International audienceThe aim of inverting seismic waveforms is to obtain the “best” earth model. The best model is defined as the one producing seismograms that best match (usually under a least‐squares criterion) those recorded. Our approach is nonlinear in the sense that we synthesize seismograms without using any linearization of the elastic wave equation. Since we use rather complete data sets without any spatial aliasing, we do not have the problem of secondary minima (Tarantola, 1986). Nevertheless, our gradient methods fail to converge if the starting earth model is far from the true earth (Mora, 1987; Kolb et al., 1986; Pica et al., 1989)

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We present a new subsurface angle-domain seismic imaging system for generating and extracting high-resolution information about subsurface angle-dependent reflectivity. The system enables geophysicists to use all recorded seismic data in a continuous fashion directly in the subsurface local angle domain ͑LAD͒, resulting in two complementary, full-azimuth, common-imageangle gather systems: directional and reflection. The complete set of information from both types of angle gathers leads to accurate, 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 and continuity, can be derived directly from the directional angle 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, where the reflection angles are measured with respect to the derived background specular direction. The reflection-angle gathers are used for automatic picking of full-azimuth angle-domain residual moveouts ͑RMO͒ which, together with the derived 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 and azimuth ͑AVAZ͒ analysis and reservoir characterization. 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 detection and reservoir characterization.

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A method for velocity and interface depth determination based on tomography of migrated common reflecting point (CRP) gathers is presented. The method is derived from the tomographic principle that relates traveltime change along a given ray to perturbations in slowness and layer depths. The tomographic principle is used to convert depth errors in migrated CRP gathers to time errors along a CRP ray pair and thus enable use of conventional traveltime tomography. It is also used to affect a very fast prestack migration and set up the tomography matrix. The velocity‐depth determination method uses the available offsets of all CRPs and inverts for the parameters of all layers simultaneously. Hand picking of depth errors on CRP gathers is avoided by a method where the tomography matrix operates directly on the migrated gathers. The velocity‐depth determination method is demonstrated on a synthetic example and on a field example from the North Sea.

A new time integration technique for use in forward modelling programmes is introduced. The technique presents an alternative to second-order temporal differencing. It is based on a Chebyshev expansion of the formal evolution operator to the spatially discretized wave equation. The computational effort in forward modelling based on the new technique is about the same as in methods based on temporal differencing. However, machine accuracy can be obtained. The implementation of the technique to solve the acoustic wave equation in two spatial dimensions is described. Finally, an example of using the technique to solve a problem of wave propagation in a single layer is presented. I N T R O D U C T I O NA new time integration technique is proposed for applications in direct forward modelling algorithms. The technique can be applied to a number of methods including the finite-difference method, the finite-element method and the Fourier method. It is very accurate, yet involves about the same computational effort as second-order temporal differencing. It is therefore most suitable for spatially accurate methods like high-order finite differences or the Fourier method. The technique has already been successfully applied to solve the one-way wave equation in one dimension (1-D) (Tal-Ezer 1986), and to the Schrodinger wave equation in one and two spatial dimensions (Tal-Ezer and Kosloff, R. 1984). In both cases comparison with known solutions showed machine accuracy.In most direct methods there are separate temporal and spatial approximations. For the temporal approximation the most common practice has been to use secondorder differencing (e.g. Kelly, Ward, Treitel

The complete solution to an inverse problem, including information on accuracy and resolution, is given by the a posterJori probability density in the model space. By running a modified simulated annealing, samples from the model space can be drawn in such a way that their frequencies of occurrence approximate their a posteriori likelihoods. Using this method, maximum likelihood estimation and uncertainty analysis of seismic background velocity models are performed on multioffset seismic data. The misfit between observed and synthetic waveforms within the time windows along computed multioffset travel times, is used as an objective function for the simulated annealing approach. The real medium is modeled as a series of layers separated by curved interfaces. Lateral velocity variations within the layers are determined by interpolation from specified values at a number of sampling points. The input data consists of multioffset seismic data. Additionally, zerooffset times are used to migrate the reflectors in time to the depth domain. The multioffset times are calculated by an efficient ray-tracing algorithm .which allows inversion of a large number of seismograms. The a posteriori probability density for this problem is highly multidimensional and highly multimodal. Therefore, the information contained in this distribution cannot be adequately represented by standard deviations and covariances. However, by sequentially displaying a large number of images, computed from the a posterjori background velocity samples and the data, it is possible to convey to the spectator a better understanding of what information we really have on the subsurface.

A linear gradient elution method has been applied to the HPLC analysis of plant and scale insect red anthraquinonoid mordant dyes and molluscan blue and red‐purple indigoid vat dyes. The method enables the use of the same elution program for the determination of different chemical classes of dyes. In addition, it significantly shortens the retention times of natural anthraquinonoid dyes over those previously published. For the first time a new dye, probably dibromoindirubin, has been detected in the Murex trunculus sea snail. The dye families investigated include the ones most often found on ancient textiles and shards from dyeing vessels in Israel and other regions.