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Hydrocarbon reservoir characterization commonly combines seismic, petrophysical, and well-log information in a variety of procedures. As an inference problem, this combination can be formulated in a unified inverse framework, reducing the bias of nonlinear relationships among intermediate variables and providing a comprehensive calculation of uncertainties at final estimates of the medium parameters. In addition, the unified formulation leads to the joint estimation of reservoir and medium elastic properties as well as related parameters of interests. This problem is formulated from a set of continuous variables that commonly characterizes the reservoir (total porosity, shale volume fraction, and water saturation), which can be related to the medium mechanical properties with a petrophysical model calibrated to the specific setting of the reservoir and target stratum. The joint model property configuration is related to the observed seismic data via Zoeppritz incidence-angle-dependent reflectivity and convolution with a source wavelet for each CDP gather. Data and calibrated information are combined in a posterior probability density of the model parameters that is evaluated with a sampling approach, using a Markov-chain Monte Carlo algorithm. From a large number of realizations, one can calculate expected values and full marginal probability distributions for reservoir properties and elastic properties. The method is illustrated with the estimation of reservoir parameters at a gas reservoir presenting a Class 2 AVA response, with focus on the estimation of water saturation. The calculated saturation probability distributions show coherent results with the known saturation at various well locations.

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In complex areas, the attenuation of specular and diffracted multiples in image space is an attractive alternative to surface-related multiple elimination ͑SRME͒ and to data space Radon filtering. We present the equations that map, via waveequation migration, 2D diffracted and specular water-bottom multiples from data space to image space. We show the equations for both subsurface-offset-domain common-imagegathers ͑SODCIGs͒ and angle-domain common-image-gathers ͑ADCIGs͒. We demonstrate that when migrated with sediment velocities, the over-migrated multiples map to predictable regions in both SODCIGs and ADCIGs. Specular multiples focus similarly to primaries, whereas diffracted multiples do not. In particular, the apex of the residual moveout curve of diffracted multiples in ADCIGs is not located at the zero aperture angle. We use our equation of the residual moveout of the multiples in ADCIGs to design an apex-shifted Radon transform that maps the 2D ADCIGs into a 3D model space cube whose dimensions are depth, curvature, and apex-shift distance. Well-corrected primaries map to or near the zero-curvature plane and specularly reflected multiples map to or near the zero apex-shift plane. Diffracted multiples map elsewhere in the cube according to their curvature and apex-shift distance. Thus, specularly reflected as well as diffracted multiples can be attenuated simultaneously. We show the application of our apex-shifted Radon transform to a 2D seismic line from the Gulf of Mexico. Diffracted multiples originate at the edges of the salt body and we show that we can successfully attenuate them, along with the specular multiples, in the image Radon domain.

A very important aspect of removing multiples from seismic data is accurate prediction of their kinematics. We cast the multiple prediction problem as an operation in the image space parallel to the conventional surface-related multipleprediction methodology. Though developed in the image domain, the technique shares the data-driven strengths of datadomain surface-related multiple elimination ͑SRME͒ by being independent of the earth ͑velocity͒ model. Also, the data are used to predict the multiples exactly so that a Radon transform need not be designed to separate the two types of events. The cost of the prediction is approximately the same as that of data-space methods, though it can be computed during the course of migration. The additional cost is not significant compared to that incurred by shot-profile migration, though split-spread gathers must be used. Image-space multiple predictions are generated by autoconvolving the traces in each shot-gather at every depth level during the course of a shotprofile migration. The prediction in the image domain is equivalent to that produced by migrating the data-space convolutional prediction. Adaptive subtraction of the prediction from the image is required. Subtraction in the image domain, however, provides the advantages of focused energy in a smaller domain since extrapolation removes some of the imperfections of the input data.