3D SIP inversion algorithm involves multiple parameters, and the key is the calculating speed and memory. A whole set of quasi-linear (QL) theories has taken shape in recent years, including the QL approximation method proposed by Zhdanov, quasi-analytic approximation, and localized quasi-linear (LQL) approximation. They are characterized by high speed and accuracy in electromagnetic field numerical modeling. The above-based 3D QL inversion algorithm, boasting quicker calculating speed plus more stable and favorable inversion effect, has been adopted profoundly in electromagnetic prospecting, whereas its frequent source conversion requires recalculating the dyadic Green’s function and primary field each time, thus delaying the 3D SIP modeling speed. This study makes use of the spatial symmetry in the primary field and Green function to propose an effective and quicker QL forward modeling method, which has the hallmark of higher calculating speed owing to less calculating times, and makes feasible the 3D SIP conjugate gradient inversion algorithm with Cole–Cole parameter range constraints.

中文翻译：

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带参数范围约束的3D SIP共轭梯度反演算法研究

3D SIP 反演算法涉及多个参数，关键是计算速度和内存。近年来形成了一整套拟线性（QL）理论，包括Zhdanov提出的QL逼近方法、拟解析逼近和局部拟线性（LQL）逼近。它们的特点是电磁场数值建模速度快、精度高。基于上述的3D QL反演算法，计算速度更快，反演效果更稳定、更有利，在电磁勘探中得到了广泛的应用，而其频繁的源转换需要每次重新计算二元格林函数和一次场，从而延迟了3D SIP 建模速度。