A framework for inferring field‐scale rock physics relationships through numerical simulation

Abstract

Rock physics attempts to relate the geophysical response of a rock to geologic properties of interest, such as porosity, lithology, and fluid content. The geophysical properties estimated by field‐scale surveys, however, are impacted by additional factors, such as complex averaging of heterogeneity at the scale of the survey and artifacts introduced through data inversion, that are not addressed by traditional approaches to rock physics. We account for these field‐scale factors by creating numerical analogs to geophysical surveys via Monte Carlo simulation. The analogs are used to develop field‐scale rock physics relationships that are appropriate for transforming the geophysical properties estimated from a survey into geologic properties. We demonstrate the technique using a synthetic example where radar tomography is used to estimate water content.

Fusion of hydrologic and geophysical tomographic surveys

“…On the other hand, analysis of geophysical surveys yields electrical resistivity or permittivity, which has to be translated into hydrologic properties via some constitutive relation. This relation is often empirical, site specific, scale-dependent, and perhaps ambiguous (Day-Lewis et al, 2005, Moysey et al, 2005, DayLewis, and Lane, 2004 and the translated hydrologic properties, as such, could be misleading. Spatial variability of the relation, as noticed by , further complicates this translation.…”

Simulated-annealing-based conditional simulation for the local-scale characterization of heterogeneous aquifers

“…In both of the examples presented in this paper, we chose to estimate one conditional relationship from the velocity-porosity scatter plot that can be used throughout the entire modeling region. Clearly, this does not address the fact that the velocity-porosity relationship will in reality vary in space due to differences in tomographic resolution throughout the image plane (e.g., Day-Lewis and Lane, 2004; Moysey et al, 2005). However, it avoids significant complications and ambiguities associated with accurately estimating the spatially variable relationship, and it is a reasonable and pragmatic approach since the velocity resolution with crosshole georadar tomography is worst at the borehole locations.…”

“…Although for hydrogeophysical applications the simplest approach is to attempt to relate the parameters using laboratory-derived petrophysical relationships, such relationships are usually only valid at the small scale, and tend to encounter problems when they are used to "convert" geophysical images to true subsurface properties. In an attempt to address this problem, Moysey et al (2005) developed a Monte-Carlo approach involving numerical forward modeling to upscale petrophysical relationships from the laboratory scale to the scale of a geophysical survey. Day-Lewis et al (2005) also addressed this issue by quantifying the correlation loss that occurs between a geophysical image and model of subsurface properties as a result of geophysical inversion.…”

Near Surface Electrical Characterization of Hydraulic Conductivity: From Petrophysical Properties to Aquifer Geometries—A Review

“…The primary limitation of such approaches has been the questionable validity of assumed petrophysical relationships at the field scale. In order to address this, efforts have been made to determine how to upscale petrophysical relationships identified at the corescale to petrophysical relations that are statistically meaningful at the scale of a tomographic survey (Day-Lewis et al 2005;Moysey et al 2005). A more recent joint inversion approach, that excludes the requirement of the existence of a specific site petrophysical relationship, is the 'structural approach', which assumes that changes in different physical properties occur in the same direction for a given position (Gallardo and Meju 2003;Gallardo and Meju 2004;Haber and Oldenburg 1997).…”