On the spectral changes of seismic wave energy by a partially saturated crack due to the hysteresis of liquid bridges phenomenon

Abstract

Low-frequency shadows are frequently interpreted as attenuation phenomena due to partial saturation with free gas. However, several researchers have argued that shadows are not necessarily a simple attenuation phenomenon because low-frequency energy must have been added or amplified by some physical or numerical process. Attenuation alone should attenuate higher frequencies, not boost lower frequencies. The physical or numerical effects explaining this phenomenon are still debatable in the literature. To better understand the elastic wave energy’s spectral changes in partially saturated rock, we have considered the hysteresis of liquid bridges phenomena inside the crack. We determine that liquid bridges’ hysteresis leads to the nonlinear energy exchange between frequencies, explaining the wave energy boost at lower frequencies. We find that the energy exchange between different frequencies depends on the wave amplitude and the seismic wave spectrum. The low-frequency energy boost is stronger for a continuous spectrum of seismic waves, smaller for the discrete spectrum, and zero for the monochromatic spectrum of seismic waves. In addition, we find that at seismic frequencies, the attenuation 1/ Q-factor due to the friction of the contact line can be much larger than the attenuation due to viscous fluid flow inside the partially saturated crack. Our model depends on the wave amplitude and weakly depends on the wave frequency. The suggested model can help interpret the low-frequency shadows, bright spots, and attenuation anomalies frequently observed around hydrocarbon fields.