Application of wavelet transforms to reservoir data analysis and scaling
General characterization of physical systems uses two aspects of data analysis methods: decomposition of empirical data to determine model parameters and reconstruction of the image using these characteristic parameters. Spectral methods, involving a frequency based representation of data, usually assume stationarity. These methods, therefore, extract only the average information and hence are not suitable for analyzing data with isolated or deterministic discontinuities, such as faults or fractures in reservoir rocks or image edges in computer vision. Wavelet transforms provide a multiresolution framework for data representation. They are a family of orthogonal basis functions that separate a function or a signal into distinct frequency packets that are localized in the time domain. Thus, wavelets are well suited for analyzing non-stationary data. In other words, a projection of a function or a discrete data set onto a time-frequency space using wavelets shows how the function behaves at different scales of measurement. Because wavelets have compact support, it is easy to apply this transform to large data sets with minimal computations. We apply the wavelet transforms to one-dimensional and two-dimensional permeability data to determine the locations of layer boundaries and other discontinuities. By binning in the time-frequency plane with wavelet packets, permeability structures of arbitrary size are analyzed. We also apply orthogonal wavelets for scaling up of spatially correlated heterogeneous permeability fields.
- OSTI ID:
- 471900
- Report Number(s):
- CONF-961003--
- Country of Publication:
- United States
- Language:
- English
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