高密度电阻率勘探反演的非线性方法研究
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摘要
电法勘探在采矿工程领域有着广阔的应用前景,尤其是在矿井水害超前预警探测方面正在发挥着重要作用。然而由于对实测数据采用线性方法处理,反演结果往往与实际情况有较大的偏差,解译精度难以满足矿井生产的要求。高密度电阻率法是电法勘探的一个重要分支,常用的数据处理方法主要包括有限差分法、有限单元法、共轭梯度法和最小二乘法等,应用最多的是由M.H.Loke开发的二维、三维电阻率法反演软件Res2dinv和Res3dinv,但使用效果并不十分理想。因此提高高密度电法反演精度的研究不仅可丰富采矿地球物理勘查的数据处理理论,而且对矿井安全生产和解决一些工程地质等问题均具有重要的理论意义和实用价值。
目前非线性反演技术已应用于地球物理反演领域,而电法非线性反演却未得到广泛的应用。近年来随着非线性反演技术的深入研究,许多学者提出了非线性联合反演技术,但至今仍未有实质性的进展,为此本文就神经网络算法(BP)、模拟退火法(SA)、遗传算法(GA)和蚁群算法(ACO)这四种具有代表意义的非线性算法,及各自在地球物理反演领域的应用,尤其在电法反演方面的使用进行了阐述,并针对各自不同反演计算的局限性,将非线性联合算法引入到电法反演之中,从而实现了不同方法间的优化联合,并将此类联合方法应用于高密度电法的非线性反演,满足了解译精度的要求。
本文依据不同非线性反演方法的特点,将具有局部搜索优势的神经网络算法分别与具有良好全局搜索优势的模拟退火法、遗传算法和蚁群算法进行联合反演,即利用SA、GA、ACO这三种算法的全局搜索优势,对BP网络算法的初始权值、阙值矩阵进行优化,从而大大地缩短了反演计算时间、极大地提高了BP神经网络进行电法数据反演的成功率,达到了提高反演精度的目的。
论文在提出了联合优化算法的框架与步骤,得到了SA-BP算法、GA-BP算法和ACO-BP算法之后,通过计算机编程对这三种典型的模型进行了反演运算,实现了高密度电阻率法的电阻率非线性反演；通过三种联合算法和单一BP算法反演数据的SURFER成图可以看出,三种非线性方法的高密度电法反演结果均明显优于传统线性反演结果,非线性方法反演结果反映出的异常体赋存状态更接近于理论模型。
为显示联合算法相对于单一BP算法的优势,文中对各联合算法的反演与BP神经网络反演分别做出比较,结果显示联合算法可以克服BP神经网络反演方法的不足,避免陷入局部最优解现象,同时还可减少训练次数、节约训练时间,高效地获得高精度反演结果；而且联合算法的稳定性和模型的吻合性都比BP神经网络独立反演要好。
通过比较各联合算法对数值模型做出的反演运算结果,采用判断系数R2以及均方差E进行各联合方法的评价,得出不同联合方法反演的优势：ACO-BP方法在反演中用时最短,反演精度高,反演稳定性好(E值较小),判断系数R2更接近数值1,反演模型适宜性最强；GA-BP方法由于GA的非并行寻优方式,使得GA对BP神经网络的初值优化耗时较长,但最终反演精度较高；SA-BP方法在这三种联合算法中无明显优势,无论反演所需时间还是模型精度都不及前两种方法。
最后选取ACO-BP联合反演方法和GA-BP联合反演方法应用到山西中煤潘家窑煤业有限公司的地下采空充水区探测数据处理中。采用传统的反演方法进行高密度电阻率法数据反演处理,反演结果与已知钻孔资料有一定的偏差。而利用非线性联合优化反演方法ACO-BP和GA-BP进行反演时,结果与实际采空区的位置吻合较好,验证了非线性联合算法应用于高密度电阻率法数据反演中的实用性和可操作性。
本文研究结论表明了非线性联合方法在高密度电法反演中的有效性,对今后其它电法勘探方法的反演技术提出可借鉴的经验。
As is known by us all, the electrical prospecting method is gaining a wide application prospect and playing an increasingly important role especially in advanced warning and detection of water disaster in coal mines. However, the inversion result always shows a significant deviation compared with the reality due to the linear processing method towards the original data, so the interpreting accuracy can hardly meet the requirements of the mining production. As an important branch of electrical prospecting, the data processing methods that are most commonly used for the high density resistivity method include the finite difference method, the finite element method, the conjugate gradient method as well as the least square method, among which the two dimensional inversion software RES2DINV and the three dimensional software RES3DINV developed by M. H. Loke are the most frequently used ones, however, the result is also beyond satisfaction. Therefore, research on the promotion of inversion accuracy of the high density electrical method would not only enrich the data processing theory of mining geophysical exploration, but also provide a theoretical significance as well as practical utility to the safety in mine production and some problems in engineering geology.
Although nonlinear inversion method had already been applied in the geophysical inversion field, there are fairly few applications of nonlinear method in electrical exploration. Many researchers had attempt the nonlinear joint inversion technology with the intensively research in the nonlinear method in recent years, however, there are still no substantial progress. As a result, the application in geophysical inversion field especially in electrical prospecting method of four representational nonlinear method including neural network algorithm (BP), simulated annealing method (SA), genetic algorithm (GA) and ant colony optimization (ACO) are stated in this thesis, besides, the joint nonlinear algorithm is also introduced in according to the limitations of the four algorithms, so the majorization and combination of the four above mentioned algorithms is fulfilled, from the utilization of which the requirements of interpreting accuracy can be met in the inversion of high density electrical method.
Based on the characteristics of different kinds of nonlinear inversion method, the joint inversion between neural network algorithm and other three kinds of algorithms is carried out, in which the overall search advantage of SA, GA and ACO is introduced in optimizing the original weight and weight matrix of the BP neural network algorithm, by doing that, the calculation time of the inversion could be shorten, so the efficient of the inversion of the BP neural network algorithm could be enhanced to a large extent, from which the inversion accuracy could eventually be promoted.
In this thesis, the overall framework and procedures of joint optimized algorithm including SA-BP algorithm, GA-BP algorithm and ACO-BP algorithm is firstly worked out, after which computer programming is used to fulfill the inversion on the three typical models and eventually the nonlinear inversion of the high density resistivity method. Through the result graph of the three joint inversion method and the single BP algorithm generated by SURFER, a conclusion can be drawn that the inversion result of the three joint algorithms are significantly better than the single BP algorithm, and the occurrence form of abnormal body from using the nonlinear inversion method is more close to the theoretical model.
In order to display the advantage of the joint algorithm over the single algorithm, the comparison between those two algorithm is also stated in this thesis, the result shows that joint algorithm could overcome the disadvantage to avoid the optimal explain phenomena and to save the training time through reduce training time, besides, higher inversion accuracy could be obtained through the joint algorithm, apart from which, the stability and similarity with the model of joint algorithm are better than the single algorithm.
Through the comparison between the three different joint algorithm in the inversion results from judge coefficient and mean square error, advantages of different method could be concluded that the ACO-BP method has a advantage of short time consumption, high inversion accuracy, low E value, a suitable judge coefficient close to 1 and good suitability to the model, while the GA-BP method has a relatively higher time consumption due to the non-parallel optimal way, however, the inversion accuracy is high. As to the SA-BP method, it hardly has advantages over the other two methods.
Lastly, the inversion method of ACO-BP and GA-BP is applied to the data processing of the detection of the goaf filled with water in panjiayao coal mine in Shanxi province, the inversion result of which is more highly closed to the reality compared with the results obtained from the traditional inversion method, which illustrates the utility and feasibility of joint nonlinear inversion method in the processing of the data of the high density resistivity method.
The conclusion of this thesis illustrates the efficiency of the joint nonlinear inversion method, which would provide some experience to the inversion technology used in other kinds of electric method in future.
目前非线性反演技术已应用于地球物理反演领域,而电法非线性反演却未得到广泛的应用。近年来随着非线性反演技术的深入研究,许多学者提出了非线性联合反演技术,但至今仍未有实质性的进展,为此本文就神经网络算法(BP)、模拟退火法(SA)、遗传算法(GA)和蚁群算法(ACO)这四种具有代表意义的非线性算法,及各自在地球物理反演领域的应用,尤其在电法反演方面的使用进行了阐述,并针对各自不同反演计算的局限性,将非线性联合算法引入到电法反演之中,从而实现了不同方法间的优化联合,并将此类联合方法应用于高密度电法的非线性反演,满足了解译精度的要求。
本文依据不同非线性反演方法的特点,将具有局部搜索优势的神经网络算法分别与具有良好全局搜索优势的模拟退火法、遗传算法和蚁群算法进行联合反演,即利用SA、GA、ACO这三种算法的全局搜索优势,对BP网络算法的初始权值、阙值矩阵进行优化,从而大大地缩短了反演计算时间、极大地提高了BP神经网络进行电法数据反演的成功率,达到了提高反演精度的目的。
论文在提出了联合优化算法的框架与步骤,得到了SA-BP算法、GA-BP算法和ACO-BP算法之后,通过计算机编程对这三种典型的模型进行了反演运算,实现了高密度电阻率法的电阻率非线性反演；通过三种联合算法和单一BP算法反演数据的SURFER成图可以看出,三种非线性方法的高密度电法反演结果均明显优于传统线性反演结果,非线性方法反演结果反映出的异常体赋存状态更接近于理论模型。
为显示联合算法相对于单一BP算法的优势,文中对各联合算法的反演与BP神经网络反演分别做出比较,结果显示联合算法可以克服BP神经网络反演方法的不足,避免陷入局部最优解现象,同时还可减少训练次数、节约训练时间,高效地获得高精度反演结果；而且联合算法的稳定性和模型的吻合性都比BP神经网络独立反演要好。
通过比较各联合算法对数值模型做出的反演运算结果,采用判断系数R2以及均方差E进行各联合方法的评价,得出不同联合方法反演的优势：ACO-BP方法在反演中用时最短,反演精度高,反演稳定性好(E值较小),判断系数R2更接近数值1,反演模型适宜性最强；GA-BP方法由于GA的非并行寻优方式,使得GA对BP神经网络的初值优化耗时较长,但最终反演精度较高；SA-BP方法在这三种联合算法中无明显优势,无论反演所需时间还是模型精度都不及前两种方法。
最后选取ACO-BP联合反演方法和GA-BP联合反演方法应用到山西中煤潘家窑煤业有限公司的地下采空充水区探测数据处理中。采用传统的反演方法进行高密度电阻率法数据反演处理,反演结果与已知钻孔资料有一定的偏差。而利用非线性联合优化反演方法ACO-BP和GA-BP进行反演时,结果与实际采空区的位置吻合较好,验证了非线性联合算法应用于高密度电阻率法数据反演中的实用性和可操作性。
本文研究结论表明了非线性联合方法在高密度电法反演中的有效性,对今后其它电法勘探方法的反演技术提出可借鉴的经验。
As is known by us all, the electrical prospecting method is gaining a wide application prospect and playing an increasingly important role especially in advanced warning and detection of water disaster in coal mines. However, the inversion result always shows a significant deviation compared with the reality due to the linear processing method towards the original data, so the interpreting accuracy can hardly meet the requirements of the mining production. As an important branch of electrical prospecting, the data processing methods that are most commonly used for the high density resistivity method include the finite difference method, the finite element method, the conjugate gradient method as well as the least square method, among which the two dimensional inversion software RES2DINV and the three dimensional software RES3DINV developed by M. H. Loke are the most frequently used ones, however, the result is also beyond satisfaction. Therefore, research on the promotion of inversion accuracy of the high density electrical method would not only enrich the data processing theory of mining geophysical exploration, but also provide a theoretical significance as well as practical utility to the safety in mine production and some problems in engineering geology.
Although nonlinear inversion method had already been applied in the geophysical inversion field, there are fairly few applications of nonlinear method in electrical exploration. Many researchers had attempt the nonlinear joint inversion technology with the intensively research in the nonlinear method in recent years, however, there are still no substantial progress. As a result, the application in geophysical inversion field especially in electrical prospecting method of four representational nonlinear method including neural network algorithm (BP), simulated annealing method (SA), genetic algorithm (GA) and ant colony optimization (ACO) are stated in this thesis, besides, the joint nonlinear algorithm is also introduced in according to the limitations of the four algorithms, so the majorization and combination of the four above mentioned algorithms is fulfilled, from the utilization of which the requirements of interpreting accuracy can be met in the inversion of high density electrical method.
Based on the characteristics of different kinds of nonlinear inversion method, the joint inversion between neural network algorithm and other three kinds of algorithms is carried out, in which the overall search advantage of SA, GA and ACO is introduced in optimizing the original weight and weight matrix of the BP neural network algorithm, by doing that, the calculation time of the inversion could be shorten, so the efficient of the inversion of the BP neural network algorithm could be enhanced to a large extent, from which the inversion accuracy could eventually be promoted.
In this thesis, the overall framework and procedures of joint optimized algorithm including SA-BP algorithm, GA-BP algorithm and ACO-BP algorithm is firstly worked out, after which computer programming is used to fulfill the inversion on the three typical models and eventually the nonlinear inversion of the high density resistivity method. Through the result graph of the three joint inversion method and the single BP algorithm generated by SURFER, a conclusion can be drawn that the inversion result of the three joint algorithms are significantly better than the single BP algorithm, and the occurrence form of abnormal body from using the nonlinear inversion method is more close to the theoretical model.
In order to display the advantage of the joint algorithm over the single algorithm, the comparison between those two algorithm is also stated in this thesis, the result shows that joint algorithm could overcome the disadvantage to avoid the optimal explain phenomena and to save the training time through reduce training time, besides, higher inversion accuracy could be obtained through the joint algorithm, apart from which, the stability and similarity with the model of joint algorithm are better than the single algorithm.
Through the comparison between the three different joint algorithm in the inversion results from judge coefficient and mean square error, advantages of different method could be concluded that the ACO-BP method has a advantage of short time consumption, high inversion accuracy, low E value, a suitable judge coefficient close to 1 and good suitability to the model, while the GA-BP method has a relatively higher time consumption due to the non-parallel optimal way, however, the inversion accuracy is high. As to the SA-BP method, it hardly has advantages over the other two methods.
Lastly, the inversion method of ACO-BP and GA-BP is applied to the data processing of the detection of the goaf filled with water in panjiayao coal mine in Shanxi province, the inversion result of which is more highly closed to the reality compared with the results obtained from the traditional inversion method, which illustrates the utility and feasibility of joint nonlinear inversion method in the processing of the data of the high density resistivity method.
The conclusion of this thesis illustrates the efficiency of the joint nonlinear inversion method, which would provide some experience to the inversion technology used in other kinds of electric method in future.
引文
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