时间域电磁法伪随机码全波形响应变维贝叶斯反演研究

The time domain electromagnetic (TEM) method is an important tool to study the electrical contrast underground, the accuracy of the recovered near surface structure is the basis of investigating deep-seated structure, and the resolution of the near surface model depends on the high frequency components in the responses. The energy of traditional time domain electromagnetic source and its density of the frequencies are small, which impeded the recovery of the near surface model. The pseudo binary sequence (PRBS) has a flat spectra and large frequency density, which is suitable to be employed as the source waveform of TEM method. However, the conventional inversion routine based on the secondary field of TEM method cannot be directly used in the inversion of PRBS response. The trans-dimensional Bayesian method fits the response using the random sampling so that the calculation of sensitivity matrix is unnecessary and the number of the parameters can be adaptively adjusted. Hence, this project will directly invert the full waveform response from a PRBS source using the trans-dimensional Bayesian method to improve the accuracy of the TEM method. A 2.5D finite difference forward calculator based on the tree structure will be developed and incorporated into the trans-dimensional Bayesian framework. The model complexity will be adaptive obtained from the inversion procedure and the resolution of the result can be improved. Finally, to transit the theoretical research of the developed method to practical application, this project will verify the effectiveness of the inversion method by testing it on the field full waveform response from a PRBS source.

时间域电磁法是探测地下电性结构的重要手段，其浅层分辨能力决定了深部目标体探测效果且主要与响应中的高频能量相关。时间域电磁法传统源波形高频能量弱、频谱密度小，在浅层结构的精细刻画中存在局限性。伪随机码信号频谱能量分布均匀、频谱密度可调，适于作为时间域电磁法源信号，但难以采用常规基于纯二次场响应的反演方法进行数据处理。变维贝叶斯方法基于随机采样对数据进行拟合，无需计算灵敏度且模型参数个数自适应可变，适用于复杂源波形的时间域电磁法数据反演。为此，本研究将基于变维贝叶斯方法，直接针对伪随机码全波形响应进行反演，实现浅部结构精细刻画，提高时间域电磁法探测精度。拟通过树状结构网格下的2.5D有限差分正演模拟，结合变维贝叶斯反演的维度变化特性和吝啬性，由数据自适应获得与数据最佳匹配的模型复杂度，提高反演结果的分辨率。最后，为完成从理论研究到实际应用的转换，将利用典型测区的处理结果验证反演方法的应用效果。

反演是电磁探测获取地下介质电性信息的关键手段。梯度类反演方法依赖于初始电阻率模型，且难以评价反演解的可靠性。为此，本项目基于全局搜索的贝叶斯方法，发展了时间域电磁法2.5D反演方法，同时提取电阻率分布及其不确定性评价。项目的研究结果建立了时间域电磁法高维贝叶斯反演的基本框架，并在反演中通过卷积引入源波形，使得所研发的方法适用于任意波形的时间域电磁数据反演，为时间域电磁法优化源波形、提高分辨率，提供了重要的反演技术支撑。通过研发高效且稳定的数值模拟算子，奠定了贝叶斯反演的基础。通过构建源影响域的模型子空间采样和重构方法，解决了时间域电磁法高维贝叶斯反演的计算效率问题。项目的研究结果通过数值模拟算例和实测数据得到了验证。由于贝叶斯方法已随机采样的方式进行全局搜索，不依赖初始模型，相比于常规方法具有更高的稳健性。此外，贝叶斯方法可同时获得地下介质的电阻率分布及其置信度，提升了时间域电磁法数据反演的可靠性。这些优势能够为时间域电磁法在矿产资源、水资源、工程和环境等领域的应用提高重要手段和支撑。