(1. 中南大學(xué)地球科學(xué)與信息物理學(xué)院，長沙 410083；
2. 東華理工大學(xué)核資源與環(huán)境教育部重點(diǎn)實(shí)驗(yàn)室，南昌 330013)
摘 要: 利用最小梯度支撐穩(wěn)定因子進(jìn)行2.5D井地電位聚焦反演。通過對邊界近似處理、結(jié)合基于圖論理論的矩陣重排與填入元分析方法，實(shí)現(xiàn)一種快速的正演稀疏矩陣直接分解方法，提高了正演計(jì)算效率。為了突出對陡變異常體邊界的識別能力，引入最小梯度支撐穩(wěn)定因子(MGS)，采用重加權(quán)共軛梯度(RRCG)方法進(jìn)行反演目標(biāo)函數(shù)求解。結(jié)果表明：MGS具有良好的聚焦特征，RRCG反演迭代過程穩(wěn)定、收斂速度快。對“L-curve”選擇正則化因子的算法進(jìn)行改進(jìn)，避免了傳統(tǒng)采用最大曲率計(jì)算時(shí)需要對離散數(shù)據(jù)求導(dǎo)引起的誤差，同時(shí)該算法對于出現(xiàn)多個(gè)拐點(diǎn)的“L-curve”也可正確選擇正則化因子。
關(guān)鍵字: 井地電位法；重加權(quán)共軛梯度法； L-curve；最小梯度支撐穩(wěn)定因子；LDLT分解算法
（1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China;
2. Key Laboratory of Nuclear Resources and Environment, Ministry of Education,
East China Institute of Technology, Nanchang 330013, China）
Abstract:The 2.5D focusing inversion for borehole-to-ground electric potential was implemented using minimum gradient support function. The boundary approximation, matrix rearrangement and fill-in element analysis algorithm based on graph theory were adopted to complete the fast algorithm of direct decomposition method for sparse matrix, the computational efficiency was improved. In order to improve the inversion ability to discriminate boundary of abnormal bodies, the minimum gradient support stability factor (MGS) was adopted. On the other hand, re-weighted regularized conjugate gradient (RRCG) inversion method was applied to solve inverse function. The results show that the stability factor is good at invert sharp boundary of underground bodies, RRCG method is stable and fast. For the rapid selection of the most suitable regularization factor, the revised “L-curve” algorithm was studied. New method based on the simply principle of distance from point to line, the error caused by the derivation of discrete data was avoided when the regularization factor was calculated using the maximum curvature method, moreover, for multiple inflection point of the “L-curve”, it also can select the best regularization factor.
Key words: borehole-surfaceelectrical method; re-weighted regularized conjugate gradient; L-curve; minimum gradient support function; LDLT factorization
