complex-trace analysis

1. n. [Geophysics]

A mathematical method to determine seismic attributes, including reflection strength and instantaneous frequency, by using the Hilbert transform, a special form of the Fourier transform, and the quadrature trace, or the component of the signal that is 90 degrees out of phase.

The Fourier transform

a(t) = h(t) + jx(t),

h(t) = seismic trace
x(t) = quadrature trace

can be used to determine reflection strength by combining h and x:

r(t) = [h(t)2 + x(t)2]1/2,

and to determine instantaneous phase:

θ(t) = tan−1[x(t)/h(t)].

See: attribute