Probabilistic inversion of airborne electromagnetic data for a multidimensional earth (original) (raw)
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Geophysical Journal International, 2014
Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints.
7th General Assembly of IUGG Working Group of Electromagnetic Study on Earthquakes and Volcanoes (EMSEV)
This paper describes a 1-D inversion modeling of vertical electrical sounding (VES) data using Schlumberger array. The algorithm employs Markov Chain Monte Carlo (MCMC) previously applied to 1 D inversion of MT data (Grandis et al., 1999). The algorithm was tested to invert synthetic data corresponding to simple three-layer models. The method was also applied to field VES data acquired on a profile. The data were interpolated laterally resulting in denser data coverage and the inverse models were concatenated one to the other to obtain a quasi 2 D model. The model showed satisfactory agreement with 2 D inversion result. The algorithm is quite generic such that it can be used as a template to invert other geo-electromagnetic data (e.g. CSAMT, SNMR etc.) for 1-D modeling.
GEOPHYSICS, 2011
are not designed to provide a robust evaluation of uncertainty that reflects the limitations of the geophysical technique. Stochastic inversions, which do provide a sampling-based measure of uncertainty, are computationally expensive and not straightforward to implement for nonexperts (nonstatisticians). Our results include stochastic inversion for magnetotelluric and controlled source electromagnetic data. Two Markov Chain sampling algorithms (Metropolis-Hastings and Slice Sampler) can significantly decrease the computational expense compared to using either sampler alone. The statistics of the stochastic inversion allow for (1) variances that better reveal the measurement sensitivities of the two different electromagnetic techniques than traditional techniques and (2) models defined by the median and modes of parameter probability density functions, which produce amplitude and phase data that are consistent with the observed data. In general, parameter error estimates from the covariance matrix significantly underestimate the true parameter error, whereas the parameter variance derived from Markov chains accurately encompass the error.
GEOPHYSICS, 2013
Bayesian methods can quantify the model uncertainty that is inherent in inversion of highly nonlinear geophysical problems. In this approach, a model likelihood function based on knowledge of the data noise statistics is used to sample the posterior model distribution, which conveys information on the resolvability of the model parameters. Because these distributions are multidimensional and nonlinear, we used Markov chain Monte Carlo methods for highly efficient sampling. Because a single Markov chain can become stuck in a local probability mode, we run various randomized Markov chains independently. To some extent, this problem can be mitigated by running independent Markov chains, but unless a very large number of chains are run, biased results may be obtained. We got around these limitations by running parallel, interacting Markov chains with "annealed" or "tempered" likelihoods, which enable the whole system of chains to effectively escape local probability maxima. We tested this approach using a transdimensional algorithm, where the number of model parameters as well as the parameters themselves were treated as unknowns during the inversion. This gave us a measure of uncertainty that was independent of any particular parameterization. We then subset the ensemble of inversion models to either reduce uncertainty based on a priori constraints or to examine the probability of various geologic scenarios. We demonstrated our algorithms' fast convergence to the posterior model distribution with a synthetic 1D marine controlled-source electromagnetic data example. The speed up gained from this new approach will facilitate the practical implementation of future 2D and 3D Bayesian inversions, where the cost of each forward evaluation is significantly more expensive than for the 1D case.
Fast approximate 1D inversion of frequency domain electromagnetic data
Near Surface Geophysics, 2009
We present a fast approximate method for 1D inversion of frequency domain data and apply it to frequency domain helicopter-borne data from the Bookpurnong area of the Murray River, South Australia. The method is based on fast approximate forward computation of transient electromagnetic step responses and their derivatives with respect to the model parameters of a 1D model, with the frequency domain responses and derivatives then found through Fourier transformation of the time-domain counterparts. The inversion is carried out with multi-layer models in an iterative, constrained least-squares inversion scheme including explicit formulation of the model regularization through a model covariance matrix. The method is 30 times faster than conventional full inversion for a layered earth model and produces model sections of concatenated 1D models and contoured maps of mean conductivity in elevation intervals almost indistinguishable from those of a conventional full inversion. In a theoretical forward and inverse modelling study, the fast approximate and conventional computation methods are compared demonstrating the applicability of the approximate method and its limitations. Applied to the Bookpurnong RESOLVE ® FDHEM data set from South Australia, the inversion produces model sections and conductivity maps that reveal the distribution of conductivity in the area and thereby the distribution of salinity. This information is crucial for any remediation effort aimed at alleviating the salinization of the river and the degradation of floodplain vegetation and associated ecosystems. be a good approximation to the real conductivity distribution, especially if lateral constraints are included in the inversion (Auken and Christiansen 2004; Brodie and Sambridge 2006; Christensen and Tølbøll 2009). In environments with pronounced 3D model characteristics, 1D inversion will in many cases provide unreliable models with artefacts know as 'pant legs'. However, though it is not sufficient to prove that 3D effects are not present (Ellis 1998), none of these typical model artefacts have been seen in the inversion of the Bookpurnong FDHEM data. For 1D inversion, more or less sophisticated approximate methods have been developed. These are often included in software packages used for data and model display and for the handling of limited geographical information (see, for example, EMflow (Macnae et al. 1998) and EMax (Fullagar and Reid 2001)). Successful fast approximate inversion techniques based on the general theoretical framework of approximate inverse mapping where a sufficiently accurate forward mapping is combined with approximate derivatives have been presented in Oldenburg and Ellis (1991) and Li and Oldenburg (1992). A fairly comprehensive comparison between different inver-cc01453-ma003
3D inversion of airborne electromagnetic data using a moving footprint
Exploration Geophysics, 2010
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 meth...
Advanced computational methods of rapid and rigorous 3-D inversion of airborne electromagnetic data
Abs trac t. We develop a new computa tional meth od for modeling and inverting fre qu ency dom ain airborne electromag ne tic (EM) data. Our method is based on the con traction int egral equa tion meth od for forward EM modeling and on inversion using the localized qu asi-linea r (LQL) approximation followe d by the rigorous inversion, if necessary. The LQL inversion serves to provide a fast image of the tar get. These res ults are chec ked by a rigorou s update of the domain electric field, allowing a more accu ra te calcu lation of the predicted da ta. If the accuracy is poorer than de sired, rigorous inversion follows, using the resulting cond uc tivity distribu tion and electr ic field from LQL as a starting model. The rigorous inversion iteratively solves the field and do main equations, conv erting the non-linear inversion into a series of linear inversio ns. We test this method on synthetic and field data. The resu lts of the inversion are very encouraging with respect to both the speed and the accuracy of the algorithm, showing this is a useful tool for airborne EM interpretation.
2014
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. Thefirst 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.