Kansas Geological Survey, Current Research in Earth Sciences, Bulletin 247,
part 1

**Modeling Dielectric-constant Values of Geologic Materials: An Aid to Ground-penetrating Radar Data Collection and Interpretation--page 12 of 13**

### Appendix A

An Excel workbook with interactive spreadsheets that use the formulas presented in the text is described in this appendix. This full workbook can be downloaded (http://www.kgs.ku.edu/Current/2001/martinez/Appendix_A.xls) and used to determine many properties related to dielectric constant in geologic materials and to forward-model dielectric constant. These calculated values and models can in turn be used for modeling expected GPR response in field studies and aid in designing GPR surveys and interpreting GPR data. The downloadable workbook contains the worksheets listed below.

#### 1) Dielectric Constants Worksheet

This worksheet contains a summary of the mineral and fluid dielectric constant data given in table 2.

#### 2) TP Model-Porosity-Mineralogy Worksheet

This worksheet contains the TP-model equation, Eq. (1), for a three-layer example with fixed, user-defined water saturations and variable matrix mineralogy and porosity (fig. 1). Each layer provides for a two-component matrix (e.g., quartz and mica) and two fluids filling the pore volume (e.g., air and water).

#### 3) TP Model-Porosity-Sw Worksheet

This worksheet contains the Time-Propagation model equation, Eq. (1), for a three-layer example with a fixed, user-defined matrix mineralogy and variable porosity and water saturation (figs. 1 and 2). Each layer provides for a two-component matrix (e.g., quartz and mica) and two fluids filling the pore volume (e.g., air and water).

#### 4) RC-Porosity-Mineralogy Worksheet

This worksheet allows calculation of reflection-coefficient values, Eq. (3), for models with variable porosity and mineralogy (figs. 11 and 12), allowing investigation of the sensitivity of GPR response to these variables. It also contains the formula for calculation of needed stacking parameters to achieve a reflection coefficient of 0.1 (fig. 3).

#### 5) Modeled TWT and RC Worksheet

This worksheet calculates two-way travel-time and reflection coefficient for a three-layer problem with input of layer mineral and fluid properties, Eqs. (3) and (5).

#### 6) Vertical Resolution Worksheet

This worksheet contains Eq. (7), used to calculate expected resolution (fig. 4). It also contains the summary of reported bulk dielectric-constant values for earth materials given in table 1.

#### 7) Spatial Resolution Worksheet

This worksheet contains Eqs. (8) and (9), used to calculate expected spatial resolution (fig. 5).

Kansas Geological Survey

Web version December 3, 2001

http://www.kgs.ku.edu/Current/2001/martinez/martinez12.html

email:lbrosius@kgs.ku.edu