基于IBEM和QMESSA的饱和场地地下空洞反演

Inversion of subsurface cavity in saturated sites based on IBEM and QMESSA

摘要

为探究饱和场地内部空洞的分布特征，传统局部线性优化算法已被广泛用于反演问题。然而，反演问题常面临非线性和多解性等固有挑战。为此，引入一种全局非线性优化算法——基于量子计算与多策略增强的麻雀搜索算法（sparrow search algorithm based on quantum computations and multi-strategy enhancement，QMESSA），以实现高效、精确的参数优化。该算法避免了反演对初始模型较强的依赖性，通过构造自适应T分布增加种群突变概率，有效避免局部最优，加强了种群的全局寻优能力和局部精细搜索能力。正演过程采用间接边界元法（indirect boundary element method，IBEM），该方法有效降低计算维度，同时显著提升了计算效率和精度。以饱和半空间中的圆形、椭圆形和哑铃形空洞为例，验证了QMESSA与IBEM结合用于反演的有效性和稳定性。结果表明，QMESSA能够快速、准确地反演空洞的位置与尺度，且各参数的反演结果精度较高。此外，该算法的全局搜索能力在一定程度上弥补了先验信息不足的限制，展现出在饱和场地空洞反演中的良好应用潜力。

Abstract

To explore the distribution characteristics of cavity in saturated sites，traditional local optimization algorithms are commonly employed to solve inverse problems. However，such problems often involve inherent challenges，including nonlinearity and multiple solutions. To address these issues，the sparrow search algorithm based on quantum computations and multi-strategy enhancement （QMESSA） is introduced to achieve efficient and accurate parameter optimization. The algorithm reduces the inversion's strong reliance on the initial model，enhances the population's mutation probability through the use of an adaptive T-distribution，effectively mitigates the risk of local optima，and improves the population's global optimization capabilities and local fine-tuning efficiency. The forward modeling process employs the indirect boundary element method （IBEM），which effectively reduces computational dimensions while improving both efficiency and accuracy. The effectiveness and stability of combining QMESSA with IBEM for inversion are demonstrated through examples of circular，dumbbell-shaped and elliptical cavity in a saturated half-space. The results show that QMESSA can quickly and accurately determine the location and scale of cavity，producing high-accuracy results for each parameter. Furthermore，the global search capability of the algorithm compensates for the limitation of insufficient prior information and highlights its potential for applications in cavity inversion within saturated sites.

关键词

饱和场地地下空洞反演 / 反演算法 / 间接边界元法 / QMESSA / 弹性波勘探

Key words

inversion of underground cavity in saturated sites / inversion algorithm / indirect boundary element method / QMESSA / elastic wave exploration

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基金资助

国家自然科学基金资助项目(52278516)