A comparison of different radiomagnetotelluric data inversion methods for buried waste sites

https://doi.org/10.1016/j.jappgeo.2005.07.001Get rights and content

Abstract

This study deals with two-dimensional (2D) inversions of synthetic and observed radiomagnetotelluric (RMT) data on typical buried conductive waste sites in Europe, and with the practical aspects of different inversion algorithms. In the inversion calculations, we used smoothing and L2-norm stabilizers and compared the results. The resolution of the geometry of the highly conductive waste site, in particular, was investigated. In the inversion with the L2-norm stabilizer, we used the least-squares solution with singular value decomposition (LSSVD) and conjugate gradient (CG), whereas only the conjugate gradient solver was used in the 2D-inversion with the smoothing stabilizer. The inversion results of the synthetic data showed a better resolution of the geometry of the highly conductive waste site when a L2-norm stabilizer was applied in the inversion; in particular, a better detection of the bottom of the waste deposit was achieved. Additional model studies were carried out using synthetic RMT data in order to investigate the 2D inversion of RMT data observed on a 3D structure; these studies showed that the use of TM mode data yields a better resolution of the structure than joint inversion of TE and TM modes.

2D inversions of RMT data on a waste site near Cologne showed that the inversion of the TM mode could resolve well the geometry, especially the bottom of the waste site, if information about the background conductivity structure was available. In this case study, inversion with the L2-norm stabilizer produced a sharper image of the waste site than inversion with the smoothing stabilizer, as indicated also by the inversion study that used synthetic data.

Introduction

The RMT method is an extension of the well-known Very-Low-Frequency (VLF) technique to higher frequencies. RMT uses radio transmitters in a frequency range between 10 to 300 kHz with a possible extension to 1 MHz. The RMT method has been used with increasing popularity for ground-water research (Turberg et al., 1994, Beamish, 2000), waste-site studies (Zacher et al., 1996a, Tezkan et al., 1996, Tezkan et al., 2000), and archaeological investigations (Zacher et al., 1996b, Baum, 1998).

The RMT method has proven quite efficient in waste-site studies. However, it is sometimes difficult to resolve the bottom of waste deposits from the 2D inversion of the observed scalar RMT data — the main reasons being the three-dimensionality of the structure and/or screening effects of the highly conductive anomaly due to the limited frequency range of the RMT method. However, possible 3D effects on RMT data cannot be studied using scalar RMT data acquisition. In addition, the smoothing stabilizer that has been used in inversion algorithms to date (e.g., Tezkan, 1999, Tezkan et al., 2000, Newman et al., 2003) may be another reason. Therefore, two different inversion approaches (the L2 norm of model parameters and the Laplacian norm of model parameters) are compared for models of typical buried, conductive waste sites in order to study the effects of the smoothing stabilizer.

RMT data are usually collected for frequency pairs of radio transmitters situated roughly parallel and perpendicular to the assumed strike direction of a 2D conductivity structure. The RMT method uses carrier waves from high-powered civilian and military transmitters that operate in a frequency range between 10 kHz and 1 MHz. Local electromagnetic fields can be assumed to be of plane waves (McNeill and Labson, 1991) because of the great distance (> 8 times skin depth) between the survey area and such transmitters (vertical electric dipole). The EM field consists of a horizontal magnetic field perpendicular to the direction of propagation and a horizontal electric field in the direction of propagation. Model calculations also show that displacement currents can be neglected in central Europe under normal conditions (expected resistivities of less than 1000 Ω m) up to 1 MHz, and the plane-wave assumption is valid for RMT data (Schröder, 1994). Therefore, magnetotelluric (MT) inversion algorithms can be used for RMT data interpretation (e.g., Beamish, 1994, Beamish, 2000, Tezkan et al., 2000). RMT data acquisition is rapid in comparison to traditional MT measurements. However, RMT data are usually acquired in scalar mode in most applications. Bastani (2001) and Bastani and Pedersen (2001) introduced a newly developed RMT system that performs tensor measurements. Apparent resistivities and phases in scalar mode are measured parallel and perpendicular to polarization directions, which are associated – in the case of a 2D anomaly – with a known strike direction relative to the TE (transverse electric – electric field parallel to the strike direction) and TM (transverse magnetic – magnetic field parallel to the strike direction) modes.

RMT data are usually interpreted using 2D inversion calculations. The 2D inversion codes used for the interpretation of RMT data (e.g., Beamish, 1994, Beamish, 2000, Tezkan et al., 2000) are OCCAM (deGroot-Hedlin and Constable, 1990) and D2INV (Mackie et al., 1997, Rodi and Mackie, 2001). OCCAM uses the finite element algorithm, PW2D (Wannamaker et al., 1987), for forward calculations, the sensitivity-equation approach (McGillivray et al., 1994) for the Jacobian (frechet derivative or sensitivity) matrix calculation, and the least-squares solution with singular value decomposition (LSSVD) for the inverse calculation. In the code D2INV, the forward calculation is done by using the transmission-network analog of Madden (1972), and the Jacobian matrix is calculated by the adjoint-equation approach (McGillivray et al., 1994) in which the reciprocity principle is employed and the nonlinear conjugate gradient (NLCG) algorithm is used in the inverse procedure. The codes, OCCAM and D2INV, use the Laplacian norm of the model parameters as a stabilizer (smoothing inversion) in the inversion algorithm. Hence, 2D smooth inversion of RMT data at times can mask the main target structure, such as the bottom of a waste site. In such cases, different algorithms using different stabilizers, such as the L2 norm of the model parameter vector, may give more accurate results than smoothing inversion.

Candansayar, 2002a, Candansayar, 2002b developed a new code, named regularized 2D magnetotelluric inversion (R2DMTINV). He compared results of 2D inversions of M`T data using CG and LSSVD algorithms with different stabilizers with this code. He suggested that a consecutive use of LSSVD and CG algorithms (LSSVD_CG) with the L2-norm stabilizer generates more accurate results than the single use of each algorithm. Forward calculations are made by using the finite difference method, and the adjoint-equation approach is used for the calculation of the Jacobian matrix in the code. CG and LSSVD inversion algorithms can also be used separately or consecutively in this code.

Synthetic data and field data observed on a waste site are used to compare different inversion results by utilizing CG, LSSVD, and LSSVD_CG (which use the L2 norm of the model parameter as a stabilizer) algorithms with the inversion code, R2DMTINV, and NLCG (which uses the Laplacian norm of model parameters as a stabilizer) algorithms with the inversion code, D2INV. The main difference between the CG and NLCG algorithms is that the former uses the L2 norm of the model parameters as a stabilizer, whereas the latter uses the Laplacian norm of the model parameters as a stabilizer. Below we show that the L2-norm stabilizer approach is sometimes superior to the smoothing stabilizer.

Section snippets

2D inversion

The electromagnetic inverse problem which is solved with some regularization methods is nonlinear and ill-posed. The following parametric functional is minimized (Tikhonov and Arsenin, 1977) in the regularizationP(m,d)=ϕ(m,d)+αS(m)=minwhere φ(m, d) and S(m) are the misfit functional and the stabilizer (stabilizing functional or model objective functional), respectively. α is a regularization parameter (penalty parameter) that is a real number. φ(m, d) may be defined as the L2 norm of the

2D inversion of synthetic and field data

Two synthetic-data sets and one field-data set were used in order to compare the resolution capacity of the CG, LSSVD, LSSVD_CG and NLCG algorithms. The solution of Eq. (5) is realized by using CG, LSSVD, and LSSVD_CG algorithms for synthetic data and the LSSVD_CG algorithm for field data. On the other hand, smoothing inversion (the solution of Eq. (6)) is realized by using the NLCG algorithm (Mackie et al., 1997) for synthetic and field data.

The grids used for the inversion of the synthetic

First model

A synthetic data set was generated at 27 points for frequencies 234, 126, 53, and 18.3 kHz, by using the finite element modeling algorithm developed by Wannamaker et al. (1987). These frequencies are typically used for RMT surveys near Cologne. The model used is a simple waste site (Fig. 1a). The background geology is represented by a three-layer earth model with resistivities of 50, 500, and 25 Ω m, respectively, from top to bottom. The corresponding thicknesses of these layers are assumed to

Inversion of the field data

An RMT survey was carried out on a waste site near Cologne. The site was formerly a pit but is now filled with different kinds of industrial waste and household refuse (Recher, 2002, Newman et al., 2003). Newman et al. (2003) discussed the 3D inversion of the observed RMT data set. They also compared 2D and 3D inversion results for selected profiles, y =  50 and 0 m. We have applied LSSVD_CG and NLCG inversion algorithms to the same data sets. Apparent resistivities and phases for four frequency

Conclusions

2D inversion continues to play a main role in RMT data interpretation. Based on the results of synthetic data inversion, two conclusions can be drawn:

  • as expected, the inversion with the L2-norm stabilizer gives a sharper image than the inversion with the smoothing stabilizer. Results from the inversion of the 2D synthetic data show that the bottom of a waste site can be resolved by using this type of 2D inversion.

  • some valuable information can be acquired from 2D inversion of the TM-mode data

Acknowledgements

This work was conducted at the University of Cologne and Ankara University. M.E. Candansayar was granted postdoctoral fellowships by TUBITAK (Scientific and Technical Research Council of Turkey) and DFG (Deutsche Forschungsgemeinschaft). The inversion program, R2DMTINV, was developed in the Geosciences Data Processing Laboratory (YEBVIL) of Ankara University under TUBITAK Project No. YDABÇAG-553. Special thanks to Dr. A. Hördt and Dr. M. Bastani who carefully reviewed the paper and gave

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