<p>When performing "imaging" we are generally attempting to recover the reflectivity of the earth.  At zero offset the reflectivity is the <em>difference</em> 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.</p>

CC BY-SA 3.0
2015-03-18T02:27:25.513Z
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
CC BY-SA 3.0
2016-09-24T16:20:10.870Z
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, http://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 (https://en.wikipedia.org/wiki/Passive_integrator_circuit).
Antonio
CC BY-SA 3.0
2015-03-17T00:23:59.773Z
2016-09-21T04:48:32.587Z
2016-09-21T04:48:32.587Z
Mark
<p>In seismic analysis, why is a –90 degree phase rotation required on the amplitude spectrum to produce the colored inversion operator?</p>

CC BY-SA 3.0
2015-03-13T10:35:28.670Z
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?
Matt Hall
CC BY-SA 3.0
2015-03-16T04:33:12.623Z
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
<geophysics><inversion>
Why is phase rotation needed to produce the colored inversion operator?
Kunal Rathod
# Why is phase rotation needed to produce the colored inversion operator?

(Asked by: username_0 on 2015-03-13)

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

**Tags:** geophysics, inversion

> **Comments:**
> **username_1**: 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?  
> **username_0**: 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  

---

## 1 answers

### Answer by username_2 on 2015-03-17. Score: 1 | Accepted answer

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.

> **Comments:**
> **username_0**: 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  
> **username_3**: 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, http://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 (https://en.wikipedia.org/wiki/Passive_integrator_circuit).  

---

