Chapter 7: Multiple-scale-porosity Wavelet Simulation Using GPR Tomography and Hydrogeophysical Analogs
Erwan Gloaguen, Bernard Giroux, Denis Marcotte, Camille Dubreuil-Boisclair, Patrick Tremblay-Simard, 2010. "Multiple-scale-porosity Wavelet Simulation Using GPR Tomography and Hydrogeophysical Analogs", Advances in Near-surface Seismology and Ground-penetrating Radar, Richard D. Miller, John H. Bradford, Klaus Holliger
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A novel approach can be used to simulate porosity fields constrained by borehole-radar tomography images. The cornerstone of the method is statistical analysis of the approximation wavelet coefficients of a petrophysical analog scenario. The method is tested with a 2D synthetic porosity field generated from a digital picture of a real sand deposit. The porosity field is translated into electrical properties and a crosshole tomography synthetic survey is built using a finite-difference modeling algorithm. Hereafter, this synthetic survey is considered as the measured one. In parallel, an analog deposit is created based on geologic knowledge of the area under study. The analog porosity field is converted into electrical property fields using the same equation. A synthetic ground-penetrating-radar (GPR) tomography also is computed from the latter. Then, wavelet decomposition of both measured and analog tomography and porosity analog fields is calculated. Based on the assumption that geophysical data carry essentially large-scale information about the geology, statistical analysis of the approximation wavelet coefficients of each variable is carried out. From measured tomographic approximation coefficients and cross statistics evaluated on the analogs, approximation of the real porosity field is inferred. Finally, based on the statistical relationships between wavelet coefficients across the different scales, all porosity wavelet-detail coefficients are simulated using a standard geostatistical cosimulation algorithm. The wavelet coefficients then are back-transformed in the porosity space. The final simulated porosity fields contain the large wavelengths of the measured radar tomographic images and the texture of the analog porosity field.