Software

**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.

**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.