Migration in the angle domain creates seismic images for different reflection angles. We present a method for computing angle-domain common-image gathers from seismic images obtained by depth migration using wavefield continuation. Our method operates on prestack migrated images and produces the output as a function of the reflection angle, not as a function of offset ray parameter as in other alternative approaches. The method amounts to a radial-trace transform in the Fourier domain and is equivalent to a slant stack in the space domain. We obtain the angle gathers using a stretch technique that enables us to impose smoothness through regularization. Several examples show that our method is accurate, fast, robust, and easy to implement. The main anticipated applications of our method are in the areas of migration-velocity analysis and amplitude-versus-angle analysis.

Prestack depth migration of shot profiles by downward continuation is a practical imaging algorithm that is especially cost‐effective for sparse‐shot wide‐azimuth geometries. The interpretation of offset as the displacement between the downward‐propagating (shot) wavefield and upward‐propagating (receiver) wavefield enables us to extract offset‐domain common image‐point (CIP) gathers during shot‐profile migration. The offset‐domain gathers can then be transformed to the angle domain with a radial‐trace mapping originally introduced for shot‐geophone migration. The computational implications of this procedure include both the additional cost of multioffset imaging and an implicit transformation from shot‐geophone to midpoint‐offset coordinates. Although this algorithm provides a mechanism for imaging angle‐dependent reflectivity via shot‐profile migration, for sparse‐shot geometries the fundamental problem of shot‐aliasing may severely impact the quality of CIP gathers.

Seismic imaging based on single-scattering approximation is based on analysis of the match between the source and receiver wavefields at every image location. Wavefields at depth are functions of space and time and are reconstructed from surface data either by integral methods (Kirchhoff migration) or by differential methods (reverse-time or wavefield extrapolation migration). Different methods can be used to analyze wavefield matching, of which cross-correlation is a popular option. Implementation of a simple imaging condition requires time cross-correlation of source and receiver wavefields, followed by extraction of the zero time lag. A generalized imaging condition operates by cross-correlation in both space and time, followed by image extraction at zero time lag. Images at different spatial cross-correlation lags are indicators of imaging accuracy and are also used for image angle-decomposition. In this paper, we introduce an alternative prestack imaging condition in which we preserve multiple lags of the time cross-correlation. Prestack images are described as functions of time-shifts as opposed to space-shifts between source and receiver wavefields. This imaging condition is applicable to migration by Kirchhoff, wavefield extrapolation or reverse-time techniques. The transformation allows construction of common-image gathers presented as function of either time-shift or reflection angle at every location in space. Inaccurate migration velocity is revealed by angle-domain common-image gathers with non-flat events. Computational experiments using a synthetic dataset from a complex salt model demonstrate the main features of the method.

Multicomponent data are not usually processed with specifically designed procedures, but with procedures analogous to the ones used for single-component data. In isotropic media, the vertical and horizontal components of the data are commonly taken as proxies for the P-and S-wave modes which are imaged independently with acoustic wave equations. This procedure works only if the vertical and horizontal component accurately represent P-and S-wave modes, which is not true in general. Therefore, multicomponent images constructed with this procedure exhibit artifacts caused by the incorrect wave mode separation at the surface. An alternative procedure for elastic imaging uses the full vector fields for wavefield reconstruction and imaging. The wavefields are reconstructed using the multicomponent data as a boundary condition for a numerical solution to the elastic wave equation. The key component for wavefield migration is the imaging condition that evaluates the match between wavefields reconstructed from sources and receivers. For vector wavefields, a simple component-by-component crosscorrelation between two wavefields leads to artifacts caused by crosstalk between the unseparated wave modes. An alternative method is to separate elastic wavefields after reconstruction in the subsurface and implement the imaging condition as cross-correlation of pure wave modes instead of the Cartesian components of the displacement wavefield. This approach leads to images that are easier to interpret, since they describe reflectivity of specified wave modes at interfaces of physical properties. As for imaging with acoustic wavefields, the elastic imaging condition can be formulated conventionally (cross-correlation with zero lag in space and time), as well as extended to non-zero space and time lags. The elastic images produced by an extended imaging condition can be used for angle decomposition of primary (PP or SS) and converted (PS or SP) reflectivity. Angle gathers constructed with this procedure have applications for migration velocity analysis and amplitude versus angle analysis.

A B S T R A C TWe present a migration velocity analysis (MVA) method based on wavefield extrapolation. Similarly to conventional MVA, our method aims at iteratively improving the quality of the migrated image, as measured by the flatness of angle-domain commonimage gathers (ADCIGs) over the aperture-angle axis. However, instead of inverting the depth errors measured in ADCIGs using ray-based tomography, we invert 'image perturbations' using a linearized wave-equation operator. This operator relates perturbations of the migrated image to perturbations of the migration velocity. We use prestack Stolt residual migration to define the image perturbations that maximize the focusing and flatness of ADCIGs.Our linearized operator relates slowness perturbations to image perturbations, based on a truncation of the Born scattering series to the first-order term. To avoid divergence of the inversion procedure when the velocity perturbations are too large for Born linearization of the wave equation, we do not invert directly the image perturbations obtained by residual migration, but a linearized version of the image perturbations. The linearized image perturbations are computed by a linearized prestack residual migration operator applied to the background image. We use numerical examples to illustrate how the backprojection of the linearized image perturbations, i.e. the gradient of our objective function, is well behaved, even in cases when backprojection of the original image perturbations would mislead the inversion and take it in the wrong direction.We demonstrate with simple synthetic examples that our method converges even when the initial velocity model is far from correct. In a companion paper, we illustrate the full potential of our method for estimating velocity anomalies under complex salt bodies. I N T R O D U C T I O NSeismic imaging is a two-step process: velocity estimation and migration. As the velocity function becomes more complex, the two steps become increasingly interdependent. In complex depth imaging problems, velocity estimation and migration are applied iteratively in a loop. To ensure that this iterative imaging process converges to a satisfactory model, it is crucial that the migration and the velocity estimation are consistent with each other.Kirchhoff migration often fails in areas of complex geology, such as subsalt, because the wavefield is severely distorted by lateral velocity variations leading to complex multipathing. As the shortcomings of Kirchhoff migration have become apparent (O'Brien and Etgen 1998), there has been renewed interest in wave-equation migration, and computationally efficient 3D prestack depth migration methods have been developed (Biondi and Palacharla 1996;Biondi 1997;Mosher, Foster and Hassanzadeh 1997). However, no corresponding progress has been made in the development of migration velocity analysis (MVA) methods based on the wave equation. We aim at filling this gap by presenting a method that, at least in principle, can be used in conjunction with any downward-con...

Myostatin is a secreted TGF-beta family member that controls skeletal muscle growth. Humans, cattle, and dogs carrying natural loss-of-function mutations in the myostatin gene and myostatin knockout mice exhibit significant increases in skeletal muscle mass. Treatment of adult mice with antimyostatin antibodies also resulted in significant muscle mass increases. However, myostatin-knockout mice that were treated with a soluble form of the activin type II receptor (ActRII) B increased their muscle mass by an additional 15-25%, indicating that there is at least one additional ligand, in addition to myostatin, that functions to limit muscle growth. Here, both soluble ActRII and -IIB fragment-crystallizable proteins were used to affinity purify their native ligands from human and mouse sera. Using mass spectrometry-based proteomics and in vitro binding assays we have identified and confirmed that a number of TGF-beta family members, including myostatin, activins-A, -B, and -AB, bone morphogenetic proteins (BMPs) -9, -10, and -11, bind to both ActRIIs. Many of these factors, such as BMPs-11, -9, and -10 were discovered in systemic circulation for the first time, indicating that these ligands may also act in an endocrine fashion. Using a promoter-specific gene reporter assay, we demonstrated that soluble ActRIIB fragment-crystallizable proteins can inhibit the canonical signaling induced by these ligands. In addition, like myostatin, these factors were able to block the differentiation of myoblast cells into myotubes. However, in addition to myostatin, only BMP-11, and activins-A, -B, and -AB could be blocked from inhibiting the myoblast-to-myotube differentiation with both soluble ActRIIs, thus implicating them as potential novel regulators of muscle growth.

A B S T R A C TWavefield-based migration velocity analysis using the semblance principle requires computation of images in an extended space in which we can evaluate the imaging consistency as a function of overlapping experiments. Usual industry practice is to assemble those seismic images in common-image gathers that represent reflectivity as a function of depth and extensions, e.g., reflection angles. We introduce extended common-image point (CIP) gathers constructed only as a function of the spaceand time-lag extensions at sparse and irregularly distributed points in the image. Semblance analysis using CIP's constructed by this procedure is advantageous because we do not need to compute gathers at regular surface locations and we do not need to compute extensions at all depth levels. The CIP's also give us the flexibility to distribute them in the image at irregular locations aligned with the geologic structure. Furthermore, the CIP's remove the depth bias of common-image gathers constructed as a function of the depth axis. An interpretation of the CIP's using the scattering theory shows that they are scattered wavefields associated with sources and receivers inside the subsurface. Thus, when the surface wavefields are correctly reconstructed, the extended CIP's are characterized by focused energy at the origin of the spaceand time-lag axes. Otherwise, the energy defocuses from the origin of the lag axes proportionally with the cumulative velocity error in the overburden. This information can be used for wavefield-based tomographic updates of the velocity model, and if the velocity used for imaging is correct, the coordinate-independent CIP's can be a decomposed as a function of the angles of incidence.

We propose a new objective function for wave-equation inversion that seeks to minimize the norm of the weighted deconvolution between synthetic and observed data. Compared to more the conventional difference-based objective function which minimizes the norm of the residual between synthetic and observed data, the deconvolution-based objective function is less susceptible to cycle skipping and local minima. Compared to a crosscorrelation-based objective function, the deconvolution-based objective function is less sensitive to a bandlimited or non-impulsive source function, which may result in a nonzero gradient of the objective function even when the constructed velocity model matches the true model.