THIRD-ORDER NONLINEAR SEISMIC EFFECTS

Abstract

The existing experimental studies of nonlinear seismic waves have concentrated on second-order effects. The thereby-detected anomalously large values of the second-order nonlinearity parameters of geophysical media resulting from their structure suggest that there should be similarly large third-order nonlinearity constants. We made an experimental study of cross-modulation of a longitudinal acoustic wave with frequency f1 = 3 kHz by the seismic field of a vibrator operating at f2 = 50 Hz. It has been demonstrated experimentally that soil has an anomalously high third-order nonlinearity. The measured changes in the wave propagation velocities are rather high, and calculations indicate that other third-order effects may also occur, including steady-state focusing, nonsteady-state pulse-spectrum broadening and the like. The measured values of N and B indicate that the cubic terms in the equations of motion presented in our earlier papers are comparable in magnitude with the quadratic terms at ε0 ≅ 4 · 10-5. As a result, the approximate 5- or 9-constant equations of elasticity cannot be used in the near zone of the vibration sources: exact models must be employed.