Frequency Domain Electromagnetic Method Forward And Inversion Calculation And Data Interpretation For Layered Media

With the rapid development of domestic economy and progress of urbanization,the development and utilization of underground space provides new sustainable development ideas for large and medium-sized cities.Accurate detection of underground space is the key to ensuring its safe operation.As a commonly used underground detection method,frequency domain electromagnetic method has the advantages of non-invasiveness,high resolution,and strong anti-interference ability.It is widely used in geological prospecting,sea ice thickness measurement,archaeological excavation and other fields.Current applications are all oriented to underground solid media.But for urban underground space detection,targeted methods need to be adopted to achieve fine measurement and high-resolution imaging of underground space structures.Effective electromagnetic data processing method is the most important part of electromagnetic detection and the key to ensuring accurate and reliable results.This paper mainly studies and improves the forward and inversion calculation of urban underground space exploration based on frequency domain electromagnetic method and the interpretation of measured data,and applies them to the actual field exploration.The thesis first explained the secondary field response of the n-layer horizontal homogeneous medium model under the excitation of harmonic electromagnetic field,and used the method of digital filter to discretize the infinite integral in the theoretical model into data points of finite length for calculation;Two different three-layer dielectric geoelectric models with anomalies underground are designed for forward simulation.The simulation results show that the secondary field response results of the entire model are basically consistent with the structural characteristics of the preset underground anomaly bodies.The typical damped least squares inversion algorithm is introduced systematically.To solve the problem of non-convergence of some parameters in the inversion results,an improved method is proposed to adjust the order of magnitude of each element of the Jacobian matrix to obtain a good inversion result.Single-point calculation results show that the improved algorithm can make electromagnetic parameters and thickness parameters converge to the true value.In order to further verify the effectiveness of the improved algorithm,a three-layer geoelectric model containing an underground tunnel was designed,and the improved damping least squares algorithm was used to perform inversion simulation calculations to solve the electromagnetic parameters and thickness parameters.During the calculation,the forward response data of the model are overlaid with varying degrees of noise to simulate instrument observation signals with different signal-to-noise ratios;the inversion results of each model parameter under the conditions of 15 d B and 20 d B signal-to-noise ratio,the conductivity images of different sections and the thickness inversion results are compared respectively.The relative error curve shows that increasing the signal-to-noise ratio can effectively improve the quality of the inversion results;in addition,the continuously changing steps in the preset model can be clearly distinguished according to the conductivity images of different sections,and there is a clear distinction between different media layers.The underground space structure under metro station was measured in the field,and the self-developed frequency domain electromagnetic detection instrument was used to measure point by point along the survey line.According to the measurement results and observations,the horizontal position of metro tunnel was qualitatively analyzed.The measured data of some of measurement points are substituted into the inversion algorithm for calculation.According to the specific situation of the measurement area,three different calculation ideas are adopted to suppress the multi-solution of inversion results,and the results with more reasonable data are selected to draw two-dimensional profile images.The inversion results show that the spatial structure profile under the metro station is basically consistent with the actual observation and construction structure.