= 8.5) and quartz ( = 4.5) layer. When the quartz content increases to 100% in the lower layer, the reflection coefficient decreases to zero because the lower and upper layers become identical in matrix composition. When only mineralogy is changed, the amount of calcite in the matrix must be greater than 65% to produce a reflection coefficient greater than 0.10 in dry rocks for single-fold data. In water-saturated rocks, these mineralogic differences are so small compared to the dielectric constant of the water in the pore space that reflection-coefficient values never exceed the threshold of 0.10. For 128-fold data, as little as 5% calcite in a dry quartz sandstone can produce an observable reflection and 15% calcite content will produce an observable reflection when both layers are water-saturated. In rocks, such as shaly sands, where geometric and fluid-rock electrochemical interactions may significantly increase the matrix dielectric constant, the influence of these effects must be accounted for by modifying model input parameters based on measurements from representative samples. These calculated reflection-coefficient values (fig. 12) show that 128-fold data are capable of imaging interfaces between beds with relatively small differences in mineralogy provided that water saturations are known.
Fig. 12. Calculated reflection coefficients for dry and water-saturated, two-layer models plotted against the percentage of quartz in the lower layer. The upper layer is 100% quartz with a 20% porosity, and the lower layer is calcite with variable amounts of quartz and a 20% porosity. The shaded area indicates power reflectivity values of less than 0.01, a conservative estimate of the threshold at which background noise may preclude recording of reflection information (i.e., SNR 
1; Annan, 1996). Comparison with fig. 11 illustrates the greater relative influence of porosity on reflection coefficients.
Capillary-pressure differences are likely to result in low water saturations in high porosity, coarse-grained rocks and in higher water saturations in low porosity, fine-grained rocks and shales. While such differences might be expected to result in large reflection-coefficient values (as between sands and shales, for example), in fact, decreased porosity in finer-grained rocks results in less pore space available for water and a smaller bulk dielectric constant, even with the pores of the shale completely saturated. For example, in a shale that is 50% quartz ( = 4.5) and 50% mica ( = 6.5) and has 8% porosity that is water saturated ( = 81), the bulk dielectric constant, calculated using the TP model, is only 8.2. At an interface with relatively dry (Sw < 20%) quartz sand with porosity between 0% and 50% (bulk 
4.5-5.7), single-fold reflection coefficients range from 0.10 to 0.15, equal to or only slightly above background noise (RC = 0.10). For carbonates interbedded with calcareous shales (bulk 10.8), similar reflection-coefficient values are exhibited for similar ranges in porosity and water saturation.
Vertical imaging resolution can be calculated using worksheet 6 (appendix A), which utilizes Eq. (7). For rocks with a bulk dielectric constant of 2.5, vertical imaging resolution ranges from 0.2 m to 0.1 m at GPR frequencies of 200-400 MHz and decreases to 0.06-0.03 m in rocks with = 30. Thus, in rocks with low and high dielectric constants, GPR vertical resolution is capable of imaging fine-scale (less than 20 cm) bedding features. The long radii of GPR footprints for frequencies of 200-400 MHz in rocks with bulk dielectric constants ranging from 2.5 to 30 are approximately 1.7 m to 0.4 m, respectively, at 2-m depth (calculated using worksheet 7). These footprints indicate that small lateral changes in rock properties may not be precisely resolved. In addition, many GPR surveys are conducted using 125-450 MHz antennas. Whereas this difference in frequency may significantly change vertical resolution, the footprint size at 2 m decreases by less than 20% from 125 MHz to 450 MHz. This suggests that some smaller-scale features in near-surface rocks and sediments are unresolvable using GPR.
Kansas Geological Survey
Web version December 3, 2001
http://www.kgs.ku.edu/Current/2001/martinez/martinez10.html
email:lbrosius@kgs.ku.edu