Harmonic resonance structure and chaotic dynamics in the earth‐vibrator system1

Source-generated energy in seismic vibrator records includes ultraharmonics, sub-harmonics, ultra-subharmonics and possibly chaotic oscillatory behavior. Non-linear behaviors can be modeled using a ``hard-spring`` form of the Duffing equation. Modeling indicates that a qualitatively similar harmonic resonance structure is present for a broad range of possible mathematical descriptions. Qualitative global system behaviors may be examined without knowledge of actual earth parameters. Non-linear resonances become stronger, relative to fundamental sweep frequencies, as the driving force increases or damping decreases. System response energy levels are highest when non-linear resonances are strong. The presence of chaotic energy can indicate the highest energy state of a system response. Field data examples are consistent with behaviors predicted by modeling. Conventional correlation and stack uses a fraction of the energy produced in the earth-vibrator system. A correlation and filtering process that uses a representation of the source dynamics based on the system response can reduce signal degradation due to non-linear resonance.