基于时频分析的岩石超声衰减计算方法*

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摘要品质因子Q 是表征岩石非弹性性质的重要参数，准确的Q 值是深入研究岩石动力学特征的关键。准确、稳定地获得岩石Q 值参数一直是一个难点。本文利用时频谱信息进行Q 值提取，提出了基于S 变换的频谱比法（SR-ST）。该方法利用了S 变换的变时窗特性解决常规方法中的时窗问题，并对S 变换中高斯窗添加时窗因子，使得高斯窗更适合超声衰减计算。同时，通过给出频带线性回归规则，提高计算的稳定性和准确性。文中首先通过数值模拟和标准样品测量实验，研究分析了SR-ST 方法的可行性行以及影响因素；其次利用不同Q 值人工样品，研究该方法对不同Q 值样品计算的适应性和稳定性；最后通过岩石超声衰减测量实验，将该方法与常规频谱比法进行对比分析，分析SR-ST 方法的稳定性和准确性。实验结果表明：利用无时窗因子的S 变换时频谱计算，会引起36%的误差，需要对S 变换添加时窗因子，适当调整时窗大小随频率变化的程度；SR-ST 方法能够适应不同衰减特征岩石样品Q 值计算，利用给出的频带线性回归规则以及平均斜率值进行Q 值计算，能够保证不同Q 值（Q>15）的最大误差在10%以内。

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关键词： Q 值估算时频谱 S 变换时窗因子超声衰减计算

Abstract： The quality factor (or Q value) is an important parameter for characterizing the inelastic properties of rock. Achieving a Q value estimation with high accuracy and stability is still challenging. In this study, a new method for estimating ultrasonic attenuation using a spectral ratio based on an S transform (SR-ST) is presented to improve the stability and accuracy of Q estimation. The variable window of ST is used to solve the time window problem. We add two window factors to the Gaussian window function in the ST. The window factors can adjust the scale of the Gaussian window function to the ultrasonic signal, which reduces the calculation error attributed to the conventional Gaussian window function. Meanwhile, the frequency bandwidth selection rules for the linear regression of the amplitude ratio are given to further improve stability and accuracy. First, the feasibility and influencing factors of the SR-ST method are studied through numerical testing and standard sample experiments. Second, artifi cial samples with different Q values are used to study the adaptability and stability of the SR-ST method. Finally, a further comparison between the new method and the conventional spectral ratio method (SR) is conducted using rock fi eld samples, again addressing stability and accuracy. The experimental results show that this method will yield an error of approximately 36% using the conventional Gaussian window function. This problem can be solved by adding the time window factors to the Gaussian window function. The frequency bandwidth selection rules and mean slope value of the amplitude ratio used in the SR-ST method can ensure that the maximum error of different Q values estimation (Q > 15) is less than 10%.

Key words： Q value estimation Time-frequency spectrum ST Window factor Ultrasonic attenuation

收稿日期: 2019-06-22;

基金资助:

本研究项目由由中国地震局地球物理研究所专项基金 (编号：DQJB19B02 和DQJB17T04)资助。

通讯作者: 高峰（Email:gaofengcup@126.com） E-mail: gaofengcup@126.com

作者简介: 高峰，2011-2014 年于中国矿业大学（北京）攻读硕士，2014-2018 年在中国石油大学（北京）攻读地质资源与地质工程博士，现在在中国地震局地球物理研究所进行博士后工作。目前研究方向主要以地震波衰减、超声衰减计算方法、岩石物理及地震物理模拟为主。Email: gaofengcup@126.com

引用本文:

. 基于时频分析的岩石超声衰减计算方法*[J]. 应用地球物理, 2019, 16(4): 415-429.

. Ultrasonic attenuation estimation based on time-frequency analysis*[J]. APPLIED GEOPHYSICS, 2019, 16(4): 415-429.