A numerical technique for detecting the number and shape of subsurface cavities is presented, applying the particle filter and the parametric level set method to elastic wave propagation under the ground. When subsurface cavities exist, the elastic wave propagating in the ground is reflected at the boundary faces of the cavities. Observing the velocity of the reflection wave at the surface of a ground that includes multiple cavities and parameterizing the shape of the cavities by the parametric level function, both the number and the shape of the cavities can be identified by the particle filter. Numerical experimentation for detecting multiple cavities is conducted with synthetic observation data. The results show that the proposed technique enables the number of cavities to be identified by the number of peaks in the posterior probabilistic distribution function and solves geometric inverse problems by estimating the shape of the cavities through the parameter identification of the level set function.

中文翻译：

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通过弹性波传播的粒子滤波检测多个地下空腔的形状

提出了一种用于探测地下空腔数量和形状的数值技术，将粒子滤波和参数能级设置方法应用于地下弹性波的传播。当存在地下空腔时，在地下传播的弹性波在空腔的边界面反射。观察包括多个空腔的地面表面的反射波速度，并通过参数级函数对空腔的形状进行参数化，可以通过粒子滤波器识别空腔的数量和形状。利用合成观测数据进行了用于检测多个腔体的数值实验。