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Method for applying amplitude Q compensation to angle stacks and pre-stack gathers

IP.com Disclosure Number: IPCOM000250062D
Publication Date: 2017-May-24

Publishing Venue

The IP.com Prior Art Database

Abstract

Amplitude Q compensation consists of an exponential frequency boost as a function of wavelet travel time in sediments T and quality factor Q. Practical considerations require that the boost be cut off at some frequency to prevent corruption or loss of low frequency data. Distortion of the Amplitude vs. Angle (AVA) analysis can occur due to the choice of cut-off frequency and incorrect calculation of the sediment travel time. Amplitude Q compensation which does not distort AVA must consider the following issues: 1) Water column travel time: Accurate sediment travel times are required for Q correction 2) Cut-off frequency: Cut-off frequencies need to be consistent across a reflection to avoid AVA distortion 3) Stretch: Migration and the normal moveout process will stretch the data in the time domain and re-map frequencies This paper shows how to apply amplitude Q compensation in a manner that will not distort AVA analysis. Three implementations of this method are presented: 1) Post-stack approximate travel time 2) Post-stack Dix travel time 3) Pre-stack on non-flattened gathers Travel time reduction due to migration of dipping reflectors is not taken into account in this paper. The algorithms developed in this paper are strictly applicable to low dip AVA analysis with one exception: constant amplitude Q compensation applied pre-migration with a negligible water layer. However, no 1D filter approach can take dipping reflectors into account. Migration that includes an amplitude Q compensation is the only approach which handles dip correctly.

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Method for applying amplitude Q compensation to angle stacks and pre-stack gathers

Introduction

Amplitude Q compensation consists of an exponential frequency boost as a function of wavelet

travel time in sediments �� and quality factor ��. Practical considerations require that the boost

be cut off at some frequency to prevent corruption or loss of low frequency data. Distortion of

the Amplitude vs. Angle (AVA) analysis can occur due to the choice of cut-off frequency and

incorrect calculation of the sediment travel time.

Amplitude Q compensation which does not distort AVA must consider the following issues:

1. Water column travel time: Accurate sediment travel times are required for Q correction

2. Cut-off frequency: Cut-off frequencies need to be consistent across a reflection to avoid

AVA distortion

3. Stretch: Migration and the normal moveout process will stretch the data in the time

domain and re-map frequencies

This paper shows how to apply amplitude Q compensation in a manner that will not distort AVA

analysis.

Three implementations of this method are presented:

1. Post-stack approximate travel time

2. Post-stack Dix travel time

3. Pre-stack on non-flattened gathers

Travel time reduction due to migration of dipping reflectors is not taken into account in this

paper. The algorithms developed in this paper are strictly applicable to low dip AVA analysis

with one exception: constant amplitude Q compensation applied pre-migration with a

negligible water layer. However, no 1D filter approach can take dipping reflectors into account.

Migration that includes an amplitude Q compensation is the only approach which handles dip

correctly.

Amplitude Q Compensation Parameters

Amplitude Q compensation requires the application of the following time varying filter to

seismic data.

�� = ��

������ ��

(1)

Where �� is the frequency in Hz, �� is the travel time in seconds through the medium with quality

factor �� (which is unitless). In practice, the filter is not applied sample by sample. The data are

separated into overlapping time windows and a filter based on the central travel time of the

2

window is used in Equation (1). The filter is usually applied in the frequency domain for

efficiency. This windowed approach simulates the time varying nature of the inverse Q filter

particularly at longer travel times.

As a practical matter the amplitude compensation in Equation (1) should not be applied to very

high frequencies. Single precision floating point numbers only support about 72 dB of dynamic

range in the calculation of the forward or inverse Fourier transform. Because of the

exponential nature of the compensation it is easy to exceed the dynamic range of floating point

numbers. When this happens the data at lower frequencies are lost in the round off errors

generated by the higher frequencies during the Fourier transform. Therefore, even in synthetic

data a limit to the amplitude Q compensation must be imposed.

Before this numerical limit of 72 dB is...