Fast 2D Inversion of Airborne Transient ...

Fast 2D Inversion of Airborne Transient Electromagnetic Data: a Synthetic Case J. Guillemoteau, J. Guillemoteau, P. Sailhac and M. Behaegel 1st EAGE/GRSG Remote Sensing Workshop ,NSG Paris, 2012 Session: RS: Special Joint session with NSG/RS: Data Analysis and Modelling DOI: 10.3997/2214-4609.20143290

Introduction Electromagnetic methods are increasingly used in prospection; one performs new surveys with better precisions and better coverage over complex structures and topography. In this context, using 1D interpretation or thin sheet equivalent modelling only provides rough imaging when better accuracy or precision of the models would be necessary. Full three-dimensional interpretations do exist, but they may not be cost-effective for actual problems found in the near surface industry and academia. We consider new interpretation strategy developed for airborne transient electromagnetic data (ATEM) that can be used in mining and hydrogeology for instance. Modern ATEM surveys can provide data section sufficiently space-sampled to perform 2D imaging of electrical conductivity within the ground. Full 2D inversion using numerical modeling as finite difference or finite elements are still time-consuming methods to process the large amount of data acquired during airborne survey. Otherwise, as 2D structures increase considerably the complexity of eddy current pattern within the ground, fast approximate mapping using 2D sensitivities of equivalent homogenous medium is not sufficient and causes strong artifacts in the resulting model (Wolfgram, 2003). As a consequence, one prefers to use 1D inversion or 3D inversion using local sensitivity to process this kind of data. In this study, we apply the empirical 2D inversion developed by Guillemoteau et al (2012) on synthetic data in order to show that this method produces satisfying outcomes with a small computation time cost.

Method: 2D empirical inversion The inversion of TEM data consists in determining the distribution of electrical conductivity from the measurement of the vertical magnetic field decay after the turn off of the source. The 3D forward problem can be written as follows (Gomez-Trevino, 1987):

(1) where hz(rR, t) is the magnetic field decay measured at the receiver position rR is the position of the receiver and g is the sensitivity function or Frechet kernel. By using the approximate inverse mapping method (AIM) as introduced by Oldenburg and Ellis (1991) and by considering apparent conductivity as data which controls the scaling of sensitivity, the 2D equivalent problem may be written as follows:

(2) where rR = {xR, zR} is the position of the receiver. f(r, t, σa) is the 2D Frechet kernel which can be approximated in the illuminated area Ω={-dx;dx;0 dz} by the following empirical function (Guillemoteau et al , 2012) : Near Surface Geoscience 2012 – 18th European Meeting of Environmental and Engineering Geophysics Paris, France, 3-5 September 2012

(3) with

,

(4)

where cz is the scaling factor for the vertical direction defined by Christensen (2002), cx is the scaling factor for the horizontal direction, hr is the clearance, μ0 is the permeability of the free space and Г is a normalizing factor.

Figure 1 Top: Synthetic data computed by finite element with the program ArjunAir developed by CSIRO (Australia). The vertical magnetic field is showed for all the VTEM time gates along an artificial profile. Bottom: Ground conductivity model which has been used to generate the artificial profile of data. The model is characterised by an anomaly of conductivity σ = 100 mS/m embedded in an inclined half-space of conductivity σ = 1 mS/m.

The inversion scheme consists in taking the apparent conductivity versus time as data to be inverted to model the distribution of the conductivity in a vertical plane under the flight line. If we consider Ns sounding acquired at different positions along the flight line using Nt time gates, the data set is composed of Nd = Ns×Nt data. By discretizing the 2D space into Nm blocks, we can write the problem in a matrix form as follows: Near Surface Geoscience 2012 – 18th European Meeting of Environmental and Engineering Geophysics Paris, France, 3-5 September 2012

(5) where F contains the integral of f(r, σa, t) over each model block for all the data. This problem is first solved using conjugate gradient least square method and a standard Tikhonov regularization strategy. Then, the problem is reweighted iteratively in the log space in order to allow sharper contrasts by using the additional recursive filter presented in Guillemoteau et al (2011):

,

(6)

where σ0 is the initial conductivity obtained by solving the equation set (5), λP is a Lagrangian parameter which controls the difference with σ0, σa is the measured apparent conductivity, σ°a = F σ0 is the predicted apparent conductivity, Wd is a diagonal matrix weighting the data in which elements are proportional to hz(t) and F* is the logarithmic kernel given by :

(7) 2D inversion allows (or forces) us to take into account the influence of topography. Indeed, in our processing, we compute the angle φ of the slope locally over a distance equal to the early-time footprint. Then, the magnetic response is divided by the factor cos(φ)² in order to model both the inclination of the receiver and the incidence of the primary magnetic field. In addition, in the inversion, we use a sensitivity function rotated in such a way that the modelled eddy currents are parallel to the ground surface. Example of application to synthetic data

Near Surface Geoscience 2012 – 18th European Meeting of Environmental and Engineering Geophysics Paris, France, 3-5 September 2012

Figure 2 Top: Ground conductivity model resulting from 1D smooth inversion with vertical constraint. The results for all sounding are concatenated along the profile. The depth of the conductive body is overestimated and the resulting image shows the traditional pant-leg artefact. Bottom: Ground conductivity model resulting from the empirical 2D inversion. The pant leg artefact has been removed and the conductivity body appears at the right position. We simulate Bz transient responses for in-loop acquisition by using the program ArjunAir from the P223 software package (Raiche, 2008). We reproduce one artificial line of data acquired with a VTEM system (Witherly et al., 2004) at the nominal 45m clearance and a realistic waveform. We use a transmitter loop of 26m in diameter and a receiver of 1.1m in diameter, which record 27 time measurements going from t1 = 83μs to t27 = 7.8ms. This synthetic data set is related to one model of ground which presents a 2D anomaly of conductivity σ = 100 mS/m inside an inclined halfspace of conductivity σ = 1 mS/m (see Figure 1).

We apply the 2D empirical inversion scheme described before on this synthetic data set in order to compare the resulting model of conductivity to the true one. In addition, we compare 2D imaging with standard 1D imaging. The results are displayed in Figure 2 and show the superiority of 2D imaging for this geological context. Conclusion By applying the fast empirical 2D imaging method on synthetic data, we show that it eliminates 2D artefacts which are often encountered when using 1D inversion. This method is relatively fast; our Matlab code provides model sections with the speed of 1min/km of profile with a laptop (2.4GHz, 4 Go of RAM). This method is implemented as a sliding window with a width of around 2-3 km in order to process long profiles of several tens of kilometres. It would allow geophysicists to manage better the whole campaign as it provides a better understanding of the ground during the survey.

Acknowledgements This paper results from a Joint Research Project between AREVA-NC and CNRS UMR 7516. The authors thank AREVA Mining Business Group for financial support to J.G. as a PhD student. References Christensen N.B., 2002. A generic 1-D imaging method for transient electromagnetic data: Geophysics, 67, 438–447. Gomez-Trevino, E., 1987. A simple sensitivity analysis of time-domain and frequency domain electromagnetic measurements: Geophysics, 52, 1418–1423. Guillemoteau J., Sailhac P. and Behaegel M., 2011. Regularization strategy for the layered inversion of airborne transient electromagnetic data: Application to in-loop data acquired over the basin of Franceville (Gabon): Geophysical Prospecting, 59, 1132-1143. Guillemoteau J., Sailhac P. and Behaegel M., 2012. Fast approximate 2D inversion of airborne TEM data: Born approximation and empirical approach: Geophysics, In Press. Oldenburg, D., and R. Ellis, 1991. Inversion of geophysical data using an approximate inverse mapping: Geophys. J. Int., 105, 325–353. Raiche, A., 2008. The P223 software suite for planning and interpreting EM surveys: Previews, 132, 25–30.

Near Surface Geoscience 2012 – 18th European Meeting of Environmental and Engineering Geophysics Paris, France, 3-5 September 2012

Witherly, K., R. Irvine, and E. Morrison, 2004. The Geothech VTEM time domain helicopter EM system: 17th ASEG meeting, Sydney, Expanded Abstract. Wolfgram, P., D. Sattel, and N. Christensen, 2003. Approximate 2D inversion of AEM data: Exploration Geophysics, 34, 29–33.

Near Surface Geoscience 2012 – 18th European Meeting of Environmental and Engineering Geophysics Paris, France, 3-5 September 2012