3D Time-domain AEM Modeling And Inversion With FV Method

Time-domain(TD)airborne electromagnetic(AEM)methods have been used in mineral exploration,geological mapping,engineering and environmental problems for years,covering large-scale marine areas,high mountains,desert,lakes and marshes.AEM data interpretation is mainly based on one-dimensional(1D)inversion that assumes the earth is quasi-layered,while the true three-dimensional(3D)earth is always very complicated and sometimes has severe topography,for which 1D inversion cannot deliver good results.Thus 3D EM studies have become significant trends.However,the problems of instability and slow speed have limited the development of 3D modeling and inversion to industry.In my thesis,I propose an efficient 3D time-domain field-separation method based on an anomalous field volume of influence(VoI),where a finite-volume(FV)method with staggered grids has been used.I adopt Gauss-Newton method for 3D time-domain AEM data inversion,and the model and survey data inversion results both show that the time-domain inversion algorithm is very effective and efficient.Starting from Maxwell equations,I present a time-domain field-separation method by separating background field of a half-space or layered earth from anomalous field of 3D target under the earth.This method helps constrain the calculation within a small influence area that depends on the 3D target and transmitter-receiver system instead of using conventional large calculation regions,to offer a faster 3D forward modeling.A staggered grid FV method has been used,which makes the electric field and magnetic field satisfy the coupling relationship automatically in the mesh and has good numerical stability.I use a backward Euler method to discretize the time derivative term to establish a stable implicit equation,which lowers down the requirement for time steps.To further speed up the calculation,a local mesh that has fine cells near the transmitter and receiver,and coarse ones far away has been adopted instead of a global mesh that has to do the discretization in the entire region.Finally,as the coefficient matrice of the forward modelling equations are sparse,I use a direct solver – Multifrontal Massively Parallel Solver(MUMPS)to solve the equations,which is very efficient as it only needs to do the factorization once for the same time steps,and solve different time-channel equations by simply replacing the source term.Aslo I use a MPI during the factorization to make full use of MUMPS.I propose a concept of anomalous VoI for the field-separation method.Taking the 3D target under the earth as a secondary source,which produces anomalous field around it.Considering the volume where the anomalous field makes the most contributions to the response in the receiver,we take this volume as the anomalous VoI.Comparing with conventional AEM system VoI that only takes the transmitter-receiver influence volume into account,the anomalous VoI is much smaller,which can make the calculation been done within a small volume using less grids and offer a faster 3D calculation.Further,the total-field method based on system VoI has been introduced and the comparison between the total-field methd and the field-separation method shows that when we use the same grid,only the field-separation method can guarantee the accuracy;while when the results of two methods both have good accuracy,the field-separation method can be 4 times faster.As the topography influences the AEM survey data greatly,and the real earth is not an ideal flat surface,I make a study of the topography influence on the response of AEM full wave which includes both on-and off-time.I take a valley model as example to show the characteristics and influence of different topography slopes and transmitting waveforms on the AEM response.The profile response shows that topograghy has obvious anomaly in early time channels,and there is an image relationship between the profile anomaly and the topography shape.The larger slope has a wider bottom of the valley,corresponding to a larger range of the peak anomaly and a smaller range of the entire anomaly in profile.When there is transmitting waveform,the characteristics will become very complicated for the on-time data,especially for the situation when the earth includes 3D targets.While the off-time data has relatively simple characteristics and the anomaly mainly appear in the early off-time channels.From the numerical simulations,it is seen that the valley topograghy has increased the response of conductive target under the earth(except on-time),which means that if we use a flat surface to interpret the data,the results will produce large errors and even wrong answers.So when there is severe topography,we must consider its influence in data processing and interpretation.I adopt the Gauss-Newton method to conduct the 3D time-domain AEM data inversion.With the regularization theory,I obtain the final inversion equation containing Jacobian matrix,data misfit and model update parameters.The Jacobian matrix is directly calculated in time-domain with joint forward modeling method,in which through solving a time reverse(from late time channels to early time channels)equation with MUMPS for an intermediate parameter,and combining with other parameters,I obtain the Jacobian matrix for every survey station.Via a technique of matrice reconstruction,the final Jacobian matrix for all the data set has been obtained.Finally,I use a conjugate gradient method to solve the inversion equations.To demonstrate the effectiveness of the inversion algorithm and codes,I use isolated conductors(a syncline and an anticline conductor)as example to make 3D inversions,the results of which show a very good recovery to the true models.Then I take a model with two conductors,one is a horizontal plate and another is a dipping one.Three kinds of inversion methods are used,respectively 1D inversion,3D inversion based on field-separation method and 3D inversion based on total-field method.The results show that both 3D inversions have a good agreement with the two conductors,while 1D inversion can only coincide with the horizontal plate and recovered the dipping plate as a deeper horizontal one,from which we see the 3D inversion is very necessary and accurate.For the two 3D inversion methods,I conduct a comparison on the speed of forward modeling,Jacobian matrix calculation and the entire inversions,where we see that the 3D inversion with field-separation method is about 4 time faster than that of another method.Meanwhile,the inversion results with different starting models(background CDI,direct CDI,and CDI3D)show that using CDI3 D as the starting model,I obtain the best results compared with the drilling information.Also in the case when we don't have a good starting model or any priori information,chooing a warm starting model will be easier to get good results.Finally,I conduct the inversion on the GEOTEM data acquired in Lisheen deposit in Ireland,and the inversion section has a very good agreement with the geology information,which further demonstrates the validity and effectiveness of the inversion method.