Seismic signals are nonstationary and nonlinear because of excitation conditions, absorption, and the attenuation of stratum and receiving instruments. Various time-frequency analysis methods have been widely and practically applied in describing the time-varying characteristics of seismic signals. However, most methods are based on additive expansions and cannot represent the nonlinearity of signals, which is achieved by a multiplicative process. Therefore, the information provided by the time-frequency spectrum needs to be completed. The Holo-Hilbert spectral analysis (HHSA) method is introduced in this paper to show the nonlinearity of seismic signals, i.e., the modulation effect of low-frequency components on high-frequency components. HHSA contains nested empirical mode decomposition and Hilbert transforms to achieve a full informational spectrum represented by two frequency dimensions. In the Holo-Hilbert spectrum, one dimension represents the frequency-modulated frequency, which characterizes the nonstationarity of the signal, and the other dimension represents the amplitude-modulated frequency, which indicates the nonlinear effect in the signal. Synthetic and field data examples verify the feasibility of HHSA in characterizing the cross-frequency interaction of nonstationary seismic signals as a potential tool to detect reservoirs.

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