Electromagnetic full waveform inversion in Debye dispersive medium (EFWI-D) is a promising technique to reconstruct the inner structure and electrical properties of the medium such as soil, rock and biological tissues. Same as conventional full waveform inversion, EFWI-D requires high computational cost, especially in the 3D case. To reduce the long computation time, we design and implement the EFWI-D algorithm in time domain using multiple GPU cards. The inversion method is based on the L-BFGS optimization algorithm, which can increase the convergence of the misfit function, while the auxiliary differential equation (ADE) method is employed for modeling the Debye dispersive medium by using exponential time differencing (ETD) finite-difference time-domain (FDTD) approach. Moreover, a multi-stream strategy is performed in the workflow to improve the computation performance. Numerical results illustrate the improvement of the computational performance and the preliminarily feasibility of the proposed inversion algorithm.

Program summary

Program title: 3D Electromagnetic Full Waveform Inversion in Debye Dispersive Medium Based on Multi-GPU Paralleling

CPC Library link to program files: https://doi.org/10.17632/mjd9pp5dcm.1

Licensing provisions: LGPL

Programming language: C/C++, CUDA

Nature of problem: Electromagnetic FWI derives high-resolution distribution of electrical parameters by using additional information provided by the amplitude and phase of the received signals. It goes beyond ray-tracing tomography techniques, which use only the travel time kinematics of the signals. Mathematically, electromagnetic FWI is a kind of conditional extremum problem which is to minimize the difference between observed and modeled waveform of received signals under the condition of Maxwell's equation.

Solution method: The basis of inversion is the solution of the forward problem. In this program, the forward simulation is based on Auxiliary Differential Equation (ADE) method. Since the inverse problem is nonlinear, it is solved by using iterative solution which is an optimization method. As it is well known that 3D FWI requires tremendous computation, multi-GPU paralleling is used in this program to accelerate the computing process.

Additional comments including Restrictions and Unusual features: The program is mainly designed to solve the inverse problem in Debye dispersive medium, but it also can be used for solving the forward and inverse problem in nondispersive medium by setting the input parameter: poles_of_debye_dispersive_medium(non_dispersive=0,dispersive=1-5)=0.

中文翻译：

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多GPU并行加速的Debye分散介质中的3D时域电磁全波形反演

Debye分散介质中的电磁全波形反演（EFWI-D）是一种有前途的技术，可以重建土壤，岩石和生物组织等介质的内部结构和电学特性。与常规的全波形反演相同，EFWI-D需要很高的计算成本，尤其是在3D情况下。为了减少较长的计算时间，我们使用多个GPU卡在时域中设计和实现EFWI-D算法。该反演方法基于L-BFGS优化算法，可以提高失配函数的收敛性，而辅助微分方程（ADE）方法用于使用指数时差（ETD）有限元模型对Debye色散介质进行建模。时域差异（FDTD）方法。而且，在工作流中执行多流策略以提高计算性能。数值结果说明了计算性能的提高，并初步所提出的反演算法的可行性。

计划摘要

程序标题：基于多GPU并行的德拜色散介质中的3D电磁全波形反演

CPC库链接到程序文件： https : //doi.org/10.17632/mjd9pp5dcm.1

许可规定： LGPL

编程语言： C / C ++，CUDA

问题的性质：电磁FWI通过使用由接收信号的幅度和相位提供的附加信息来获得电参数的高分辨率分布。它超越了射线追踪层析成像技术，后者仅使用信号的传播时间运动学。在数学上，电磁FWI是一种条件极值问题，它是在麦克斯韦方程组的条件下，使接收信号的观测波形与建模波形之间的差异最小化。

解决方法：反演的基础是正问题的解决。在此程序中，正向仿真基于辅助微分方程（ADE）方法。由于反问题是非线性的，因此可以使用作为优化方法的迭代解来解决。众所周知3D FWI需要大量计算，因此在此程序中使用了多GPU并行化来加速计算过程。

包括限制和异常功能在内的其他注释：该程序主要用于解决Debye色散介质中的逆问题，但是它也可以通过设置输入参数来解决非色散介质中的正向和逆问题：poles_of_debye_dispersive_medium（non_dispersive = 0 ，分散= 1-5）= 0。