Complex seismic trace analysis treats a seismic trace as the product of two independent and separable functions: instantaneous amplitude and cosine of the instantaneous phase. At any given time, instantaneous amplitude is the maximum value the seismic trace can attain under a constant phase rotation, and instantaneous phase is the phase angle required to rotate the trace to the maximum. Defining these two attributes in this way permits complex seismic trace analysis to be founded without reference to the complex trace. All other complex seismic trace attributes derive from amplitude and phase through differentiation, averaging, combination, or transformation. The chief derived attributes are frequency, relative amplitude change, wavelength, dip, and azimuth. At any point on a seismic trace, the instantaneous attributes describe a sinusoid that locally matches the trace. Most instantaneous attributes are improved through filtering or weighted averaging. The phase wavenumber vector provides a convenient basis for quantifying 3D seismic properties such as reflection parallelism.

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