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Use of crosshole radar tomograms for geostatistical estimation and simulation of interwell permeability: Limitations due to tomographic resolution

Frederick D. Day-Lewis and John W. Lane, Jr.
U.S. Geological Survey
Office of Ground Water, Branch of Geophysics
11 Sherman Place, Unit 5015
Storrs, CT 06269

Abstract

Crosshole geophysical tomograms (radar, seismic, and electrical) provide qualitative information about aquifer structure and properties. Increasingly, tomograms are used as auxiliary data for quantitative geostatistical estimation and simulation of hydrologic properties. Such work requires inference of the relationship between geophysical properties (e.g., radar wave velocity) and hydrologic properties of interest (e.g., permeability). Empirical site-specific relationships between radar velocity and permeability are based on (1) co-located estimates at boreholes that bound tomograms, or (2) laboratory measurements. These approaches assume that the inferred correlation between inverted radar velocity and measured permeability applies uniformly throughout the interwell region; however, tomographic resolution is known to vary spatially due to acquisition geometry, wave behavior, data error, and regularization. Blurring and inversion artifacts occur in regions traversed by few or only low-angle raypaths; thus, the correlation between permeability and tomographic estimates of radar velocity may be considerably weaker than expected. Use of low-resolution tomograms as auxiliary data may lead to unreliable predictions of the permeability distribution and under-prediction of the connectivity of high- and low-permeability regions. Thus, tomograms that provide valuable qualitative information may have limited value for geostatistical purposes.

We demonstrate a modeling approach to assess the utility of tomograms for geostatistical simulation and estimation. In a series of realistic synthetic examples using linear straight-ray radar tomography, we consider the independent and combined effects of varying data error, permeability and velocity correlation structure, well separation, and the regularization used in inversion. For each scenario, we (1) generate realizations of velocity and log-permeability, assuming a correlation coefficient of 0.9 between the two properties, (2) simulate crosshole travel-time data, (3) perform tomographic inversion and calculate the model resolution matrix, and (4) evaluate the relationships between inverted velocity and synthetic velocity, and inverted velocity and synthetic permeability. Depending on tomographic resolution, the correlation coefficient between log-permeability and estimated radar velocity can degrade from 0.9 to less than 0.2. Our results demonstrate that (1) a correlation between permeability and velocity derived in laboratory measurements will not, in general, apply to tomograms; (2) a correlation between co-located borehole permeability measurements and tomographic velocity estimates may not be representative of the true permeability-velocity relation throughout the interwell region; and (3) the correlation between inverted velocity and synthetic permeability varies spatially and will be poorer in regions of lower tomographic resolution. These results illustrate important limitations that should be considered in utilizing tomograms for stochastic simulation and estimation of aquifer properties.

Final copy as submitted to Eos Transactions for publication as: Day-Lewis, F. and Lane, J.W., Jr, 2003, Use of crosshole radar tomograms for geostatistical estimation and simulation of interwell permeability - Limitations due to tomographic resolution [abs.]: Eos Transactions, American Geophysical Union, v. 84, no. 46, Fall Meeting Suppl., Abstract H21F-02.