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：海洋可控源电磁法已证明其在探测高阻油气储层方面的潜力。本文提出了一种新颖的频率域CSEM反演方法，该方法采用虚拟波动域时步建模技术。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到。由于反演仅需数据残差的少数离散频率，而伴随源时间函数需在时域定义，因此使用同一建模引擎模拟伴随场具有挑战性。为解决该问题，我们构建了正则化线性逆问题，从极少的频率样本中估计长时序信号，并采用线性优化技术实现无矩阵计算。不同于在各接收点逐点计算伴随源时间函数，我们开发了基函数实现方案，使得逆问题仅需求解一次并可重复用于构建所有时域伴随源。该方法无需高内存及计算开销即可一次性计算所有频率的电磁场，使高效三维CSEM反演成为可能。通过数值算例验证了本方法的实际应用效果。