Casper Kirkegaard

An integrated processing scheme for high-resolution airborne electromagnetic surveys, the SkyTEM system

The SkyTEM helicopter-borne transient electromagnetic system was developed in 2004. The system yields unbiased data from 10 to 12 μs after transmitter current turn-off. The system is equipped with several devices enabling a complete modelling of the movement of the system in the air, facilitating excellent high-resolution images of the subsurface. An integrated processing and inversion system for SkyTEM data is discussed. While the authors apply this system with SkyTEM data, most of the techniques are applicable for airborne electromagnetic data in general. Altitude data are processed using a simple recursive filtering technique that efficiently removes reflections from trees. The technique is completely general and can be used to filter altitude data from any airborne system. Raw voltage data that are influenced by electromagnetic coupling to man-made structures are culled from the dataset to avoid uncoupled data being distorted by coupled data, and geometrical corrections are applied to correct for pitch and roll of the transmitter frame. Data are de-spiked and averaged using trapezoid-shaped filter kernels. A Laterally Constrained Inversion using smooth models is actively used to evaluate the processing, and the final inversion is tightly connected to the processing procedures.

An overview of a highly versatile forward and stable inverse algorithm for airborne, ground-based and borehole electromagnetic and electric data

We present an overview of a mature, robust and general algorithm providing a single framework for the inversion of most electromagnetic and electrical data types and instrument geometries. The implementation mainly uses a 1D earth formulation for electromagnetics and magnetic resonance sounding (MRS) responses, while the geoelectric responses are both 1D and 2D and the sheet’s response models a 3D conductive sheet in a conductive host with an overburden of varying thickness and resistivity. In all cases, the focus is placed on delivering full system forward modelling across all supported types of data. Our implementation is modular, meaning that the bulk of the algorithm is independent of data type, making it easy to add support for new types. Having implemented forward response routines and file I/O for a given data type provides access to a robust and general inversion engine. This engine includes support for mixed data types, arbitrary model parameter constraints, integration of prior information and calculation of both model parameter sensitivity analysis and depth of investigation. We present a review of our implementation and methodology and show four different examples illustrating the versatility of the algorithm. The first example is a laterally constrained joint inversion (LCI) of surface time domain induced polarisation (TDIP) data and borehole TDIP data. The second example shows a spatially constrained inversion (SCI) of airborne transient electromagnetic (AEM) data. The third example is an inversion and sensitivity analysis of MRS data, where the electrical structure is constrained with AEM data. The fourth example is an inversion of AEM data, where the model is described by a 3D sheet in a layered conductive host. We present an overview of a mature and general algorithm for inversion of most electromagnetic and geoelectrical data, ground-based and airborne. The implementation uses a 1D formulation for electromagnetics and MRS responses, geoelectric responses are 1D and 2D, and the 3D sheet’s response implements an overburden of varying thickness and resistivity.

Sharp spatially constrained inversion with applications to transient electromagnetic data

Time-domain electromagnetic data are conveniently inverted by using smoothly varying 1D models with fixed vertical discretization. The vertical smoothness of the obtained models stems from the application of Occam-type regularization constraints, which are meant to address the ill-posedness of the problem. An important side effect of such regularization, however, is that horizontal layer boundaries can no longer be accurately reproduced as the model is required to be smooth. This issue can be overcome by inverting for fewer layers with variable thicknesses; nevertheless, to decide on a particular and constant number of layers for the parameterization of a large survey inversion can be equally problematic. Here, we present a focusing regularization technique to obtain the best of both methodologies. The new focusing approach allows for accurate reconstruction of resistivity distributions using a fixed vertical discretization while preserving the capability to reproduce horizontal boundaries. The formulation is flexible and can be coupled with traditional lateral/spatial smoothness constraints in order to resolve interfaces in stratified soils with no additional hypothesis about the number of layers. The method relies on minimizing the number of layers of non-vanishing resistivity gradient, instead of minimizing the norm of the model variation itself. This approach ensures that the results are consistent with the measured data while favouring, at the same time, the retrieval of horizontal abrupt changes. In addition, the focusing regularization can also be applied in the horizontal direction in order to promote the reconstruction of lateral boundaries such as faults. We present the theoretical framework of our regularization methodology and illustrate its capabilities by means of both synthetic and field data sets. We further demonstrate how the concept has been integrated in our existing spatially constrained inversion formalism and show its application to large-scale time-domain electromagnetic data inversions.

A parallel, scalable and memory efficient inversion code for very large‐scale airborne electromagnetics surveys

Over the past decade the typical size of airborne electromagnetic data sets has been growing rapidly, along with an emerging need for highly accurate modelling. Onedimensional approximate inversions or data transform techniques have previously been employed for very large-scale studies of quasi-layered settings but these techniques fail to provide the consistent accuracy needed by many modern applications such as aquifer and geological mapping, uranium exploration, oil sands and integrated modelling. In these cases the use of more time-consuming 1D forward and inverse modelling provide the only acceptable solution that is also computationally feasible. When target structures are known to be quasi layered and spatially coherent it is beneficial to incorporate this assumption directly into the inversion. This implies inverting multiple soundings at a time in larger constrained problems, which allows for resolving geological layers that are undetectable using simple independent inversions. Ideally, entire surveys should be inverted at a time in huge constrained problems but poor scaling properties of the underlying algorithms typically make this challenging. Here, we document how we optimized an inversion code for very large-scale constrained airborne electromagnetic problems. Most importantly, we describe how we solve linear systems using an iterative method that scales linearly with the size of the data set in terms of both solution time and memory consumption. We also describe how we parallelized the core region of the code, in order to obtain almost ideal strong parallel scaling on current 4-socket shared memory computers. We further show how model parameter uncertainty estimates can be efficiently obtained in linear time and we demonstrate the capabilities of the full implementation by inverting a 3327 line km SkyTEM survey overnight. Performance and scaling properties are discussed based on the timings of the field example and we describe the criteria that must be fulfilled in order to adapt our methodology for similar type problems.

An efficient hybrid scheme for fast and accurate inversion of airborne transient electromagnetic data

Airborne transient electromagnetic (TEM) methods target a range of applications that all rely on analysis of extremely large datasets, but with widely varying requirements with regard to accuracy and computing time. Certain applications have larger intrinsic tolerances with regard to modelling inaccuracy, and there can be varying degrees of tolerance throughout different phases of interpretation. It is thus desirable to be able to tune a custom balance between accuracy and compute time when modelling of airborne datasets. This balance, however, is not necessarily easy to obtain in practice. Typically, a significant reduction in computational time can only be obtained by moving to a much simpler physical description of the system, e.g. by employing a simpler forward model. This will often lead to a significant loss of accuracy, without an indication of computational precision. We demonstrate a tuneable method for significantly speeding up inversion of airborne TEM data with little to no loss of modelling accuracy. Our approach introduces an approximation only in the calculation of the partial derivatives used for minimising the objective function, rather than in the evaluation of the objective function itself. This methodological difference is important, as it introduces no further approximation in the physical description of the system, but only in the process of iteratively guiding the inversion algorithm towards the solution. By means of a synthetic study, we demonstrate how our new hybrid approach provides inversion speed-up factors ranging from ~3 to 7, depending on the degree of approximation. We conclude that the results are near identical in both model and data space. A field case confirms the conclusions from the synthetic examples: that there is very little difference between the full nonlinear solution and the hybrid versions, whereas an inversion with approximate derivatives and an approximate forward mapping differs significantly from the other results. We present a hybrid inversion scheme for airborne TEM data that introduces approximation only in the calculation of partial derivatives. The objective function is evaluated with a full nonlinear one-dimensional (1D) forward model.

Sharp Spatially Constrained Inversion

We present sharp reconstruction of multi-layer models using a spatially constrained inversion with minimum gradient support regularization. In particular, its application to airborne electromagnetic data is discussed. Airborne surveys produce extremely large datasets, traditionally inverted by using smoothly varying 1D models. Smoothness is a result of the regularization constraints applied to address the inversion ill-posedness. The standard Occam-type regularized multi-layer inversion produces results where boundaries between layers are smeared. The sharp regularization overcomes this by allowing a reconstruction with a large number of layers, while preserving abrupt changes in the conductivity distribution. Instead of minimizing the norm of the vertical spatial variation of the model, in the focusing approach, it is the number of layers where the variations occur that is minimized. Thus, the results are compatible with the data and, at the same time, favor sharp transitions. The focusing strategy can also be used to constrain the 1D solutions laterally, guaranteeing that lateral sharp transitions are retrieved without losing resolution. By means of real and synthetic datasets, sharp inversions are compared against classical smooth results and available boreholes. With the focusing approach, the obtained blocky results agree with the underlying geology and allow for easier interpretation by the end-user.

Artificial neural networks for removal of couplings in airborne transient electromagnetic data

Modern airborne transient electromagnetic surveys typically produce datasets of thousands of line kilometres, requiring careful data processing in order to extract as much and as reliable information as possible. When surveys are flown in populated areas, data processing becomes particularly time consuming since the acquired data are contaminated by couplings to man-made conductors (power lines, fences, pipes, etc.). Coupled soundings must be removed from the dataset prior to inversion, and this is a process that is difficult to automate. The signature of couplings can be both subtle and difficult to describe in mathematical terms, rendering removal of couplings mostly an expensive manual task for an experienced geophysicist. Here, we try to automate the process of removing couplings by means of an artificial neural network. We train an artificial neural network to recognize coupled soundings in manually processed reference data, and we use this network to identify couplings in other data. The approach provides a significant reduction in the time required for data processing since one can directly apply the network to the raw data. We describe the neural network put to use and present the inputs and normalizations required for maximizing its effectiveness. We further demonstrate and assess the training state and performance of the network before finally comparing inversions based on unprocessed data, manually processed data, and artificial neural network automatically processed data. The results show that a well-trained network can produce high-quality processing of airborne transient electromagnetic data, which is either ready for inversion or in need of minimal manual processing. We conclude that the use of artificial neural network scan significantly reduce the processing time and its costs by as much as 50%.

Sharp Spatially-decoupled Inversion of Airborne Electromagnetic Data for Improved Model Integration

One of the main limiting factors to the accuracy of large scale groundwater models is the scarcity of hydraulic data. High-resolution Airborne Electromagnetic Methods (AEM) are capable of mapping the electrical resistivity structure of the subsurface in great detail and covering large areas in short time and on a limited budget. As such, there is great potential in integrating AEM data in groundwater modeling as a supplementing source of an extensive amount of information. We have developed several novel techniques that in combination allows for bringing groundwater and AEM models much closer together, i.e.: (1) a novel, scalable inversion engine that allows the AEM inversion to handle arbitrarily large areas at a time; (2) the spatially-decoupled inversion approach, which decouples the inversion model from the acquisition points and can operate on the same grid/voxel cells as the groundwater model; (3) a custom regularization scheme that allows for producing geophysical models with sharp vertical/horizontal resistivity transitions. In this study we present the very first application of the sharp spatially-decoupled inversion on an AEM survey flown for improving the groundwater model in the Kasted area, in the north of Aarhus (Denmark).

Utilizing massively parallel co-processors in the AarhusInv 1D forward and inverse AEM modelling code

While the forefront of AEM research is focusing on the challenges of 3D modelling, the wide AEM community still rely on less sophisticated computational techniques for their calculations. Inversion of large time domain AEM surveys still prove a computational challenge within a 1D formulation, and require much more computational resources than can be delivered by an office workstation. Emerging Monte-Carlo based 1D Bayesian inversion schemes provide another example of applications that are currently limited by the 1D forward modelling rate. In this abstract we describe our research in modifying the AarhusInv AEM inversion code to utilize next generation massively parallel co-processors. While our results are early and based on very little optimization, we still achieve comparable levels of performance (>80%) from a single co-processor and a 48 cpu core server. We estimate that performance on the co-processor can be speeded up by approximately another 4x with a limited amount of code restructuring/rewriting.

Rapid Inversion of Large Airborne AEM Data Datasets Utilizing Massively Parallel Co-processors

While full 2D and 3D inversion schemes are emerging for airborne TEM datasets, the workhorse of large scale surveying still remains the well established 1D forward formulation. Modern airborne TEM surveys typically span several thousand line kilometers of data, which can be very time consuming to invert even within the framework of 1D forward modeling. Here, we present how we have modified our existing inversion code to offload its 1D forward computations to massively parallel Intel Xeon Phi co-processors. A prerequisite for good performance on this type of next generation technology is for a code to provide not only good parallel scaling, but also make efficient use of vector instructions. The latter is not possible without modification to the established framework of 1D forward modeling and we demonstrate how this problem can be overcome in a straight forward manner. We show how the modified algorithm provides virtually ideal parallel scaling and almost ideal use of vector instructions on both multi-core processors and massively parallel Intel Xeon Phi co-processors. The use of vector instructions alone provide a speed-up of almost 8x on the co-processor, allowing for full inversion of several thousand line kilometers of data per hour.