There is a fundamental difference between lab measurements and in situ measurements (from sonic logs to shot-geophone surveys). The lab measurements are performed with devices emitting and recording frequencies on the order of 1 MHz. The dimensions of the rock samples hardly ever exceed 1 meter. Conversely, seismic surveys are operated at frequencies around 50 Hz and are designed to highlight layers more than 100 meters thick. Biot (1956) developed a theory for wave propagation that takes into account the frequencies involved in the measurement and described, using the theory of fluid mechanics, how velocities increase with frequency. The diffraction theory introduces an interesting interpretation of the sigmoid curves relating P-velocity to frequency.

- The lens-grain analogy
- The Fresnel zone
- Diffracted waves
- The low frequency-high frequency transition
- Biot's sigmoid velocity versus frequency curves

11/17/1997