For geophysical electromagnetic (EM) forward modeling problems, the accuracy of solutions mainly depends on the numerical modeling method used and the corresponding boundary conditions. Most multi-dimensional EM studies deal with numerical methods for discretisation (e.g., finite-difference, finite-element, integral equation, etc.) and pay less attention to the boundaries. This review presents the recent research on optimizing boundary conditions for the frequency-domain marine controlled-source EM (CSEM) forward modeling algorithm. Current geophysical EM field simulation techniques usually utilize the truncated Dirichlet boundary condition, which requires the modeling domain boundaries to be far away from the area of interest and field values to be zero at the boundaries to mitigate artificial reflections/refractions resulting from truncated boundaries. The perfectly matched layer (PML) approach with few additional absorbing layers can serve as an alternative boundary to supress these truncated boundary effects. In this review, the application of the PML boundary condition to marine CSEM using a staggered finite-difference scheme for the 2.5D problem in vertical transverse isotropic (VTI) conductivity structures is introduced. This new algorithm utilizes the complex frequency-shifted PML (CFS-PML) boundary condition. The selection of optimal PML parameters are also further investigated for numerical stability. Numerical tests for several Earth conductivity models show that the CFS-PML approach is of similar high accuracy compared to using traditional Dirichlet boundary condition and exhibits additional advantages in terms of computational time and memory usage. Furthermore, the numerical tests indicate that the proposed forward modeling algorithm using CFS-PML boundary condition works well for both shallow and deep water cases, including the application to real field example from the Troll Field in Norway. The detectability of subsurface-related EM fields in airwave dominated shallow waters can be enhanced by using the weighted difference fields for mitigating the effect of airwaves on the models.

对于地球物理电磁（EM）正演建模问题，解的准确性主要取决于所使用的数值建模方法和相应的边界条件。大多数多维 EM 研究处理离散化的数值方法（例如，有限差分、有限元、积分方程等），而较少关注边界。本综述介绍了最近关于优化频域海洋受控源电磁 (CSEM) 正演建模算法的边界条件的研究。当前的地球物理电磁场模拟技术通常利用截断的狄利克雷边界条件，这要求建模域边界远离感兴趣区域，并且边界处的场值为零，以减轻由截断边界引起的人为反射/折射。具有少量附加吸收层的完美匹配层 (PML) 方法可以作为替代边界来抑制这些截断边界效应。在这篇综述中，介绍了使用交错有限差分方案将 PML 边界条件应用于海洋 CSEM，以解决垂直横向各向同性 (VTI) 电导率结构中的 2.5D 问题。这种新算法利用了复杂的频移 PML (CFS-PML) 边界条件。还进一步研究了最佳 PML 参数的选择以实现数值稳定性。几个地球电导率模型的数值测试表明，与使用传统的 Dirichlet 边界条件相比，CFS-PML 方法具有相似的高精度，并且在计算时间和内存使用方面表现出额外的优势。此外，数值测试表明，所提出的使用 CFS-PML 边界条件的正演建模算法适用于浅水和深水情况，包括在挪威 Troll 油田的实际现场示例中的应用。通过使用加权差分场来减轻电波对模型的影响，可以增强在电波占主导地位的浅水中与地下相关的电磁场的可检测性。