Marine controlled-source electromagnetic (CSEM) method has proved its potential in detecting highly resistive hydrocarbon bearing formations. A novel frequency domain CSEM inversion approach using fictitious wave domain time stepping modelling is presented. Using Lagrangian-based adjoint state method, the inversion gradient with respect to resistivity can be computed by the product between the forward and adjoint fields. Simulation of the adjoint field using the same modelling engine is challenging as it requires time domain adjoint source time functions while only a few discrete frequencies of the data residual are available for the inversion. A regularized linear inverse problem is formulated in order to estimate a long time series from very few frequency samples. It can then be solved using linear optimization technique, yielding a matrix-free implementation. Instead of computing adjoint source time function one by one at each receiver location, a basis function implementation has been developed such that the inverse problem can be solved only once and reused every time to construct all time-domain adjoint sources. The method allows computing all frequencies of the EM fields in one go without heavy memory and computational overhead, making efficient 3D CSEM inversion feasible. Numerical examples are employed to demonstrate the application of our method.

翻译：海洋可控源电磁法在探测高阻油气层方面已展现出其潜力。本文提出了一种基于虚波数域时间步进建模的新型频域CSEM反演方法。利用基于拉格朗日伴随状态法，反演梯度可通过正演场与伴随场的乘积计算得出。然而，使用同一建模引擎模拟伴随场面临挑战，因为反演仅需数据残差的少数离散频率值，却要求提供时域伴随源的时间函数。为此，我们建立了一个正则化线性反问题，从极少数频率样本中估计长时间序列，并通过线性优化技术求解，从而实现无矩阵存储的计算框架。不同于在每个接收点逐一计算伴随源时间函数，我们开发了基函数实现方法：反问题仅需求解一次即可重复用于构造所有时域伴随源。该方法可一次性计算电磁场的所有频率成分，无需大量内存与计算开销，使得高效三维CSEM反演成为可能。最后通过数值算例验证了该方法的有效性。