horizon-oriented velocity analysis is based on so-called OCO rays. These OCO rays describe the output point of an OCO as a function of the Root Mean Square (RMS) velocity. The intersection point of an OCO ray with the picked traveltime curve in the acquired data corresponding to the output half-offset defines the RMS velocity at that position. We theoretically relate the OCO rays to the kinematic properties of OCO image waves that describe the continuous transformation of the common-offset reflection event from one offset to another. By applying the method of characteristics to the OCO image-wave equation, we obtain a raytracing-like procedure that allows to construct OCO trajectories describing the position of the OCO output point under varying offset. The endpoints of these OCO trajectories for a single input point and different values of the RMS velocity form then the OCO rays. A numerical example demonstrates that the developed ray-tracing procedure leads to reliable OCO rays, which in turn provide high-quality RMS velocities. The proposed procedure can be carried out fully automatically, while conventional velocity analysis needs human intervention. Moreover, since velocities are extracted using offset sections, more redundancy is available or, alternatively, OCO velocities can be studied as a function of offset.

2.5D reverse-time migration

Reverse-time migration (RTM) in 2.5D offers an alternative to improve resolution and amplitude when imaging 2D seismic data. Wave propagation in 2.5D assumes translational invariance of the velocity model. Under this assumption, we implement a finite-difference (FD) modeling algorithm in the mixed time-space/wavenumber domain to simulate the velocity and pressure fields for acoustic wave propagation and apply it in RTM. The 2.5D FD algorithm is truly parallel, allowing an efficient implementation in clusters. Storage and computing time requirements are strongly reduced compared to a full 3D FD simulation of the wave propagation. This feature makes 2.5D RTM much more efficient than 3D RTM, while achieving improved modeling of 3D geometrical spreading and phase properties of the seismic waveform in comparison to 2D RTM. Together with an imaging condition that compensates for uneven illumination and/or the obliquity factor, this allows recover of amplitudes proportional to the earth’s reflectivity. Numerical...

Fast estimation of common-reflection-surface parameters using local slopes

Present-day techniques to estimate the traveltime parameters of the common-reflection-surface (CRS) stack are tedious, time-consuming, and expensive processes based on local coherence analyses along a large number of trial surfaces. With the 2D CRS method, faster and cheaper determination is possible. The complete set of CRS parameters can be extracted from seismic data by an application of modern local-slope-extraction techniques. The necessary information about the CRS parameters is contained in the slopes of the common-midpoint section at the central point and one or several common-offset sections in its vicinity. We studied two procedures for the CRS parameter extraction technique. Their difference lies in the way the common-offset parameters are determined. One technique requires slope-derivative information (a possible source of instability); the other uses slope information at two different locations and less data redundancy. Testing on a synthetic data example proved that the procedures are suffic...

Migration Velocity Analysis Using Residual Diffraction Moveout in the Pre-stack Depth Domain

In this paper we present a methodology for migration velocity improvement and diffraction localisation based on a moveout analysis of over- or undermigrated diffraction events in the depth domain. The method does not depend on any requirement apart from a fairly arbitrary initial velocity model as input. We demonstrate that the method can be applied in both the pre- or post-stack domains without any restrictions. For each iteration, the method provides an update to the velocity model and consequently to the diffraction locations. The algorithm is based on the focusing of remigration velocity rays from uncollapsed migrated diffraction curves. These velocity rays are constructed from a ray-tracing like approach applied to the image-wave equation for velocity continuation. After choosing and picking the diffraction events in the pre-stack migrated domain, the method has a very low computational cost, and the diffraction points are located automatically. We demonstrate the feasibility of our method using a synthetic nonzero-offset data example.

A Comparison of Splitting Techniques for 3D Complex Padé Fourier Finite Difference Migration

Three-dimensional wave-equation migration techniques are still quite expensive because of the huge matrices that need to be inverted. Several techniques have been proposed to reduce this cost by splitting the full 3D problem into a sequence of 2D problems. We compare the performance of splitting techniques for stable 3D Fourier finite-difference (FFD) migration techniques in terms of image quality and computational cost. The FFD methods are complex Pade FFD and FFD plus interpolation, and the compared splitting techniques are two- and four-way splitting as well as alternating four-way splitting, that is, splitting into the coordinate directions at one depth and the diagonal directions at the next depth level. From numerical examples in homogeneous and inhomogeneous media, we conclude that, though theoretically less accurate, alternate four-way splitting yields results of comparable quality as full four-way splitting at the cost of two-way splitting.

2.5D Elastic Finite-Difference Modeling

Finite difference modeling of elastic wavefields in 2.5D is described in the velocity-stress formulation for anisotropic media. The 2.5D modeling computes the 3D elastic wavefield in a medium which is translation invariant in one coordinate direction. The approach is appealing due reduced storage and computing time when compared to full 3D finite difference elastic modeling. The scheme handles inhomogeneities in mass density and elastic moduli, includes free-surface and perfect matched layers as absorbing boundaries. High order finite difference operator allows the use of a coarse mesh, reducing the storage even more without producing numerical dispersion and numerical anisotropy. Numerical experiments show the accuracy of the scheme, its computational efficiency and the importance of 2.5D modeling in complex elastic media.

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.