  Multiple scattering of wave in strong heterogeneity can cause resonance-like
wave anomaly where the signal exhibits low-frequency, high intensity, and
slowly propagating wave packet velocity. For example, long period event in
volcanic seismology and plasma oscillations in wave-particle interactions.
Collective behaviour in a many-body system is thought to be the source for
generating the anomaly, however the detailed mechanism is not fully understood.
Here I show that the physical mechanism is associated with low-frequency
resonance (LFR) in strong small-scale heterogeneity through seismic wave field
modeling for bubble cloud heterogeneity and 1D heterogeneity. LFR is a kind of
wave coherent scattering enhancement or emergence phenomenon that occurs in
transient regime. Its resonance frequency decreases with increasing
heterogeneous scale, impedance contrast, or random heterogeneous scale and
velocity fluctuations; its intensity diminishes with decreasing impedance
contrast or increasing random heterogeneous scale and velocity fluctuations.
LRF exhibits the characteristics of localized wave in space and the shape of
ocean wave in time and is a ubiquitous wave phenomenon in wave physics. The
concept of LFR can open up new opportunities in many aspects of science and
engineering.
