Combined-harmonic Analysis of Seismic Data Acquired with Two Vibrators Driven at Different Frequencies

The presence of hydrocarbons cannot be verified directly with current linear seismic relection methods. However, several studies suggest that third-order elastic moduli in reservoir rocks are anomalously large. This presents an opportunity to directly detect hydrocarbons by investigating nonlinear seismic responses. Although the existence of nonlinear seismic signals is well established, their generating mechanism is not known. Nonlinear seismic experiments are difficult to interpret. Vibrators are nonlinear targets and under the influence of a vibration at a different frequency, they may also emit combined harmonics. Hence, the observation of combined harmonics alone doesnot prove nonlinear generation in the subsurface. However, the presence of growing nonlinear responses is a characteristic signature of intrinsic nonlinearities in the medium. By observing this growth, medium nonlinearity can be discriminated from nonlinearities introduced by the source. We theoretically estimate the growth of nonlinear harmonic. Next we discuss an experiment in which two vibrators were driven at different frequencies in order to understand the source and propagation characteristics of nonlinear harmonics. We observe nonlinear harmonics. Comparing their amplitude decay with the theoretically estimated behaviour of nonlinear harmonics, we conclude that they are most likely generated by the sources and not in the medium.