Wepresentanoverviewofamature,robustandgeneralalgorithmprovidingasingleframeworkfortheinversion 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 thicknessandresistivity.Inallcases,thefocusisplacedondeliveringfullsystemforwardmodellingacrossallsupportedtypes 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 accesstoarobustandgeneralinversionengine.Thisengineincludessupportformixeddatatypes,arbitrarymodelparameter constraints, integration of prior information and calculation of both model parameter sensitivity analysis and depth of investigation.Wepresentareviewofourimplementationandmethodologyandshowfourdifferentexamplesillustratingthe 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 airbornetransientelectromagnetic(AEM)data.ThethirdexampleisaninversionandsensitivityanalysisofMRSdata,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.

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

It is often argued that 3D inversion of entire airborne electromagnetic (AEM) surveys is impractical, and that 1D methods provide the only viable option for quantitative interpretation. However, real geological formations are 3D by nature and 3D inversion is required to produce accurate images of the subsurface. To that end, we show that it is practical to invert entire AEM surveys to 3D conductivity models with hundreds of thousands if not millions of elements. The key to solving a 3D AEM inversion problem is the application of a moving footprint approach. We have exploited the fact that the area of the footprint of an AEM system is significantly smaller than the area of an AEM survey, and developed a robust 3D inversion method that uses a moving footprint. Our implementation is based on the 3D integral equation method for computing data and sensitivities, and uses the re-weighted regularised conjugate gradient method for minimising the objective functional. We demonstrate our methodology with the 3D inv...

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3D inversion of airborne electromagnetic data using a moving footprint

SUMMARY A meaningful interpretation of geophysical measurements requires an assessment of the space of models that are consistent with the data, rather than just a single, ‘best’ model which does not convey information about parameter uncertainty. For this purpose, a trans-dimensional BayesianMarkovchainMonteCarlo(MCMC)algorithmisdevelopedforassessingfrequencydomain electromagnetic (FDEM) data acquired from airborne or ground-based systems. By sampling the distribution of models that are consistent with measured data and any prior knowledge, valuable inferences can be made about parameter values such as the likely depth to an interface, the distribution of possible resistivity values as a function of depth and non-unique relationships between parameters. The trans-dimensional aspect of the algorithm allows the number of layers to be a free parameter that is controlled by the data, where models with fewer layers are inherently favoured, which provides a natural measure of parsimony and a significant degree of flexibility in parametrization. The MCMC algorithm is used with synthetic examples to illustrate how the distribution of acceptable models is affected by the choice of prior information, the system geometry and configuration and the uncertainty in the measured system elevation. An airborne FDEM data set that was acquired for the purpose of hydrogeological characterization is also studied. The results compare favourably with traditional least-squares analysis, borehole resistivity and lithology logs from the site, and also provide new information about parameter uncertainty necessary for model assessment.

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A trans-dimensional Bayesian Markov chain Monte Carlo algorithm for model assessment using frequency-domain electromagnetic data

DIRECTION DETERMINATION The three degrees of freedom, latitude, longitude, and elevation (or equivalents), constitute a rectangular coordinate system (neglecting earth curvature effects), and clearly determination of the orientations of the axes is important. The vertical direction is usually defined by means of a level or plumb line. Horizontal orientation can be determined with respect to the position of a celestial body, the Earth's rotation, magnetic north, or a previously known orientation. Although the most obvious celestial orientation is by sighting on Polaris (which is not exactly at the celestial pole), any star can be used. Sighting on the Sun ( sun shots ) permits orientation during daylight. Nightime observations can establish orientation to a fraction of an arc second (arcsec). Gyrocompass orientation is extensively used in marine and airborne surveys. A gyrocompass gives orientation with respect to true north within about 20 arcsec. A magnetic compass is often used to determine direction with respect to magnetic north, correction for the magnetic declination giving true north. Diurnal variations may create 10 min of error, more during magnetic storms. Care has to be exercised that no local iron or electric currents distort the magnetic field. Benchmarks (identified points of known location) often have nearby reference points (azimuth bars) that can be used to establish orientation. DISTANCE MEASUREMENT Direct measurement of distance is done by seeing how many times a standard measure will fit between points whose separation is to be determined, a technique called chaining , the unit of measure usually being a steel tape (a chain ) of precise length.

Applied Geophysics: Appendix B. Location Determination

During the last century, electrical geophysics has been transformed from a simple resistivity method to a modern technology that uses complex data-acquisition systems and high-performance computers for enhanced data modeling and interpretation. Not only the methods and equipment have changed but also our ideas about the geoelectrical models used for interpretation have been modified tremendously. This paper describes the evolution of the conceptual and technical foundations of EM methods. It outlines a framework for further development, which should focus on multitransmitter and multireceiver surveys, analogous to seismic data-acquisition systems. Important potential topics of future research efforts are in the areas of multidimensional modeling and inversion, including a new approach to the formulation and understanding of EM fields based on flux and voltage representation, which corresponds well to geophysical experiments involving the measurement of voltage and flux of electric and magnetic fields.

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Electromagnetic geophysics: Notes from the past and the road ahead

Time-domain airborne surveys gather hundreds of thousands of multichannel, multicomponent samples. The volume of data and other complications have made 1D inversions and transforms the only viable method to interpret these data, in spite of their limitations. We have developed a practical methodology to perform full 3D inversions of entire time- or frequency-domain airborne electromagnetic (AEM) surveys. Our methodology is based on the concept of a moving footprint that reduces the computation requirements by several orders of magnitude. The 3D AEM responses and sensitivities are computed using a frequency-domain total field integral equation technique. For time-domain AEM responses and sensitivities, the frequency-domain responses and sensitivities are transformed to the time domain via a cosine transform and convolution with the system waveform. We demonstrate the efficiency of our methodology with a model study relevant to the Abitibi greenstone belt and a case study from the Reid-Mahaffy test ...

3D inversion of airborne electromagnetic data

GiventherangeofgeologicalconditionsunderwhichairborneEMsurveysareconducted,thereisanexpectation that the 2D and 3D methods used to extract models that are geologically meaningful would be favoured over 1D inversion and transforms. We do after all deal with an Earth that constantly undergoes, faulting, intrusions, and erosive processes that yield a subsurface morphology, which is, for most parts, dissimilar to a horizontal layered earth. We analyse data from a survey collected in the Musgrave province, South Australia. It is of particular interest since it has been used for mineral prospecting and for a regional hydro-geological assessment. The survey comprises abrupt lateral variations, more-subtle lateral continuous sedimentary sequences and filled palaeovalleys. As consequence, we deal with several geophysical targets of contrasting conductivities, varying geometries and at different depths. We invert the observations by using several algorithms characterised by the different dimensionality of the forward operator. Inversion of airborne EM data is known to bean ill-posed problem.We can generate a variety of models that numerically adequately fit the measured data, which makes the solution non-unique. The application of different deterministic inversion codes or transforms to the same dataset can give dissimilar results, as shown in this paper. This ambiguity suggests the choice of processes and algorithms used to interpret AEM data cannot be resolved as a matter of personal choice and preference. The degree to which models generated by a 1D algorithm replicate/or not measured data, can bean indicator of thedata's dimensionality, which perse does not imply that data that can be fitted with a 1D model cannot be multidimensional. On the other hand, it is crucial that codes that can generate 2D and 3D models do reproduce the measured data in order for them to be considered as a plausible solution. In the absence of ancillary information, it could be argued that the simplest model with the simplest physics might be preferred.

Airborne electromagnetic modelling options and their consequences in target definition

Helicopter electromagnetic surveying is a standard reconnaissance method in the mining industry. Typical surveys may cover tens to hundreds of square kilometers with hundreds of thousands of multifrequency soundings. Interpreting this volume of data is problematic. Yet each sounding location is sensitive to an area of less than 1 km, not the entire survey area. We suggest an inversion scheme, based on the integral equation method, in which the entire survey is inverted simultaneously with each transmitter-receiver pair being sensitive only to a relatively small area around each sounding location. We show that this method is as accurate as standard integral equation inversion methods, yet it inverts the data much faster. The technique is able to invert entire HEM surveys with over 500,000 inversion cells and tens of thousands of transmitter positions in less than one day on a single PC.

Large Scale 3D Inversion of HEM Data Using a Moving Footprint

We develop a new computational method for modeling and inverting fre- quency domain airborne electromagnetic (EM) data. Our method is based on the con- traction integral equation method for forward EM modeling and on inversion using the localized quasi-linear (LQL) approximation followed by the rigorous inversion, if necessary. The LQL inversion serves to provide a fast image of the target. These results are checked by a rigorous update of the domain electric field, allowing a more accu- rate calculation of the predicted data. If the accuracy is poorer than desired, rigorous inversion follows, using the resulting conductivity distribution and electric field from LQL as a starting model. The rigorous inversion iteratively solves the field and do- main equations, converting the non-linear inversion into a series of linear inversions. We test this method on synthetic and field data. The results of the inversion are very encouraging with respect to both the speed and the accuracyof the algorithm, showing this is a useful tool for airborne EM interpretation.

Leif H. Cox

Papers

3D inversion of airborne electromagnetic data using a moving footprint

3D inversion of airborne electromagnetic data

Airborne electromagnetic modelling options and their consequences in target definition

Large Scale 3D Inversion of HEM Data Using a Moving Footprint

Advanced Computational Methods of Rapid and Rigorous 3-D Inversion of Airborne Electromagnetic Data