复杂岩性解释模型稳定性和可靠性评价
EVALUATION OF STABILITY AND RELIABILITY OF COMPLEX LITHOLOGY INTERPRETING MODELS
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摘要: 对解释模型进行评价以及如何选择合适的解释模型是复杂岩性解释中非常重要的问题。本文应用统计学的理论以及非线性优化技术,系统研究了在线性约束条件下对储层参数的置信区域和误差大小进行估计的问题,通过将梯度投影算法与奇异值分解技术相结合的方法给出了计算储层参数置信区域与误差大小的公式,以及对复杂岩性解释模型的稳定性和可靠性进行合理评价的具体方法。最后通过数值计算实例研究了一种能够有效提高解释模型稳定性和可靠性的措施,数值计算结果证明解释模型响应函数的最小非零奇异值大小是影响稳定性和可靠性的一个重要参数,当最小非零奇异值较大时,模型的稳定性往往较好,否则较差,因此通过对解释模型进行适当组合并选取最小非零奇异值较大的综合解释模型,可以大大提高其稳定性和可靠性。Abstract: Interpretation of well-logging data for complex lithology is an optimization problem under the linear constraint condition,and ill-posed because of the solution nonuniqueness and instability.So it is very important how to evaluate and choose an interpretation model.In this paper,the problem to evaluate the confidence region of reservoir parameters and to calculate their errors under the linear constraint condition is systematically studied using statistical theory and non-linear optimization technique. The formula to compute their confidence region and errors for the complex model is given by combination of gradient projection method and singular-value-decomposition （SVD）.The method to evaluate the stability and reliability of the model is advanced. Finally the effective measure to enhance the stability and reliability is performed through numerical examples.The size of minimum singular value of the response function is the main element to affect the stability and reliability of the models.When the size is higher,the model is usually good,otherwise is not.So choosing the comprehensive model with higher singular values can increase interpreting model quality by amalgamation of some unknown parameters of complex models.
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