We introduce a new tomographic method for estimating velocity macro‐models from seismic reflection data. In addition to traveltimes picked on locally coherent reflected events, the method requires that the associated local slopes of the events be picked simultaneously in the common‐shot and common‐receiver trace gathers. The data then consist of a discrete collection of traveltimes, positions and slopes for selected reflected events. Unlike traveltime tomography, picked events are only required to be locally coherent. It is not necessary to follow continuous arrivals all over the trace gathers. Indeed, the method does not require the introduction of interfaces in the model description.  Several approaches of tomography using the slope have already been proposed. We present a unified formulation for slope tomography methods, in which the model is described by the velocity field and a set of ray‐segment pairs associated with the reflected/diffracted events. We propose a new robust slope tomography method, which we call ‘stereotomography’. It consists of fitting all observed data (positions, slopes and traveltimes) to data calculated by ray tracing. There are no theoretical limitations in stereotomography for laterally heterogeneous velocity macro‐models.  Practically, traveltimes and slopes are picked on local slant stack panels. Ray multipathing can be accounted for since paths are discriminated by their associated slopes. The non‐linear inverse problem is iteratively resolved by a local optimization. The Fréchet derivatives are estimated by paraxial ray tracing.  Validation tests on 1‐D and 2‐D synthetic data are analysed. In the first 1‐D example, we study the sensitivity of the method to model parameters (using a singular‐value decomposition). The second 1‐D example evaluates picking precision and shows that it is sufficient for constraining the velocity field. The last example is a 2‐D application in which data are calculated directly by ray tracing. It shows the performance of the method in the presence of strong lateral velocity variations.

Seismic data regularization, which spatially transforms irregularly sampled acquired data to regularly sampled data, is a long-standing problem in seismic data processing. Data regularization can be implemented using Fourier theory by using a method that estimates the spatial frequency content on an irregularly sampled grid. The data can then be reconstructed on any desired grid. Difficulties arise from the nonorthogonality of the global Fourier basis functions on an irregular grid, which results in the problem of “spectral leakage”: energy from one Fourier coefficient leaks onto others. We investigate the nonorthogonality of the Fourier basis on an irregularly sampled grid and propose a technique called “antileakage Fourier transform” to overcome the spectral leakage. In the antileakage Fourier transform, we first solve for the most energetic Fourier coefficient, assuming that it causes the most severe leakage. To attenuate all aliases and the leakage of this component onto other Fourier coefficients, the data component corresponding to this most energetic Fourier coefficient is subtracted from the original input on the irregular grid. We then use this new input to solve for the next Fourier coefficient, repeating the procedure until all Fourier coefficients are estimated. This procedure is equivalent to “reorthogonalizing” the global Fourier basis on an irregularly sampled grid. We demonstrate the robustness and effectiveness of this technique with successful applications to both synthetic and real data examples.

Stereotomography is a new velocity estimation method. This tomographic approach aims at retrieving subsurface velocities from prestack seismic data. In addition to traveltimes, the slope of locally coherent events are picked simultaneously in common offset, common source, common receiver, and common midpoint gathers. As the picking is realized on locally coherent events, they do not need to be interpreted in terms of reflection on given interfaces, but may represent diffractions or reflections from anywhere in the image. In the high‐frequency approximation, each one of these events corresponds to a ray trajectory in the subsurface. Stereotomography consists of picking and analyzing these events to update both the associated ray paths and velocity model. In this paper, we describe the implementation of two critical features needed to put stereotomography into practice: an automatic picking tool and a robust multiscale iterative inversion technique. Applications to 2D reflection seismic are presented on synthetic data and on a 2D line extracted from a 3D towed streamer survey shot in West Africa for TotalFinaElf. The examples demonstrate that the method requires only minor human intervention and rapidly converges to a geologically plausible velocity model in these two very different and complex velocity regimes. The quality of the velocity models is verified by prestack depth migration results.

We propose an iterative method for the linearized prestack inversion of seismic profiles based on the asymptotic theory of wave propagation. For this purpose, we designed a very efficient technique for the downward continuation of an acoustic wavefield by ray methods. The different ray quantities required for the computation of the asymptotic inverse operator are estimated at each diffracting point where we want to recover the earth image. In the linearized inversion, we use the background velocity model obtained by velocity analysis. We determine the short wavelength components of the impedance distribution by linearized inversion of the seismograms observed at the surface of the model. Because the inverse operator is not exact, and because the source and station distribution is limited, the first iteration of our asymptotic inversion technique is not exact. We improve the images by an iterative procedure. Since the background velocity does not change between iterations. There is no need to retrace rays, and the same ray quantities are used in the iterations. For this reason our method is very fast and efficient. The results of the inversion demonstrate that iterations improve the spatial resolution of the model images since they mainly contribute to the increase in the short wavelength contents of the final image. A synthetic example with one‐dimensional (1-D) velocity background illustrates the main features of the inversion method. An example with two‐dimensional (2-D) heterogeneous background demonstrates our ability to handle multiple arrivals and a nearly perfect reconstruction of a flat horizon once the perturbations above it are known. Finally, we consider a seismic section taken from the Oseberg oil field in the North Sea off Norway. We show that the iterative asymptotic inversion is a reasonable and accurate alternative to methods based on finite differences. We also demonstrate that we are able to handle an important amount of data with presently available computers.