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Measurements were made of the fractal properties of sandstones, shales, and carbonates using a statistical analysis of structural features on fracture surfaces. Fractal behavior is associated with power law behavior for the number of features as a function of the feature size. on the pore-rock interface. Only one sedimentary rock, a novaculite, was found not to have a fractal structure. The fractal dimensions range from 2.27 to 2.89, and the long-length limits to the fractal regime range from 2 ttm to over 50 ttm. In all cases, the fractal behavior extends to less than 0.2 ttm which is the measurement resolution. The porosity associated with the fractal pore-rock interface can be calculated from the fractal parameters. Some of the samples have additional porosity not associated with power law behavior. Photographs and other evidence are used to show that the fractal structures are the result of diagenesis. Fractal diagenetic structures include euhedral quartz overgrowths, druse quartz, calcite, dolomite, clays, and chert.

An automatic technique has been developed to measure precisely the fractal dimension of the microstructure of sandstones from scanning-electron-microscope (SEM) images of fracture surfaces.The technique involves digitizing the images, filtering, counting geometrical features as a function of feature size, and fitting feature histograms. The magnification of the SEM is changed to cover 2.5 orders of magnitude in feature sizes. A po~er-law model, which includes the resolution of the digital filter, accounts for the feature size distributions for all magnifications and the scaling from magnification to magnification. Results have been obtained for a dozen sandstones, and the fractal dimension is observed to range from 2.55 to 2.85. The precision for averaged images is +0.01. In addition, a long-length limit to the fractal regime is defined and measured.

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Geometrical measurements of pore microstructure indicate that the pore volume distributions for sandstones can be separated into two regimes: a short-length regime with fractal behavior and a longlength regime with no fractal behavior. The fractal part of the distribution is statistically described by a power law, and it appears to be governed by the growth of minerals and cements in the pore space. The nonfractal or Euclidean part of the distribution is dominated by a characteristic length, and it apparently reflects the original unaltered porosity. Two of the sandstones have both fractal and Euclidean regimes, and two of the sandstones have only the fractal regime. The latter two samples are more highly cemented than the former two. Fractal porosities calculated from the fractal parameters measured on fracture surfaces agree with the porosity in the fractal regime measured on thin sections. Criteria developed to determine the relative porosity associated with the fractal and Euclidean regimes could be used to characterize the amount of diagenetic alteration of the pore volume. Photographs are used to support conclusions derived from the geometrical measurements.

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This paper proposes an approach to speed up seismic forward modeling when the Green's function of a given model is structured in the sense that the Green's function has a sparse representation in some known transform domain. The first step of our approach runs a forward finite-difference (FD) simulation for a duration longer than each conventional run, but with all sources activated simultaneously using different long random noise waveforms. The cumulative responses to the simultaneous sources are measured at all receivers. The second step separates the interfering Green's functions from the receiver measurements by exploiting prior knowledge of the random waveforms and the sparsity of the Green's function in a suitable domain. Simulation results demonstrate such a simultaneous source approach is indeed promising. * Though the curvelet transform is not an orthonormal transform (its a tight frame), it enjoys several desirable properties of orthonormal transforms.