Multicomponent seismic studies using complex trace analysis

Abstract

The methods of complex signal analysis are applicable to multicomponent trace is defined by real orthogonal components derived by applying the Hilbert transform to the real components. Polarization attributes, including the instantaneous phase difference, signed reciprocal ellipiticity, tilt angle, and rise angle, can be displayed in trace format or in radial time-attribute plots. Polarization attributes are readily interpreted despite the non‐stationary character of seismic signals. Average attributes are defined by weighting with the geometric mean of instantaneous amplitudes. Multicomponent walkaway data have been obtained by detonating explosives in air and using triaxial in‐clined (Gal[Formula: see text]erin) geophones on a mud flat in the Great Salt Lake Desert, Utah. Polarization attributes of these data define some of the principal characteristics of both ambient noise and source‐generated waves. The direct, critical refraction, and reflection events show linear polarization with a slight forward tilt of the particle motion. Polarization of the air wave and the initial por‐tion of the air‐coupled wave is consistent across all traces in the walkaway data. The air wave begins with prograde particle motion; after approximately 2 1/2 cycles, particle motion changes to a retrogade elliptic phase. In the data considered, most of the air‐coupledwave is due to higher modes of the Rayleigh wave ( [Formula: see text], [Formula: see text],…). The [Formula: see text] and [Formula: see text] modes generated in the immediate vicinity of the explosive source exhibit opposite polarities of phase difference, corresponding to retrograde and prograde elliptic particle motions, respectively. By zeroing all data with average signed reciprocal ellipticity outside the range between −0.125 and −1, the [Formula: see text] waves are automatically selected for subsequent display with little contamination by other waves. Such procedures facilitate identification of waves according to their polarization characteristics. A desert mud flat may provide an excellent environment for study of Rayleigh waves, including air‐coupled waves, due to its flat terrain, sparse vegetation, and lateral uniformity of sediments.