This article introduces a new optimisation algorithm designed for sampling the solution space of non-linear, non-convex quadratic problems. This method has been specifically designed for inversion problems where multiple distinct scenarios must be explored, which would not be achievable with a standard ensemble-based optimisation method (EnOpt). A prior ensemble is used to sample the uncertainty of the parameters before updating each member of the ensemble independently in order to find the minimum of an objective function. This update is given by a Gauss–Newton-like approach, where the first-derivative matrix is adaptively estimated from sub-ensembles of parameters and their corresponding forward model responses. As the first-derivative matrix is statistically computed from an ensemble of realisations, the forward model does not need to be known and the algorithm is independent of it. The final ensemble provides an estimation of the uncertainty after the inversion process. The efficiency of this adaptive ensemble optimisation (A-EnOpt) method is first tested on simple two-dimensional problems where known mathematical functions are used as forward models. The results show that the method minimises the objective functions and samples the final uncertainties of the problems to a better degree than a standard EnOpt. The A-EnOpt method is then applied to a real heavy-oil field petrophysical inversion. Porosity, shale fraction and fluid saturations are inverted under continuity and Lagrange constraints, conditioned by P-impedance models from stochastic seismic inversion. The updated properties are incorporated in a fluid flow model of the field. The simulation results produce a better match to historical production data at one well than equivalent flow simulations using the properties before inversion. This shows that conditioning by seismic data improves the quality of the geological models.

本文介绍了一种新的优化算法，该算法设计用于对非线性，非凸二次问题的解空间进行采样。此方法专门针对必须研究多个不同场景的反演问题而设计，而这是标准的基于集成的优化方法（EnOpt）无法实现的。先验集合用于在独立更新集合的每个成员之前采样参数的不确定性，以便找到目标函数的最小值。此更新通过类似高斯-牛顿的方法给出，其中一阶导数矩阵是根据参数的子集合及其对应的正向模型响应自适应估计的。由于一阶导数矩阵是从一组实现中统计得出的，前向模型不需要已知，并且算法与之无关。最终集合提供了反演过程后不确定性的估计。首先在简单的二维问题上测试这种自适应集成优化（A-EnOpt）方法的效率，在该问题上，已知的数学函数用作正向模型。结果表明，与标准EnOpt相比，该方法可最大程度地减少目标函数并对问题的最终不确定性进行采样。然后，将A-EnOpt方法应用于实际的重油田岩石物理反演。孔隙度，页岩分数和流体饱和度在连续性和拉格朗日约束下被反转，这是由随机地震反演中的P阻抗模型决定的。更新的属性被合并到该领域的流体模型中。与使用反演前的属性进行等价的流量模拟相比，模拟结果在一口井中与历史生产数据更匹配。这表明通过地震数据进行条件处理可以改善地质模型的质量。