| 分数阶时间导数计算方法在含黏滞流体黏弹双相VTI介质波场模拟中的应用 |
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| 引用本文： | 胡宁,刘财.分数阶时间导数计算方法在含黏滞流体黏弹双相VTI介质波场模拟中的应用[J].吉林大学学报(地球科学版),2018,48(3):900-908. |
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| 作者姓名： | 胡宁 刘财 |
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| 作者单位： | 吉林大学地球探测科学与技术学院, 长春 130026 |
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| 基金项目： | 国家自然科学基金重点项目(41430322)Supported by State Key Program of National Natural Science of China (41430322) |
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| 摘 要： | 相对于整数阶导数，分数阶微分算子可以更简洁地描述具有历史依赖性和空间全域相关性的复杂力学和物理过程。但是对分数阶波动方程进行数值模拟，计算量和存储量均较大，尤其对长时间或大计算域的模拟更是如此。文中给出了3种计算方法：全局记忆法、短时记忆法、自适应记忆法，并将这3种方法应用于含黏滞流体黏弹双相VTI （横向各向同性）介质分数阶波传播方程正演。通过对比3种方法的模拟精度、计算时间及占用内存发现：虽然短时记忆法可以通过设置短时记忆长度来调整计算时间与所占内存，但是短时记忆长度越短，精度越差；而自适应记忆法在保证精度的前提下，是短时记忆法与全局记忆法在计算时间与占用内存两方面的折衷。最后对各方法的利弊进行总结，为后续正演模拟及新的分数阶数值算法开发提供方法上的参考。在正演过程中，不仅要使所建模型更贴近实际地下介质，还需对选取的数值算法在计算时间、计算存储量和精度之间进行利弊权衡，以得到一个比较合理的数值算法。
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| 关 键 词： | 分数阶时间导数 短时记忆法 自适应记忆法 黏弹 双相介质 |
| 收稿时间： | 2017-09-16 |
Fractional Temporal Derivative Computation Method for Numerical Simulation of Wavefield in Viscous Fluid-Saturated Viscous Two-Phase VTI Medium |
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| Hu Ning,Liu Cai.Fractional Temporal Derivative Computation Method for Numerical Simulation of Wavefield in Viscous Fluid-Saturated Viscous Two-Phase VTI Medium[J].Journal of Jilin Unviersity:Earth Science Edition,2018,48(3):900-908. |
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| Authors: | Hu Ning Liu Cai |
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| Institution: | College of GeoExploration of Science and Technology, Jilin University, Changchun 130026, China |
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| Abstract: | Compared with the integer derivative,the fractional differential operator can describe a complex mechanical and physical process with historical dependence and spatial global correlation more succinctly.But the computational complexity and the storage capacity of the numerical simulation of fractional wave equations will increase,especially for the simulation of long or large computational domains.In this paper,three kinds of calculation methods are given:global memory method,short-term memory method,and adaptive memory method.These three methods were applied to the simulation of the fractional-order wave propagation equations in a vicious fluid-saturated vicious two-phase VTI medium.Comparing the simulation accuracy,calculation time and memory usage of the three methods,we found that although the short-term memory method could adjust the calculation time and memory by setting the short-term memory length,the shorter the short-term memory length,the worse the accuracy.On the premise of ensuring accuracy,the adaptive memory method is a compromise between the short-term memory and the global memory methods in terms of calculation time and memory occupation.In the process of forward modeling,not only should the model be closer to the actual underground media,but also the selected numerical algorithm needs to balance the calculation time,the calculated storage capacity,and the precision.This method provides a reference for the follow-up forward modeling and the development of the new fractional numerical algorithm. |
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| Keywords: | fractional temporal derivative short-term memory method adaptive memory method viscoelasticity two-phase medium |
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