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The scale property of the wavelet transform provides a framework for studying the scale properties of seismic and reservoir data. Seismic data are influenced by variations in earth properties that change over distances that are comparable to the wavelength of the seismic source, typically tens of meters. Log and outcrop measurements of earth properties cover a wide range of scales, from millimeter to kilometers. For petroleum exploration, 3D seismic data can be acquired over an entire producing field, but log and outcrop measurements are limited to well bores and the surface of the earth. Geostatistics provides a framework for combining fine scale measurements of rock properties in wells and at the surface of the earth with estimates of the variance of the properties. Based on these inputs, realizations are produced that match the actual field measurements and the estimated variance statistics of a given property. Geostatistical realizations of rock properties are accurate at the well locations, but can become unconstrained between well locations. In current practice, interpreted horizons and facies from seismic data are used as constraints. This requires interpretation, and the seismic data are rarely used directly. We propose using the scale property of the wavelet transform as a means for direct combination of reservoir and seismic data. Previous studies of each properties suggest a fractal relationship between scales. A given geostatistical realization of rock properties contains data (or estimates of data) from a wide range of scales. We propose using a 3D wavelet transformation of geostatistical reservoir data to characterize the reflectivity scale spectrum and the relation between reflectivity at different scales in the reservoir. 3D seismic data from the reservoir will contain information at a much narrower range of scales. Using the extracted scale information from the geostatistical data, we replace the geostatistical data at seismic scales with normalized wavelet transform coefficients from the seismic data. An inverse wavelet transform would then provide a realization of reflectivity that is constrained by both seismic and reservoir data. In the initial phase of this research, we are using wavelet transforms to characterize the scale properties of synthetic reservoir and seismic data. If successful, the technique will be tested on field data.
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