Research And Application On The 3D Forward Modeling And Inversion Of Frequency-Domain Controlled-Source Electromagnetic Method In Coal Goaves

With the continuous exploitation of coal resources in China,a large number of coal goaves have been produced in coal-producing areas such as Shanxi,Shaanxi and Inner Mongolia.These coal goaves have destroyed the stress balance of surrounding rock mass structure,resulting in cracks,ground collapse,and uneven settlement within a certain area,endangering the safety of humans’ lives and property.It is important to detect the specific location of the coal goaves,to ensure the safe production of the coal mines and protect the safety of humans.Therefore,it is of great significance to carry out the research on geophysical methods of coal goaves.In the geophysical methods,the frequency-domain controlled-source electromagnetic method has the advantages of high accuracy,high efficiency,and low cost.It is widely used in the exploration of metal minerals,oil and gas resources,engineering geology,hydrological resources,etc.,and can also be used in the exploration of coal goaves.With the formation of large-scale coal goaves,it has become a new trend to use frequency-domain controlled-source electromagnetic method to detect coal goaves.Taking coal goaves as the research object,it is imperative to carry out high-precision and high-efficiency data interpretation of frequency-domain controlled-source electromagnetic method.Aiming at the coal goaves,this article focused on the study of three-dimensional forward modeling and inversion of frequency-domain controlled-source electromagnetic method.The main content of this article included:(1)It introduced relevant exploration methods of coal goaves,including their geological background and geophysical characteristics,and briefly discussed some commonly used geophysical exploration methods.(2)Next,based on the Maxwell equations satisfied by the total electric field,the three-dimensional(3D)vector finite-element forward modeling theory of the frequencydomain controlled-source electromagnetic method was examined in detail;Unstructured grid cells were used to discretize the model area,and complex goaves and other target bodies were constructed;The electric dipole dispersion technology was introduced to simulate the electromagnetic field distribution,where the shape of the power supply wire changed because of various factors,such as undulating terrain and anthropogenic influence;The transmitting wire was dispersed into a series of electric dipoles;Following the vector superposition,the transmitting source of arbitrary geometry could be constructed;The parallel direct solver,MUMPS,was used to improve the efficiency of solving finite element equations.Thus,a set of high-efficiency and high-precision,three-dimensional,forward modeling algorithms were developed for the frequencydomain controlled-source electromagnetic method to investigate coal goaves.(3)Based on the developed forward algorithms,the 3D inversion algorithm was developed using an unstructured mesh generation technology,inaccurate Gauss-Newton algorithm,forward and inverse grid separation strategies,and other technologies to obtain the frequency-domain controlled-source electromagnetic method data for coal goaf investigation.By implicitly calculating the products of the Jacobian matrix and its transposed matrix and vector,the Jacobian matrix display calculation and storage could be avoided,effectively reducing the memory requirement;Using the forward and inversion grid separation strategies,the number of inversion unknowns could be reduced while maintaining the forward calculation accuracy,thus reducing the impact of inversion multiplicity and forming a set of high-efficiency and high-precision,threedimensional,inverse algorithm for the frequency-domain controlled-source electromagnetic method for investigating coal goaves.(4)The forward and inverse algorithms developed in this study were tested using a series of theoretical models.The actual effect of the frequency-domain controlled-source electromagnetic method in detecting coal goaves was analyzed using an engineering test of CSAMT in a coal mine in Taiyuan City,Shanxi Province.By theoretical analysis and numerical simulation,based on the unstructured grid finite element method,a 3D forward modeling of frequency-domain controlled-source electromagnetic field in coal goaves was realized,providing a theoretical basis for the detection in coal goaves;Based on the forward and inverse grid separation strategy and Gaussian-Newton method,3D inversion of frequency-domain controlled-source electromagnetic method was realized,providing an effective tool for the interpretation of frequency-domain controlled-source electromagnetic data;The effectiveness of frequency-domain controlled-source electromagnetic method in detecting coal goaves were proved through conducting a testing project.