
科学技术与工程

中国技术经济学会
分数阶窜流对弹性波频散和衰减的影响
Effect of Fractional Interporosity Flow on the Dispersion and Attenuation of Elastic Wave
流体在基质孔隙和裂缝间的窜流,是弹性波在地震频段强衰减和频散的主要原因。给出一种分数阶导数描述的窜流方程。在频域对双孔隙介质的本构关系进行改进,引入了表示窜流效应的因子。将改进的本构关系代入拉格朗日方程,给出了考虑分数阶窜流的双孔隙介质波动方程。给出了波速和逆品质因子的解析表达式,并通过作图进行了分析。相对于传统窜流,分数阶窜流对弹性波在地震频段频散和衰减的描述,更加灵活、准确。
The interporosity flow between matrix pores and fractures is the main cause of strong attenuation and dispersion of elastic wave in the seismic frequency band. A fractional equation for interporosity flow is developed. The constitutive relationship of double-porosity medium was improved in the frequency domain, in which three factors representing the effects of fractional interporosity flow were introduced. A wave equation considering fractional interporosity flow for a double-porosity medium was developed by substituting the improved constitutive relationship into the Lagrangian equation. The wave velocity and inverse quality factor was obtained and analyzed by plotting. Comparing to the traditional interporosity flow, the fractional interporosity flow provides a more flexible and accurate description for the dispersion and attenuation of elastic waves in the seismic frequency band.
double-porosity medium / elastic wave / interporosity flow / dispersion and attenuation
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