# Why is phase rotation needed to produce the colored inversion operator?

In seismic analysis, why is a –90 degree phase rotation required on the amplitude spectrum to produce the colored inversion operator?

• Welcome to Earth Science Stack Exchange! You might need to add some details to your question, for example, what have you read about coloured inversion? – kwinkunks Mar 13 '15 at 10:35
• In coloured inversion there is a single operator, O, which is applied to the seismic trace Sto transform it directly into the inversion result Z: Z=O*S. Where operator O is in frequency domain.So we produce the amplitude spectrum,Z and the average seismic spectrum, S in order to obtain Operator,O. Thenafter finding Z/S, and shifting the phase of operator by -90deg. will produce the coloured inversion operator. Somebody please explain why the phase shift/rotation of -90deg is necessary asap – Kunal Rathod Mar 16 '15 at 4:33

When performing "imaging" we are generally attempting to recover the reflectivity of the earth. At zero offset the reflectivity is the difference in Acoustic Impedance (AI) normalized by the sum. When performing colored inversion we are seeking to recover a layered representation of the band limited AI and not the reflectivity. As we go from an AI log to a reflectivity log by differentiating we need to integrate to go the other way. In the frequency domain integration is a -90 degree phase term and an amplitude weight term. The amplitude term (1/freq) is taken care of when matching the spectra to that of the well log in the amplitude term.

• can u pls explain the line below " In the frequency domain integration is a -90 degree phase term and an amplitude weight term" u can send any external weblink also if need again tq sir – Kunal Rathod Mar 18 '15 at 2:27
• The normal incidence reflectivity function can be approximated by applying a differentiator operator to the one-half natural logarithm of acoustic impedance (Peterson et al, 1955, library.seg.org/doi/pdf/10.1190/1.1438155). As such, to recover the acoustic impedance function from reflectivity, we must apply an integrator operator. This operator is a low-pass filter with a -90 degree phase rotation (en.wikipedia.org/wiki/Passive_integrator_circuit). – Antonio Sep 24 '16 at 16:20