Leveling And Holistic Inversion Of Fixed-wing Time Domain Electromagnetic Data

Fixed-wing time domain electromagnetic method is a geophysical exploration method based on Faraday law of electromagnetic induction.For fixed-wing time-domain electromagnetic system,the transmitting system is mounted on an aircraft and the receiving system is towed behind the aircraft.The fast flight measurement is performed on the survey area.Then the geoelectric distribution information is acquired through the inversion imaging after electromagnetic data processing.The method has advantages such as high efficiency and greater investigation depth,which has been used extensively in the search for mineral deposits and metallic ores,etc.In the airborne electromagnetic(AEM)survey,the mobile platform method of system may cause the changes of flight direction,flying altitude,external temperature,crosswind,flight speed and other factors.In particular,the fixed-wing electromagnetic systems are usually based on dipole-dipole soft connection.These factors lead to the flight line data with leveling errors,transmitting coil and receiving coil with flight attitude and data with uncorrelated noise.Them will affect the inversion quality and reduce the detection capability.This paper is supported by the National Natural Science Foundation of China "Research on the holistic inversion of fixed-wing time domain electromagnetic data" and National Major Scientific Research Equipment Special Project "Data processing and inversion of airborne electromagnetic data".According to the particularity of geophysical data,two leveling methods are proposed,the constrained leveling along the survey line direction and the micro-leveling algorithm along the cross line direction.The horizontal and vertical leveling methods are used to calibrate the AEM data to make sure the survey area data at the same data level.Based on the continuity of the geophysical field,the spatial constraint is constructed for the survey points in the system footprint.And the flight attitude angles are introduced as the inversion parameter.The paper proposes the quasi-three-dimensional(3D)holistic inversion of fixed-wing time domain electromagnetic data to obtain more accurate information of underground electrical distribution in the survey area.The main contents of this paper are as follows:(1)The paper analyzed the influence factors of the AEM data inversion.AEM survey are non-stationary because of the measurement mode and flight process of mobile platform.The paper derives the calculation expression of electromagnetic secondary field response under attitude angle of the transmitter and receiver coils.And the influence processes on the second electromagnetic field response are researched for the the pitch attitude angle of the transmitting coil,the pitch attitude angle of the receiving coil and the swing attitude angle of the bird.Through quasi 3D layered-earth model,the influences of leveling errors,noise and flight attitude angle on the inverse problem are analyzed quantitatively.(2)The traditional AEM leveling methods adopt leveling of total survey area data which may lead to false leveling errors.Through quasi 3D layered-earth model,the paper researches the reasons for survey anomaly area to cause false leveling errors.In order to avoid the survey anomaly area,a pseudo tie-line is chosen from non-anomalous area.Then a non-anomalous data set is constructed by calculating the correlation of other pseudo tie-lines with non-anomalous pseudo tie-line.Based on the continuity of electromagnetic response,the optimization equation of leveling error function is established by using difference data between adjacent flight line data and reference flight line data.At the same time,according to the attenuation law of the airborne time-domain electromagnetic(ATEM),the attenuation constraint of channel data is implemented by inequality for the survey data.The least squares equations under inequality constraints are constructed which can be solved by quadratic programming.The constraint leveling method along the flight line direction is used to solve the problem that the traditional single-channel independent leveling method may change the attenuation law of ATEM data.(3)For the residual leveling errors of AEM data,a new microleveling method is proposed based on line difference and principal component analysis.Based on the continuity of geophysical field,the electromagnetic response parts of adjacent flight line data have strong correlation.However,the leveling error parts are uncorrelated among flight lines.Through the line difference of the survey area data,the relevant electromagnetic response parts between the flight lines can be removed,thus the leveling error characteristics in the data can be enhanced.Usually,the AEM response parts are larger than the leveling error parts for airborne electromagnetic survey.It is difficult to extract the AEM leveling error directly when the amplitude of the leveling error is small.Line difference of AEM data can increase the proportion of leveling error.Based on the correlation of leveling error along the tie-line direction,the principal component analysis is applied on the pseudo tie-line data following line difference.The eigenvalues and corresponding eigenvectors are obtained by singular value decomposition of the data covariance matrix.Using the rotation matrix(transposition of the eigenvector matrix),the pseudo tie-line data can be the linearly mapped to the principal component domain.The data is reconstructed by using low-order principal components and eigenvectors which can extract the spatial characteristics of the leveling error.The leveling errors of each flight line in the survey area data are calculated by the inverse line difference.The AEM microleveling results along the tie-line direction are obtained based on line difference and principal component analysis.(4)For the inversion of fixed-wing time domain electromagnetic data,the flight attitude angle in non-stationary measurement has an effect on the process.In order to avoid the influence,the flight attitude angles are taken as the model parameters.The holistic inversion algorithm inverts the flight attitude angle and the earth model parameters simultaneously.Because the survey points in the AEM system footprint are continuous.The space model roughness is constructed through inverse distance weighted multistep accumulation algorithm.Based on the regularized inversion theory,the prior information and vertical roughness of the model are introduced as constraints.The paper forms the holistic inversion algorithm of fixed-wing time domain electromagnetic data with the space constraint.Let the partial derivative of the objective function to the inversion model parameters be equal to zero,we can solve the optimal solution of the objective function and obtain the geodetic model parameters of the survey area.By simulating quasi 3D layered-earth model,the inversion result verifies that the quasi 3D holistic inversion algorithm can avoid the influence of the attitude angle on the inversion and suppress the uncorrelated noise of the survey data.Simulation results show that the quasi 3D holistic inversion can improve precision of inversion.The main innovation lies as follow:(1)The constraint leveling method along the flight line direction is proposed for ATEM data.Based on the continuity of electromagnetic response of adjacent flight lines,the optimization equation of leveling error function is established by using the data difference between adjacent flight lines and reference lines.At the same time,according to the attenuation law of airborne electromagnetic off-time data,the inequality attenuation constraints are constructed on the channel data of each survey point.Quadratic programming is used to solve the least squares equations constrained by inequalities,and the constrained leveling method along the flight line is realized.The constraint leveling method has solved the problem that the traditional single-channel independent method may change the ATEM off-time data attenuation law which affects the data inversion imaging.(2)Based on line difference and principal component analysis,the paper proposes a microleveling method for AEM data.Through the line difference,the leveling error characteristics in the data can be enhanced and the proportion of leveling error in raw data has increased.Based on the correlation of leveling error along the tie-line direction,the principal component analysis is applied on the pseudo tie-line data following line difference.The spatial characteristics of the leveling errors are extracted by reconstructing low-order principal components and eigenvectors.The leveling errors of each flight line in the survey area are calculated by the inverse line difference,and the residual leveling error in the data is eliminated from the tie-line direction.(3)A quasi 3D holistic inversion method is proposed for fixed wing time domain electromagnetic data.The flight attitude angle in non-stationary flight is taken together as the inversion parameters with the geodetic model parameters.Based on the AEM system,the space roughness in the footprint region of the survey points is constructed through inverse distance weighted multistep accumulation algorithm.The quasi 3D holistic inversion objective function is composed of data misfit term,reference-model misfit term,vertical model roughness term and space model roughness term,which effectively eliminates the influence of flight attitude angle on data inversion.The quasi 3D holistic inversion can ensure spatial continuity of inversion results and suppresses the uncorrelated noise in the measurement area.So we can conclude that the quasi 3D holistic inversion can improve precision of inversion.Airborne electromagnetic system includes transmitting system,receiving system,data processing system and inversion imaging system.Using transmitting system and receiving system to measure data is the foundation of airborne electromagnetic system.Data processing system and inversion imaging system are necessary approaches to improve the capability of airborne electromagnetic method.Optimizing the data processing and inversion is an essential factor to improve the airborne electromagnetic technology.The fixed-wing time domain electromagnetic data leveling and quasi 3D holistic inversion algorithm studied in this paper have certain theoretical and practical value for improving the processing and interpretation of airborne electromagnetic data.