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AVO friendly Q compensation on angle stacks

IP.com Disclosure Number: IPCOM000244375D
Publication Date: 2015-Dec-07
Document File: 8 page(s) / 42K

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Abstract

An approximate way to correct angle stacks for attenuation and scattering is derived in this short note. Attenuation and scattering will collectively be referred to as Q loss in this paper. Loss due to Q needs to be taken into account for amplitude vs. angle analysis (AVA). The need for some form of amplitude spectrum correction is generally recommended to restore resolution on modern broad band processing flows. Broad band processing includes receiver and source deghosting which will reduce the peak frequency and bandwidth of most data. The most theoretically correct way to compensate for Q is to include compensation in the migration or imaging algorithm. This can take the offset, time and structure dependence of the Q loss into account. The next best theoretical approach is pre-migration Q-compensation. In principle, this approach can correctly handle the offset and time dependence for flat reflections but will not correctly handle structural dependence. However, very few processing software systems have an offset and time dependent algorithm which correctly handles the Q effect for non-zero offset. In principle, post migration Q compensation can correctly handle the offset and time dependence for flat reflections but will be the least correct in handling structural dependence. The travel time of dipping reflectors is reduced after migration and the Q correction will be too small. The same algorithm used for pre-migration would be the required algorithm for post-migration Q offset and time dependent compensation. As already mentioned, these algorithms are not universally available. Post migration Q compensation has three advantages: 1. Less noise will be boosted because migration remaps frequencies to lower values and Q compensation boosts high frequencies. 2. Operationally, it is convenient to wait until after migration which is an expensive process. Testing Q compensation parameters will be cheaper after migration. 3. If it is possible to apply the process post-stack, then it would be even more convenient and cheaper. It could also be applied to legacy data that lacks Q compensation. What follows is a derivation of an approximate technique to apply post-stack Q compensation that is still consistent with AVA.

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AVO friendly Q compensation on angle stacks

Introduction

An approximate way to correct angle stacks for attenuation and scattering is derived in this short note.  Attenuation and scattering will collectively be referred to as Q loss in this paper.    Loss due to Q needs to be taken into account for amplitude vs. angle analysis (AVA).  The need for some form of amplitude spectrum correction is generally recommended to restore resolution on modern broad band processing flows.  Broad band processing includes receiver and source deghosting which will reduce the peak frequency and bandwidth of most data.

The most theoretically correct way to compensate for Q is to include compensation in the migration or imaging algorithm.  This can take the offset, time and structure dependence of the Q loss into account.

The next best theoretical approach is pre-migration Q-compensation.  In principle, this approach can correctly handle the offset and time dependence for flat reflections but will not correctly handle structural dependence.  However, very few processing software systems have an offset and time dependent algorithm which correctly handles the Q effect for non-zero offset.

In principle, post migration Q compensation can correctly handle the offset and time dependence for flat reflections but will be the least correct in handling structural dependence.  The travel time of dipping reflectors is reduced after migration and the Q correction will be too small.  The same algorithm used for pre-migration would be the required algorithm for post-migration Q offset and time dependent compensation.  As already mentioned, these algorithms are not universally available.

Post migration Q compensation has three advantages:

1.      Less noise will be boosted because migration remaps frequencies to lower values and Q compensation boosts high frequencies.

2.      Operationally, it is convenient to wait until after migration which is an expensive process.  Testing Q compensation parameters will be cheaper after migration.

3.      If it is possible to apply the process post-stack, then it would be even more convenient and cheaper.  It could also be applied to legacy data that lacks Q compensation.

What follows is a derivation of an approximate technique to apply post-stack Q compensation that is still consistent with AVA.

Derivation

It will be assumed that the amplitude portion of the Q compensation can be represented as an exponential that is a function of wavelet frequency f and reflection time T as follows:

 

(1)

Where f is the wavelet frequency, T is the two way travel time of the reflection and Q is the quality factor which describes the degree of frequency loss due to attenuation and scattering.  In practice this correction will be limited to a maximum boost, because the exponential factor can become very large.  In practice the Q compensation may actually involve a high cut filter beyond the maximum boost frequency.  For the purposes of this paper these details...