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储层方面已展现出潜力。本文提出了一种采用虚拟波动域时间步进建模的新型频域CSEM反演方法。基于拉格朗日伴随状态法，通过正向场与伴随场的乘积即可计算电阻率反演梯度。由于反演仅需数据残差的若干离散频率，而伴随场模拟需时域伴随源时间函数，导致采用同一建模引擎实现伴随场仿真颇具挑战。为此，本文构建了正则化线性逆问题，从极少量频域样本中估计长时间序列，并采用线性优化技术求解，实现免矩阵计算。不同于逐接收点逐一计算伴随源时间函数，本文发展了基函数实现方案：逆问题仅需单次求解，即可重复用于构建所有时域伴随源。该方法能一次性计算所有频率的电磁场，避免繁重的内存与计算开销，使高效三维CSEM反演成为可能。数值算例验证了所提方法的有效性。