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Modeling


PIE3D ver. 2015, Release March 2016. The PIE3D ver. 2016 is parallel EM forward modeling software based on the IE method. PIE3D ver. 2016 is designed for distributed memory machines (e.g., PC clusters) and is portable on any computer that supports message passing interface (MPI). This code simulates frequency-domain EM responses of multiple-domain (MD) 3D anomalous resistivity structures in a horizontally layered medium.
For this release the functionality remains the same, except for a few minor bug fixes both in PIE3D and in GREEN3D. The major improvement is providing binaries for the Windows and Linux 64 bit, including all the external libraries and tools. Therefore PIE3D can run without any effort spent on installing external packages. The binaries have been tested on Windows 7 and 10 and on CentOS 6 and 7, Ubuntu 14.04, and Debian 8.
Authors: Martin Cuma and Michael Zhdanov
References:
    Endo, M., M. Čuma, and M. S. Zhdanov, 2009, Application of a multiple-domain, integral-equation method for 3D electromagnetic modeling in complex geoelectrical structures: Proceedings of the Annual Meeting, Consortium for Electromagnetic Modeling and Inversion, 27-48.
    Endo, M., M. Čuma, and Zhdanov, M. S., 2009, Large-scale electromagnetic modeling for multiple inhomogeneous domains: Communications in Computational Physics, 6, 269-289.
    Hursán, G., and M. S. Zhdanov, 2002, Contraction integral equation method in three-dimensional electromagnetic modeling: Radio Science, 37 (6), 1089, doi: 10.1029/ 2001RS002513.
    Yoshioka, K., and M. S. Zhdanov, 2005, Electromagnetic forward modeling based on the integral equation method using parallel computers: Proceedings of the Annual Meeting, Consortium for Electromagnetic Modeling and Inversion, 25-44.
    Yoshioka, K., and M. S. Zhdanov, 2006, Modeling large-scale geoelectrical structures with inhomogeneous backgrounds using the integral equation method: application to the bathymetry effects in marine CSEM data: Proceedings of the Annual Meeting, Consortium for Electromagnetic Modeling and Inversion, 159-180.
    Zhdanov, M. S., S. K. Lee, and K. Yoshioka, 2006, Integral equation method for 3D modeling of electromagnetic fields in complex structures with inhomogeneous background conductivity: Geophysics, 71 (6), G333-G345, doi: 10.1190/1.2358403.
    Ueda, T., and M. S. Zhdanov, 2006, Fast numerical modeling of multitransmitter electromagnetic data using multigrid quasi-linear approximation: IEEE Transactions in Geoscience and Remote Sensing, 44, 1428-1434.
    Zhdanov, M. S., 2002, Geophysical inverse theory and regularization problems: Elsevier.

EdgeHexTop ver. 2015, release March 2016. The EdgeHexTop is a MATLAB software package for 3D numerical modeling of controlled source electromagnetic (CSEM) data using edge-based finite element method (Cai et al., 2015). The package solves the low frequency Maxwell's equation for a secondary electric field (Zhdanov, 2009). Compared to our previous release, this version of the code uses a distorted hexahedral mesh to account for topography and bathymetry effects. The algorithm is capable of solving the diffusive EM problem in an anisotropic medium. The background electromagnetic field is calculated using our Green3d software, which is based on the fast Hankel transform (Anderson, 1989; Guptasarma and Singh, 1997). The sparse finite element system of equations is solved using the quasi-minimum residual method with a simple and effective Jacobian preconditioner.
    Authors: Hongzhu Cai and Michael S. Zhdanov.
    References:
    Anderson, W. L., 1989, A hybrid fast hankel transform algorithm for electromagnetic modeling: Geophysics, 54, 263-266.
    Cai, H., B. Xiong, M. Han, and M. S. Zhdanov, 2014, 3D controlled-source electromagnetic modeling in anisotropic medium using edge-based finite element method: Computers & Geosciences, 73, 164-176.
    Guptasarma, D., and B. Singh, 1997, New digital linear filters for Hankel J0 and J1 transforms: Geophysical Prospecting, 54, 263-266.
    Zhdanov, M. S., 2009, Geophysical electromagnetic theory and methods: Elsevier.

FDIE3D ver. 2015, release March 2016. The FDIE3D is a MATLAB software package for 3D numerical modeling and controlled source electromagnetic (CSEM) data using the hybrid finite difference (FD) and integral equation (IE) method (Yoon et al., 2015). This hybrid FD-IE method solves the low frequency Maxwell's equations for anomalous electric fields using FD approximation on the staggered grid (Newman and Alumbaugh, 1995), and calculates the EM fields at the receiver positions based on the Green's tensor approach. This approach makes it possible to compute the fields at the receivers accurately without mesh refinement near the receiver or the source positions. The sparse finite difference system of equations is solved using the quasi-minimum residual method with a Jacobian preconditioner.
    Authors: Daeung Yoon and Michael S. Zhdanov.
    References:
    Newman, G. A., and D. L. Alumbaugh, 1995, Frequency-domain modelling of airborne electromagnetic responses using staggered finite differences: Geophysical Prospecting, 43, 1021--1042.
    Yoon, D., M. S. Zhdanov, H. Cai, and A. Gribenko, 2015, A hybrid finite difference and integral equation method for modeling and inversion of marine CSEM data: Consortium for Electromagnetic Modeling and Inversion, Proceedings of 2015 Annual Meeting.

GREEN3D, release March 2010. The MatLab shell of the Fortran 77 library GREENLIB for computing the normal fields and volume integrals of electromagnetic Green's tensors. This program is designed to help the development of electromagnetic modeling and inversion programs. It is an easy-to-use MATLAB function which can be called up anywhere in the MATLAB environment. Using this library, the software developer is freed from coding the excessively complex algorithms for Green's tensors and different electromagnetic fields in a layered medium.
Author: Gabor Hursan
References:
Xiong, Z., 1992, EM modeling of three-dimensional structures by the method of system iteration using integral equations, Geophysics, 57, 1556-1561.
Zhdanov, M. S., and G. V. Keller, 1994, The geoelectrical methods in geophysical exploration: Elsevier, 873 pp.
G. Hursan, 1999, A Fortran 77 Library for Computing the Normal Fields and Volume Integrals of Electromagnetic Green's Tensors: Proceedings of the CEMI 1999 Annual Meeting.

INTEM3DQLIP ver. 2014, release March 2015. INTEM3DQLIP_2014 is designed for frequency domain electromagnetic (EM) modeling of three-dimensional anisotropic geoelectrical structures embedded in horizontally layered earth based on the integral equation (IE) method (Hursán and Zhdanov, 2002). The following sources can be modeled using this program::
- plane wave propagating vertically toward the Earth (magnetotelluric);
- current bipoles along the x, y, and z directions;
- horizontal rectangular loop:
- horizontal circular loop;
- moving horizontal loops;
- magnetic dipoles oriented in the x, y, and z directions.
Authors: Masashi Endo and Michael Zhdanov
Hursan, G., and M. S. Zhdanov,  2002, Contraction integral equation method in three-dimensional electromagnetic modeling: Radio Sci., 37 (6), 1089, doi: 10.1029/ 2001RS002513.
Zhdanov, M. S., 2002, Geophysical inverse theory and regularization problems: Elsevier.
Zhdanov, M. S., 2009, Geophysical electromagnetic theory and methods: Elsevier.

EdgeFEM3D ver. 2014, release March 2015. The EdgeFEM3D is a MATLAB software package for 3D numerical modeling of controlled source electromagnetic (CSEM) data using edgebased finite element method (Cai et al., 2014). The package solves Maxwell’s equations for the anomalous electric field (Zhdanov, 2009). The algorithm is capable of solving the diffusive EM problem in anisotropic medium. The background electromagnetic field is calculated using CEMI GREEN3D software, which is based on the fast Hankel transform (Anderson, 1989; Guptasarma and Singh, 1997). The sparse finite element system of equations is solved using quasi minimum residual method with a Jacobian preconditioner.
Authors: Hongzhu Cai and Michael Zhdanov
Anderson, W. L., 1989, A hybrid fast hankel transform algorithm for electromagnetic modeling: Geophysics, 54, 263-266.
Cai, H., B. Xiong, M. Han, andM. S. Zhdanov, 2014, 3D controlled-source electromagnetic modeling in anisotropic medium using edge-based finite element method: Computers & Geosciences, 73, 164-176.
Guptasarma, D., and B. Singh, 1997, New digital linear filters for Hankel J0 and J1 transforms: Geophysical Prospecting, 54, 263-266.
Zhdanov, M. S., 2009, Geophysical electromagnetic theory and methods: Elsevier.

Inversion

MT3D ver. 2015, Released March 2016. MATLAB software package for 3D inversion of the magnetotelluric (MT) and magnetovariational (MV) data. The predicted data are calculated rigorously by the PIE3D integral equation (IE) modeling code (Čuma and Zhdanov, 2014; Hursán and Zhdanov, 2002). The fast Fréchet derivative computation is based on the quasi-Born (QB) approximation (Gribenko and Zhdanov, 2010). The standard approach of minimizing the Tikhonov parametric functional (Tikhonov and Arsenin, 1977) is realized in the code. The preconditioned regularized conjugate-gradient method is used for the parametric functional minimization (Zhdanov, 2002). 1D inversion of the principal impedance data is applied to obtain the initial model. Besides the 3D conductivity distribution the code recovers the complex impedance distortion matrix (Groom and Bailey, 1989; Chave and Jones, 2012). The variable sensitivity domain size is computed based on the skin depth for each frequency. The code outputs 3D conductivity distribution, predicted impedance and/or tipper data, and RMS misfit values. The solution and predicted fields can be visualized by the code. The new release includes bug fixes and optimized memory management.
Authors: Alexander Gribenko and Michael S. Zhdanov
References:
Chave, A. D., and A. G. Jones, 2012, The magnetotelluric method theory and practice: Cambridge University Press.
Cuma, M., and M.S. Zhdanov, 2014, The PIE3D ver. 2013, Consortium for Electromagnetic Modeling and Inversion annual meeting, CEMI, Expanded Abstracts , 307-308.
Hursán, G., and M. S. Zhdanov, 2002, Contraction integral equation method in three-dimensional electromagnetic modeling: Radio Science, 37 (6), 1089, doi: 10.1029/ 2001RS002513.
Gribenko, A., and M. S. Zhdanov, 2010, Rigorous 3D inversion of marine CSEM data based on the integral equation method: Geophysics, 72, WA73.
Groom, R. W., and R. C. Bailey, 1989, Decomposition of magnetotelluric impedance tensors in the presence of local three dimensional galvanic distortion, Journal of Geophysical Research, 94, 1913-1925.
Tikhonov, A. N., and V. Y. Arsenin, 1977, Solution of ill-posed problems: V. H. Winston and Sons.
Zhdanov, M. S., 2002, Geophysical inverse theory and regularization problems: Elsevier.

JOINT3D ver. 2015, Released March 2016. The JOINT3D software package performs 3D joint inversion of gravity and magnetic data. It works for any combination of the gravity (Gx, Gy, Gz, Gxx, Gyy, Gzz, Gxy, Gzx, Gzy, Gd) and magnetic components (TMI, Hx, Hy, Hz). The joint inversion code uses the Gramian constraints (Zhdanov et al., 2012) to enhance either direct or structural correlations between two physical properties, which are the density and magnetic susceptibility or the density and magnetization vector, depending on the existence or not of remanent magnetization. We discretize the modeling domain into a set of rectangular prisms and evaluate the volume integral in each prism using single-point Gaussian integration in the forward modeling and Fréchet computation. The code is compatible with both minimum norm and maximum smooth stabilizers. We solve the joint inversion problem using the regularized conjugate gradient method (Zhdanov, 2002).
Authors: Yue Zhu and Michael S. Zhdanov.
References:
Zhdanov, M. S., 2002, Geophysical inverse theory and regularization problems: Elsevier.
Zhdanov, M. S., 2015, Inverse theory and applications in Geophysics: Elsevier.
Zhdanov, M. S., A. Gribenko, and G. Wilson, 2012, Generalized joint inversion of multimodal geophysical data using Gramian constraints: Geophysical Research Letters, 39, L09301.

MCSEM3D ver. 2012, Release March 2013. Matlab software package for 3D inversion of the marine controlled source electromagnetic (MCSEM) data. The predicted data are calculated rigorously by the PIE3D integral equation (IE) modeling code. The fast Fréchet derivative computation is based on the quasi-Born (QB) approximation (Gribenko et al., 2010). The standard approach of minimizing the Tikhonov parametric functional (Tikhonov and Arsenin, 1977) is realized in the code. The regularized conjugategradient method with re-weightings and adaptive regularization is used for parametric functional minimization (Zhdanov, 2002). At the first stage, the code uses a minimum norm stabilizer, minimum gradient stabilizers, or their combination, which produces smooth conductivity distributions (Gribenko and Zhdanov, 2011). At the consequent stages (re-weightings), the user has a choice of minimum norm, minimum support (Portniaguine and Zhdanov, 1999), minimum vertical support (Zhdanov et al., 2007) stabilizers, or their combination. Appropriate selection of the stabilizing functional allows the user to find a solution with sharp geoelectrical boundaries.
Unlike the previous versions, the code allows several transmitter lines with inline MCSEMdata. The code uses the parallel version of the 3D electromagnetic (EM) forward modeling code (PIE3D). MCSEM3D is written in the MATLAB language for the versions 2006b or later. MATLAB license is required to run MCSEM3D. MCSEM3D is platform independent.,   
Authors: Alexander Gribenko, Daeung Yoon, and Michael S. Zhdanov   
References:   
    Hursán, G., and M. S. Zhdanov, 2002, Contraction integral equation method in three-dimensional electromagnetic modeling: Radio Science, 37 (6), 1089, doi:
10.1029/ 2001RS002513.
Gribenko, A., and M. S. Zhdanov, 2010, Rigorous 3D inversion of marine CSEM data based on the integral equation method: Geophysics, 72, WA73.
Gribenko, A., and M. S. Zhdanov, 2011, Joint inversion of MT and MCSEM data in off-shore exploration: Proceedings of 2011 CEMI Annual Meeting.
Gribenko, A., L. Wan, and M. S. Zhdanov, 2010, Three-dimensional inversion of magnetotelluric data for complex resistivity: Proceedings of 2010 CEMI Annual
Meeting, 269-294.
Gribenko, A., A. M. Green, M. Cuma, and M. S. Zhdanov, 2010, Efficient 3D inversion of MT data using integral equations method and the receiver footprint approach:
application to the large-scale inversion of the EarthScope MT data: 80th Annual InternationalMeeting, SEG, Expanded Abstracts, 655-659, doi:10.1190/1.3513865.
Portniaguine, O., and M. S. Zhdanov, 1999, Focusing geophysical inversion images: Geophysics, 64, 874-887.
Tikhonov, A. N., and V. Y. Arsenin, 1977, Solution of ill-posed problems: V. H. Winston and Sons.
Zhdanov, M. S., 2002, Geophysical inverse theory and regularization problems: Elsevier.
Zhdanov, M.S., 2009, Geophysical electromagnetic theory and methods: Elsevier.
Zhdanov, M. S., A. Gribenko, and M. Cuma, 2007, Regularized focusing inversion of marine CSEM data using minimum vertical-support stabilizer: 77th Annual International Meeting, SEG, Expanded Abstracts, 579-583.

MCSEM_MT3D ver. 2014. Release March 2015. MATLAB software package for joint 3D inversion of the marine controlled source electromagnetic (MCSEM) and magnetotelluric (MT) data. The predicted data are calculated rigorously by the PIE3D integral equation (IE) modeling code. The fast Fréchet derivative computation is based on the quasi-Born (QB) approximation (Gribenko and Zhdanov, 2007). The standard approach of minimizing the Tikhonov parametric functional (Tikhonov and Arsenin, 1977) is realized in the code. The regularized conjugate-gradient method with re-weightings and adaptive regularization is used for the parametric functional minimization (Zhdanov , 2002). At the first stage the code uses a minimum norm stabilizer, minimum gradient stabilizers,or their combination, which produces smooth conductivity distributions (Gribenko and Zhdanov, 2011). At the consequent stages (re-weightings) the user has a choice of minimum norm, minimum support (Portniaguine and Zhdanov, 1999), minimum vertical support (Zhdanov et al., 2007) stabilizers, or their combination. Appropriate selection of the stabilizing functional allows the user to find a solution with sharp geoelectrical boundaries. An adaptive data weighting technique is implemented in the code.
Authors: Alexander Gribenko and Michael S. Zhdanov   
References:   
Hursán, G., andM. S. Zhdanov, 2002, Contraction integral equation method in three-dimensional electromagneticmodeling: Radio Science, 37 (6), 1089, doi:10.1029/2001RS002513.
Gribenko, A., and M. S. Zhdanov, 2007, Rigorous 3D inversion of marine CSEM data based on the integral equation method: Geophysics, 72, WA73.
Gribenko, A., and M. S. Zhdanov, 2011, Joint inversion of MT and MCSEM data in off-shore exploration: Proceedings of 2011 CEMI Annual Meeting.
Gribenko, A., L. Wan, and M. S. Zhdanov, 2010, Three-dimensional inversion of magnetotelluric data for complex resistivity: Proceedings of 2010 CEMI Annual Meeting, 269-294.
Portniaguine, O., and M. S. Zhdanov, 1999, Focusing geophysical inversion images: Geophysics, 64, 874-887.
Tikhonov, A. N., and V. Y. Arsenin, 1977, Solution of ill-posed problems: V. H. Winston and Sons.
Zhdanov, M. S., 2002, Geophysical inverse theory and regularization problems: Elsevier.
Zhdanov, M.S., 2009, Geophysical electromagnetic theory and methods: Elsevier
Zhdanov, M. S., A. Gribenko, and M. ˇCuma, 2007, Regularized focusing inversion of marine CSEM data using minimum vertical-support stabilizer: 77th Annual International Meeting, SEG, Expanded Abstracts, 579-583.

PF3D ver. 2011, Release March 2012. The PF3D ver. 2011 is a MATLAB software package for 3D modeling and inversion of potential field data which includes magnetic field, magnetic gradient tensor components, gravity field, and gravity gradient tensor components. The code is designed for 3D inversion of the data collected on a variable surface, including the option for joint inversion of the different gravity or magnetic field and tensor field components. For inversion, the code uses the approach known as the re-weighted regularized conjugant gradient method, or RRCG method, with focusing stabilizers to produce compact geophysical images. It also utilizes a technique to naturally impose model constraints by computing iterations in the space of logarithmic model parameters.
Authors: Martin Cuma and Michael S. Zhdanov   
References:   
    Portniaguine, O., and M. S. Zhdanov, 1999, Focusing geophysical inversion images: Geophysics, 64, 874-887.
    Zhdanov, M. S., 2002, Geophysical inverse theory and regularization problems: Elsevier.

GG3Dmigration ver. 2013, Release March 2014.The GG3Dmigration ver. 2014 is a MATLAB software package for migration of the gravity and/or gravity gradiometry data in order to image a 3D density distribution. The gravity and/or gravity gradiometry data can be collected on a variable surface. The major novel feature of the code is the ability to select an arbitrary combination of gravity field and gravity tensor components and migrate them jointly. The migration can be done on a large scale and within an arbitrary selected domain. The software package includes the source code, user manual and examples. Also, it includes a code to produce the cross-section image for a convenience. The software is easy to maintain and to use.
Authors: Le Wan and Michael S. Zhdanov
References: 
    Zhdanov, M. S., X. Liu, G. A. Wilson, and L. Wan, 2011, Potential field migration for rapid imaging of gravity gradiometry data: Geophysical Prospecting, 59, 1052--1071.

CauchyGrav3D ver. 2014, Release March 2015. The CauchyGrav3D ver. 2014 is a MATLAB software package for 3D modeling and inversion of gravity data caused by a density contrast interface model. The code uses a novel approach based on 3D analogs of Cauchy type integrals for the modeling and inversion of gravity and gravity gradiometry data caused by the density contrast model (Zhdanov, 1988; Cai and Zhdanov, 2014, 2015). The code can be used in Windows or Linux machine with MATLAB installed. For this release, the density contrast is assumed to be a given constant in the inversion. The code outputs the depth to basement. This package contains two main programs for forward modeling and inversion. The program Cauchy3DFWD is the program for forward modeling, while the program Cauchy3DInv is for inversion.
Authors: Hongzhu Cai and Michael S. Zhdanov
References: 
Cai, H., and M. S. Zhdanov, 2014, Modeling and inversion of magnetic anomalies caused by sediment-basement interface using 3D Cauchy-type integrals: IEEE Geoscience Remote Sensing and Letters, 12 (3), 477—481.
Cai, H., and M. S. Zhdanov, 2015, Application of Cauchy-type integrals in developing effective methods for depth-to-basement inversion of gravity and gravity gradiometry data: Geophysics, 80 (2).
Zhdanov, M. S., 1988, Integral transforms in geophysics: Springer-Verlag.


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