Physics of the Earth and Planetary Interiors 173 (2009) 317–329 Contents lists available at ScienceDirect Physics of the Earth and Planetary Interiors journal homepage: www.elsevier.com/locate/pepi WSINV3DMT: Vertical magnetic field transfer function inversion and parallel implementation Weerachai Siripunvaraporn a,∗ , Gary Egbert b a Department of Physics, Faculty of Science, Mahidol University, Rama VI Rd., Rachatawee, Bangkok 10400, Thailand b College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331, USA article info Article history: Received 15 September 2008 Received in revised form 21 January 2009 Accepted 25 January 2009 Keywords: Magnetotellurics Vertical magnetic transfer function Data space method 3-D inversion Occam’s inversion abstract We describe two extensions to the three-dimensional magnetotelluric inversion program WSINV3DMT (Siripunvaraporn, W., Egbert, G., Lenbury, Y., Uyeshima, M., 2005, Three-dimensional magnetotelluric inversion: data-space method. Phys. Earth Planet. Interiors 150, 3–14), including modifications to allow inversion of the vertical magnetic transfer functions (VTFs), and parallelization of the code. The parallel implementation, which is most appropriate for small clusters, uses MPI to distribute forward solutions for different frequencies, as well as some linear algebraic computations, over multiple processors. In addition to reducing run times, the parallelization reduces memory requirements by distributing storage of the sensitivity matrix. Both new features are tested on synthetic and real datasets, revealing nearly linear speedup for a small number of processors (up to 8). Experiments on synthetic examples show that the horizontal position and lateral conductivity contrasts of anomalies can be recovered by inverting VTFs alone. However, vertical positions and absolute amplitudes are not well constrained unless an accurate host resistivity is imposed a priori. On very simple synthetic models including VTFs in a joint inversion had little impact on the inverse solution computed with impedances alone. However, in experiments with real data, inverse solutions obtained from joint inversion of VTF and impedances, and from impedances alone, differed in important ways, suggesting that for structures with more realistic levels of complexity the VTFs will in general provide useful additional constraints. © 2009 Elsevier B.V. All rights reserved. 1. Introduction WSINV3DMT (Siripunvaraporn et al., 2005) has been developed to invert Magnetotelluric (MT) impedance tensor components for three-dimensional (3-D) Earth conductivity. It was made freely available to the MT research community in 2006 and has since become one of the standard tools for 3-D inversion and interpre- tation (e.g., Tuncer et al., 2006; Heise et al., 2008; among others). The inversion algorithm used closely follows the two-dimensional (2-D) data space Occam’s inversion of Siripunvaraporn and Egbert (2000) which has also been widely used for 2-D interpretation (e.g., Pous et al., 2002; Oskooi and and Perdersen, 2005; Toh et al., 2006; among others). Here we describe extensions to this code, which we illustrate with tests on synthetic and real data. We first briefly summarize WSINV3DMT; see Siripunvaraporn et al. (2005) for more technical details. The algorithm used is based on the classic Occam’s inversion introduced by Constable et al. (1987) for the one-dimensional (1-D) MT and DC resistivity sound- ing problems. The Occam inversion seeks a minimum structure ∗ Corresponding author. Tel.: +662 201 5770; fax: +662 354 7159. E-mail address: scwsp@mahidol.ac.th (W. Siripunvaraporn). model (as defined by some model norm which penalizes rough- ness) subject to an appropriate fit to the data. The minimization is accomplished with a modified Gauss–Newton algorithm, in which the regularization parameter (which controls the tradeoff between model roughness and data fit) is also used for step length control (Parker, 1994). The main advantages of the Occam approach are its stability and robustness, and the fact that the scheme often con- verges to the desired misfit in a relatively small number of iterations (e.g., Siripunvaraporn and Egbert, 2000). Occam was extended to treat two-dimensional MT data by deGroot-Hedlin and Constable (1990), but for multi-dimensional inversion the originally pro- posed scheme can be computationally impractical, as the system of normal equations is explicitly formed and solved in the model space. Siripunvaraporn and Egbert (2000) transformed the inverse problem into the data space (e.g., Parker, 1994). If the number of data (N) is small compared to the number of model parameters (M), as will typically be the case in 3-D, the data space variant requires a fraction of the CPU time and memory compared to a model space scheme. This data space Occam scheme forms the basis for the WSINV3DMT algorithm, which is summarized in Fig. 1. The initial version of WSINV3DMT was only capable of inverting the impedance tensor Z, the 2 × 2 complex frequency dependent 0031-9201/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.pepi.2009.01.013