Correct identification of geologic discontinuities, such as faults, pinch-outs, and small-size scattering objects, is a primary challenge of the seismic method. Seismic response from these objects is encoded in diffractions. Our method images local heterogeneities of the subsurface using diffracted seismic events. The method is based on coherent summation of diffracted waves arising in media that include interface discontinuities and local velocity heterogeneities. This is done using a correlation procedure that coherently focuses diffraction energy on a seismic section by flattening diffraction events using a new local-time-correction formula to parameterize diffraction traveltime curves. This time correction, which is based on the multifocusing method, depends on two parameters: the emergent angle and the radius of curvature of the diffracted wavefront. These parameters are estimated directly from prestack seismic traces. The diffraction multifocusing stack (DMFS) can separate diffracted and reflected energy on a stacked section by focusing diffractions to the diffraction location and defocusing the reflection energy over a large area.

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The problem of multiple attenuation has been solved only partially. One of the most common methods of attenuating multiples is an approach based on the Radon transform. It is commonly accepted that the parabolic Radon transform method is only able to attenuate multiples with significant moveouts. We propose a new 2-D method for attenuation of both surface‐related and interbed multiples in the parabolic τ-p domain. The method is based on the prediction of a multiple model from the wavefront characteristics of the primary events. Multiple prediction comprises the following steps: 1) For a given multiple code, the angles of emergence and the radii of wavefront curvatures are estimated for primary reflections for each receiver in the common‐shotpoint gather. 2) The intermediate points which compose a specified multiple event are determined for each shot‐receiver pair. 3) Traveltimes of the multiples are calculated. Wavefields within time windows around the predicted traveltime curves may be considered as multiple model traces which we use for multiple attenuation process. Using the predicted multiple traveltimes, we can define the area in the τ-p domain which contains the main energy of the multiple event. Resolution improvement of the parabolic Radon operator can be achieved through a simple multiplication of each sample in the τ-p space by a nonlinear semblance function. In this work, we follow the idea of defining the multiple reject areas automatically by comparing the energy of the multiple model and the original input data in the τ-p space. We illustrate the usefulness of this algorithm for the attenuation of multiples on both synthetic and real data.

A new method for predicting different kinds of multiples and peg‐leg reflections in unstacked seismic data is discussed. The basis for this method is the fact that kinematic properties of multiples can be represented as a combination of kinematic properties of primary reflections. The prediction is made using a two‐step process. In the first step, the values for the angle of emergence and radius of curvature of the wavefront for primary reflections from ‘multiple‐generating’ interfaces are obtained. These parameters are estimated directly from unstacked data for every source point using the homeomorphic‐imaging technique. The second step consists of prediction of multiples from primary reflections that satisfy a so‐called ‘multiple condition’. This condition is the equality of the absolute values of the angles of emergence calculated from the first step. This method is effective even in complex media and information on the subsurface geology is not required. The parameters are estimated directly from the unstacked data and do not require any computational efforts such as in wavefield extrapolation of data.

A tomographic imaging technique combined with coherence inversion is proposed for constructing a near-surface model from refraction events. A model obtained from coherence inversion serves as a good background model for the tomographic reconstruction. A simultaneous iterative reconstruction technique (SIRT) algorithm was used for this purpose. This is a simple algorithm and can be easily adapted to irregular acquisition geometry and limited angular aperture. Using synthetic data it was shown that the proposed procedure can be used for determination of local velocity anomalies in a shallow subsurface. The technique was also tested on a real data set. lntroduction Seismic refracted waves have different applications in seismic prospecting. They can be relatively easily identified on seismic records in first arrivals. First breaks are the most useful arrivals on shot records for solving the problem of field static correction (Palmer 1986;Russell 1989). Refraction tomography has recently been used to compute low-velocity near-surface models. In these methods the initial velocitydepth model above the refractor is modified to minimize the difference between observed and calculated refraction traveltimes. The latter are computed by tracing refraction waves through the model. A number of tomographic techniques have been described. Some of them assume that the velocity in the first layer is known from direct wave arrivals or uphole measuring (Hampson and Russell 1984;Schneider and I(uo 1985). In practice, however, it is not always available. In the other group algorithms, the velocity in the first layer is estimated together with the refractor velocity and depth (de Amorim, Hubral and Tygel 1987; C)lsen 1989;Docherty 1992).It is assumed that the velocity can vary laterally and the weathering layer is divided into vertical bars of constant velocity. Each bar is bounded above by the observation surface and below by the refractor. A number of authors have proposed dividing the weathering layer into a grid of rectangular cells and taking into account diving rays travelling subhorizontally (White