This paper focuses on the application of hp hierarchic genetic strategy (hp–HGS) for solution of a challenging problem, the inversion of 3D direct current (DC) resistivity logging measurements. The problem under consideration has been formulated as the global optimization one, for which the objective function (misfit between computed and reference data) exhibits multiple minima. In this paper, we consider the extension of the hp–HGS strategy, namely we couple the hp–HGS algorithm with a gradient based optimization method for a local search. Forward simulations are performed with a self-adaptive hp finite element method, hp–FEM. The computational cost of misfit evaluation by hp–FEM depends strongly on the assumed accuracy. This accuracy is adapted to the tree of populations generated by the hp–HGS algorithm, which makes the global phase significantly cheaper. Moreover, tree structure of demes as well as branch reduction and conditional sprouting mechanism reduces the number of expensive local searches up to the number of minima to be recognized. The common (direct and inverse) accuracy control, crucial for the hp–HGS efficiency, has been motivated by precise mathematical considerations. Numerical results demonstrate the suitability of the proposed method for the inversion of 3D DC resistivity logging measurements.

中文翻译：

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一种用于3D DC电阻率测井测量反演的混合方法。

本文重点介绍了hp分层遗传策略（hp –HGS）在解决难题方面的应用，即3D直流电（DC）电阻率测井反演。所考虑的问题已被表述为全局最优化问题，其目标函数（计算数据与参考数据之间的不匹配）表现出多个极小值。在本文中，我们考虑了hp –HGS策略的扩展，即将hp –HGS算法与基于梯度的优化方法结合起来进行局部搜索。使用自适应hp有限元方法hp –FEM进行正向仿真。失配评估的计算成本hp –FEM很大程度上取决于假定的精度。此准确性适用于hp –HGS算法生成的种群树，这使全局阶段便宜得多。而且，界域的树结构以及分支的减少和有条件的发芽机制减少了昂贵的本地搜索次数，直至可识别的最小值。对hp –HGS效率至关重要的通用（正向和反向）精度控制是出于精确的数学考虑。数值结果表明，该方法适用于3D DC电阻率测井测量的反演。