Dr. Doherty is the author of PEST and its supporting utility software. He is a self-employed consultant who also holds an honorary position as a professor with the National Centre for Groundwater Research and Training, Australia. He is an associated expert with SSP&A and has collaborated closely with SSP&A staff since 2001.
Dr. Doherty started his career as an exploration geophysicist, but then moved to environmental modelling. He has since worked in the government, private, and tertiary sectors. His research interests include the continued development of software and methodologies for solution of inverse problems using environmental models, quantification of model predictive uncertainty, and appropriate use of models in the decision-making. Much of his recent consulting work has involved assessment of water-use sustainability, and the assessment of the impact on regional groundwater systems of coal seam gas extraction. SSP&A staff have collaborated with Dr. Doherty on model development, training, and publication on advanced modeling techniques. Two SSP&A staff undertook their graduate studies under his tutelage.
EDUCATION
- PhD, Ci Physics, University of Queensland, 1987
- BSc, Geophysics, University of Queensland, 1975
AREAS OF EXPERTISE
- Groundwater Flow and Contaminant Transport Simulation
- Model Calibration and Uncertainty Analysis
- Development of Regional and Local Groundwater Models for Coal-Seam Gas-Impact Assessments
- Development, Documentation and Training on Utilities Linking Multiple Numerical Simulators with the Programs of the PEST and PEST++ Suites
- Supervision of Postgraduate Students Undertaking Research Into Improved Decision-Support Modeling
AWARDS AND HONORS
- NGWA Darcy Lecturer: 2019
- WRR editors’ choice award: 2011 (shared with other authors)
- NGWA M. King Hubbert Award: 2009
- University Medal: 1975
- H. C. Richards Prize (Geology): 1973
- W. H. Bryan Prize (Geology): 1972
More about PEST:
WATER RESOURCES SOFTWARE
2018 – 2020: Continual improvement of the PEST and PEST_HP suites. Continued development of utility software to expedite the use of these suite sin a variety of decision-support modeling contexts.
2019: Development of TS6PROC and OLPROC. The former is a time series process for use in conjunction with MODFLOW 6; the latter is a general model post-processor and PEST input dataset constructor.
2017: PWHISP_HP is a “PEST whisperer”. It reads files read and written by PEST_HP and, using a variety or metrics, judges the setup and performance of PEST_HP both during and after an inversion process that is being conducted under its supervision. It records its ruminations to a text output file; the information recorded on this file can assist a user in assessing current performance, and improving future performance, of PEST_HP.
2016 – 2017: PEST_HP — A version of PEST optimized for use in highly parallelized computing environments such as the cloud. This has proven itself to be more efficient than PEST or BEOPEST and provides superior accommodation of suboptimal model numerical behavior.
2013 – 2014: PEST — Continued development of PEST and associated utility support software, with focus on the use of complex models in conjunction with simple models or proxy models to assist in calibration and uncertainty analyses based on the former where model run times are large.
2012: PLPROC (“parameter list processor”) — This model is a pre-processor that uses a Python-like command-line syntax to manipulate model parameters, and to undertake spatial interpolation of model parameters. Functionality includes use of 2D and 3D radial basis functions for pilot point interpolation, as well as embedded functions in generalized model input template files.
2010: BEOPEST — In conjunction with Willem Shreuder of Principia Mathematica, a version of PEST named “BEOPEST” was developed to replace Parallel PEST. This software uses TCP/IP as a means of communication between master and model-running slaves. Hence model runs can be parallelized using cores on a user’s computer, on an office network, or around the world.
2009: Pareto Mode — A new mode of operation based on the exploration of the Pareto front was added to PEST. This software was designed for use in highly parameterized contexts where expert-based subjective judgments must be used in determining optimality of imposition of regularization constrains during calibration, and optimality of imposition of calibration constraints during predictive uncertainty analysis.
2007: Null Space Monte Carlo — This software required modifications to PEST and the development of a number of utility support software to allow rapid generation of multiple parameter realizations that, on the one hand, respect a user-specified stochastic distribution, while on the other hand provide a fit between model outputs and field data that are as good as that of the “calibrated model”.
2006: Improvements to PEST — These included improvements to its regularization of capabilities, new algorithms for accommodation of poor model performance with respect to derivatives calculation, improved recording of history of the calibration process, incorporation of the LSQR solver for highly parameterized systems, and parallelized versions of the CMA and SCE global inversion engines as calibration alternatives to PEST.
2005: Advanced Model Predictive Error Analysis — Based on theory published in a number of scientific journals (see below), utility software was developed to carry out fast and efficient model predictive error analysis as an adjunct to regularized inversion. This software allows rapid analysis of the uncertainty range of model parameters; and source terms and predictions that are compatible with a given suite of historical measurements of system state and with the known or inferred level of geological heterogeneity prevailing in a study area. This technology is unique to PEST.
2004: Advanced Regularization — In 2004, a unique hybrid regularization methodology known as “SVD-Assist” was added to PEST. This was supported by the addition of a number of new programs to the PEST utility suite. Use of SVD-Assist realizes great gains in the numerical stability of a regularized inverse problem, at the same time as it results in large efficiency gains.
2003: MICA — This model-independent Markov Chain Monte Carlo program was developed under contract with the U.S. Environmental Protection Agency for calculation of model predictive uncertainty in a Bayesian framework.
2002 – 2003: Improvements to PEST — These improvements include functionality for adaptive regularization, compressed data storage, and other devices to improve the use of PEST in highly parameterized contexts. They also include drivers that allow PEST to avoid entrapment in local minima during surface-water model calibration.
2001: TSPROC — TSPROC is a comprehensive time-series processor developed for use as an adjunct to PEST in the calibration of surface-water models on the basis of many different kinds of measured and/or processed data.
2001: Pilot Point Utilities — A number of programs were added to the Groundwater Data Utility Suite that facilitate the use of PEST in MODFLOW and MT3D spatial parameterization. Sophisticated, geostatistically-based, regularization conditions are introduced to the parameterization process, making use of PEST-ASP’s advanced regularization capabilities.
2000: MF2PEST — MF2PEST is a MODFLOW2000-to-PEST dataset translator, allowing use of PEST as an enhancement to MODFLOW. This is complemented by MODFLOW-ASP, an enhanced version of MODFLOW-2000 that includes a PEST interface, the ability to parameterize a model domain using pilot points, and better handling of drying/re-wetting conditions.
2000: PEST-ASP (“Advanced Spatial Parameterization”) — In late 2000, PEST was upgraded to include sophisticated regularization capabilities to enhance its use in the calibration of complex distributed-parameter models in heterogenous settings.
2000: PEST Interface to GMS Version 3.1 — This version was developed jointly with personnel from Brigham Young University.
1999: Composite IQQM/MODFLOW Model — MODFLOW96 was linked to IQQM, a basin-scale hydrologic and water- management model developed by the New South Wales Department of Land and Water Conservation.
1999: PEST2000 — A major PEST upgrade including the addition of nonlinear predictive uncertainty analysis functionality.
1999: PEST Surface-Water Utilities — A suite of software tools developed to enhance the use of PEST in the calibration of surface-water models.
1998: Utilities for use of PEST with HSPF — Written on behalf of the U.S. Environmental Protection Agency.
1998: PEST98 — A major upgrade for PEST, including the addition of user-intervention functionality.
1997: PEST GMS Utilities — A set of programs that facilitates the use of PEST with the popular “Groundwater Modelling System” developed by Brigham Young University.
1997: Parallel PEST — A version of PEST that dramatically reduces optimization time by undertaking simultaneous model runs across a PC network.
1996: SENSAN: A Model-Independent Sensitivity Analyzer — Uses the PEST model interface protocol for the construction of a model-independent sensitivity analyzer.
1995: Groundwater Data Utilities — A suite of programs to undertake certain aspects of groundwater model pre- and post-processing, and to facilitate data transfer between MODFLOW, MT3D, MICROFEM, PEST, SURFER, GIS and various visualization/display packages.
1994: PEST Utilities for MODFLOW/MT3D Parameter Estimation — A set of utilities to facilitate the use of PEST with MODFLOW and MT3D.
1994: PEST —A model-independent nonlinear parameter estimator that is presently used worldwide for the calibration of hydrological and other engineering/scientific models, and for interpretation of field data based on mathematical inversion. PEST is supported by a number of commercial modelling graphical-user interfaces including FEFLOW, Visual MODFLOW, Groundwater Vistas, GMS, PMWIN and BASINS.
1991: MODINV — A MODFLOW-specific parameter estimator, MODINV was used at over 250 sites worldwide.
BOOKS
Doherty, J., 2015. Calibration and uncertainty analysis for complex environmental models. Published by Watermark Numerical Computing, Brisbane, Australia. 227pp. ISBN: 978-0-9943786-0-6. Downloadable from www.pesthomepage.org.
JOURNAL PUBLICATIONS
Khambhammettu, P.K., Renard, P. and J. Doherty, 2020. The Traveling Pilot Point method. A novel approach to parameterize the inverse problem for categorical fields. Accepted for publication in Advances in Water Resources.
Doherty, J. and C. Moore, 2019. Decision Support Modeling: Data Assimilation, Uncertainty Quantification and Strategic Abstraction. Groundwater. doi: 10.1111/gwat.12969
Fang, Q., Ma, L., Harmel, R. D., Yu, Q., Sima, M. W., Bartling, P. N. S., Malone, R. W., Nolan, B. T. and J. Doherty, 2019. Uncertainty of crop model calibration with irrigation treatments using PEST optimization algorithm. Agronomy. Accepted for publication.
Gianni, G., Doherty, J. and P. Brunner, 2019. Conceptualization and Calibration of Anisotropic Alluvial Systems: Pitfalls and Biases. Groundwater, v. 57, no. 3, pp. 409-419.
Saide, A.J., Rathi, B., Prommer, H., Welter, D. and J. Doherty, 2019. Using heuristic multi-objective optimization for quantifying predictive uncertainty associated with groundwater flow and reactive transport models. Journal of Hydrology, v. 577.
Burrows, W. and J. Doherty, 2016. Gradient-Based Model Calibration with Proxy-Model Assistance. Journal of Hydrology, v. 533, pp. 114-127.
Lotti, F. and J. Doherty, 2016. The role of numerical models in environmental decision-making. Acque Sotterraee – Italian Journal of Groundwater. AS18-23, 63-64.
White, J.T., M.N. Fienen, and J.E. Doherty, 2016. pyEMU: A Python Framework for Environmental Model Uncertainty Analysis. Environ Modell Software, v. 85, pp. 217-228.
Doherty, J. and R. Vogwill, 2015. Models, Decision-Making and Science. Solving the Groundwater Challenges of the 21st Century. Vogwill, R. ed. CRC Press.
Herckenrath, D., J. Doherty, and W. Panday, 2015. A Methodology for Assessing the Impact of Coal Bed Methane Extraction on Regional Groundwater Systems. Journal of Hydrology, 523 (2015), pp, 587-601.
Moore, C.R., J.E. Doherty, S. Howell, and L. Erriah, 2015. Some Challenges Posed by Coal Bed Methane Regional Assessment Modelling. Ground Water, v. 53, no.5, pp. 737-747.
Welter, D.E., J.T. White, J.E. Doherty, and R.J. Hunt, 2015. PEST++ Version 3. A Parameter ESTimation and Uncertainty Analysis Software Suite Optimized for Large Environmental Models. U.S. Geological Survey Techniques and Methods Report. Book 7, Section C, Chapter 12.
Burrows, W. and J. Doherty, 2014. Efficient Calibration/Uncertainty Analysis Using Paired Complex/Surrogate Models. Groundwater, v. 53, no. 4, pp. 531-541.
Nolan, B.T., R.W. Malone, R.W., J. Doherty, J.E. Barbash, L. Ma, D.L. Shner, 2014. Data Worth and Prediction Uncertainty for Pesticide Transport Fate in Nebraska and Maryland, USA. Pest Management Science. doi: 10.1002/ps.3875
Rossi, P.K., P. Ala-aho, J. Doherty, and B. Klove, 2014. Impact of Peatland Draining and Restoration on Esker Groundwater Resources—Modelling Future Scenarios for Management. Hydrogeology Journal. doi: 10.1007/s10040-014-1127-z
Schilling, O., P. Brunner, J. Doherty, Y. Pengnian, W., Haijing, and W. Kinzelbach, 2014. The Worth of Tree Ring Data in Modelling the Interaction Between Surface Water, Groundwater and Vegetation on the lower Tarim River. Journal or Hydrology. Accepted for publication: in press.
Sepulveda, N., and J. Doherty, 2014. Uncertainty Analysis of a Groundwater Flow model in East-Central Florida. Groundwater, v. 53, no. 3, pp. 464-474.
White, J.T., J.E. Doherty, and J.D. Hughes, 2014. Quantifying the Predictive Consequences of Model Error with Linear Subspace Analysis. Water Resources Research, v. 50, no. 2, pp. 1152-1173. doi: 10.1002/2013WR014767
Doherty, J. and C.T. Simmons, 2013. Groundwater Modelling in Decision Support: Reflections on a Unified Conceptual Framework. Hydrogeology Journal, 21: pp. 1531–1537.
Fienen, M.M., M. D’Oria, J. Doherty, and R. Hunt, 2013. Approaches to Highly Parameterized Inversion: bgaPEST, a Bayesian Geostatistical Approach Implemented with PEST — Documentation and Instructions. USGS Techniques and Methods Report 7-C9. Groundwater Resources Program.
Watson, T.A., J.E. Doherty, and S. Christensen, 2013. Parameter and Predictive Outcomes of Model Simplification. Water Resources. Research, v. 49, no. 7, pp. 3952-3977. doi: 10.1002/wrcr.20145
Brunner, P., J. Doherty, and C.T. Simmons, 2012. Uncertainty Assessment and Implications for Data Acquisition in Support of Integrated Hydrologic Models. Water Resources Research. doi: 10.1029/2011WR011342
Muffels, C.T., W.A. Schreüder, J.E. Doherty, M. Karanovic, M.J. Tonkin, R.J. Hunt, and D.E. Welter, 2012. Approaches in Highly Parameterized Inversion — GENIE, a General Model-Independent TCP/IP-run Manager. U.S. Geological Survey Techniques and Methods, Book 7, Section C6, 26 p.
Welter, D.E., J.E. Doherty, R.J. Hunt, C.T. Muffels, M.J. Tonkin, and W.A. Schreüder, 2012. Approaches in Highly Parameterized Inversion: PEST++, a Parameter ESTimation Code Optimized for Large Environmental Models. U.S. Geological Survey Techniques and Methods, Book 7, Section C5, 47 p.
Wilsnack, M.M., J.E. Doherty, and D.E. Welter, 2012. A Pareto-based Methodology for Calibration and Uncertainty Analysis of Gated Culvert Flows. Journal of Irrigation and Drainage Engineering (ASCE), v. 138, no. 7, pp. 675-684. doi: 10.1061/(ASCE)IR.1943-4774.0000431
Doherty, J., 2011. Modeling: Picture Perfect or Abstract Art? Ground Water, v.49, no. 4, pp. 455-456.
Doherty, J. and S. Christensen, 2011. Use of Paired Simple and Complex Models in Reducing Predictive Bias and Quantifying Uncertainty. Water Resources Research (featured article). doi: 10.1029/2011WR010763. WRR
Herckenrath, D., C.D. Langevin, and J. Doherty, 2011. Predictive Uncertainty Analysis of a Saltwater Intrusion Model Using Null-space Monte Carlo. Water Resources Research, v. 47. W05504. doi:10.1029/2010WR009342
Hunt, R.J. and J. Doherty, 2011. Interesting or Important? Resetting the Balance of Theory and Application. Guest editorial in Ground Water, v. 49, no. 3, p. 301.
Doherty, J., M.N. Fienen, and R.J. Hunt, 2010. Approaches to Highly Parameterized Inversion: Pilot-Point Theory, Guidelines and Research Directions. USGS Scientific Investigations Report 2010-5169. http://pubs.usgs.gov/sir/2010/5168/
Doherty, J. and D. Welter, 2010. A Short Exploration of Structural Noise. Water Resources. Research (featured article), v. 46, W05525. doi: 10.1029/2009WR008377
Doherty, J., and R.J. Hunt, 2010. Response to Comment on “Two Statistics for Evaluating Parameter Identifiability and Error Reduction.” Journal of Hydrology, v. 380, pp. 489-496.
Doherty, J., and R.J. Hunt, 2010. Approaches to Highly Parameterized Inversion: A Guide to Using PEST for Groundwater-Model Calibration. USGS Scientific Investigations Report 2010-5169. http://pubs.usgs.gov/sir/2010/5169/
Doherty, J., R.J. Hunt, and M.J. Tonkin, 2010. Approaches to Highly Parameterized Inversion: A Guide to using PEST for Model Parameter and Predictive Uncertainty Analysis. USGS Scientific Investigations Report 2010-5211. http://pubs.usgs.gov/sir/2010/5211/
Dausman, A.M., J. Doherty, C.D. Langevin, and M.C. Sukop, 2010. Quantifying Data Worth toward Reducing Predictive Uncertainty. Groundwater, v.48, no. 5, pp. 729-740.
Fienen, M.N., J.E. Doherty, R.J.., Hunt, and H.W. Reeves, 2010. Using Prediction Uncertainty Analysis to Design Hydrologic Monitoring Networks: Example Applications from the Great Lakes Water Authority Availability Pilot Project. USGS Scientific Investigations Report 2010-5159, 44 p.
Hunt, R.J., J. Luchette, W.A. Shreuder, J. Rumbaugh, J. Doherty, M.J. Tonkin, and D. Rumbaugh, 2010. Using the Cloud to Replenish Parched Groundwater Modeling Efforts. Rapid Communication for Ground Water. doi: 10.1111/j.1745-6584.2010.00699
Keating, E., J. Doherty, J.A. Vrugt, and Q. Kang, 2010. Optimization and Uncertainty Assessment of Strongly Nonlinear Groundwater Models with High Parameterization Dimensionality. Water Resources Research, v. 46, W10517, 18 p. doi: 10.1029/2009WR008584 (Winner of the Water Resources Research Editor’s Choice Award for 2010).
Moore, C., T. Wöhling, and J. Doherty, 2010. Efficient regularization and uncertainty analysis using a global optimization methodology. Water Resources Research, v. 46, W08527. doi: 10.1029/2009WR008627
Doherty, J. and R.J. Hunt, 2009. Two Statistics for Evaluating Parameter Identifiability and Error Reduction. Journal of Hydrology, v. 366, pp. 119-127.
Dausman, A.M, J. Doherty, C.D. Langevin, J. and Dixon, 2009. Hypothesis Testing of Buoyant Plume Migration Using a Highly Parameterized Variable-Density Groundwater Model. Hydrogeology Journal. doi: 10.1007/s10040-009-0511-6
Ellis, R.J., J. Doherty, R.D. Searle, and K. Moodie, 2009. Applying PEST (parameter ESTimation) to Improve Parameter Estimation and Uncertainty Analysis in WaterCAST Models. in RS Anderssen, R.S., R.D. Braddock and L.T. Newham, eds., 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation, Cairns, Australia, pp. 3158-3164.
James, S.C., J. Doherty, J. and A.-A. Eddebarh, 2009. Post-calibration Uncertainty Analysis: Yucca Mountain, Nevada, USA. Ground Water, v. 47, no. 6, pp. 851-869.
Tonkin M.J., and J. Doherty, 2009. Calibration-Constrained Monte Carlo Analysis of Highly Parameterized Models Using Subspace Techniques. Water Resources Research, v. 45, W00B10. doi: 10.1029/2007WR006678
Doherty, J., 2008. Model Predictive Error: How it Arises and How it can be Accommodated. in Proceedings of MODELCARE 2007: Calibration and Reliability in Ground Water Modelling: Credibility of Modelling. Copenhagen, Denmark. IAHS Publishers.
Banta, E.R., M.C. Hill, E. Poeter, J. Doherty, and J. Babendreier, 2008. Building Model Analysis Applications with the Joint Universal Parameter Identification and Evaluation of Reliability (JUPITER) API. Computers & Geosciences, v. 34 (2008), pp. 310–319.
Christensen S. and J. Doherty, 2008. Using Many Pilot Points and Singular Value Decomposition in Groundwater Model Calibration. in Proceedings of MODELCARE 2007: Calibration and Reliability in Ground Water Modelling: Credibility of Modelling. Copenhagen, Denmark. IAHS Publishers.
Christensen, S. and J. Doherty, 2008. Predictive Error Dependencies when using Pilot Points and Singular Value Decomposition in Groundwater Model Calibration. Advances in Water Resources, v. 31, Issue 4 (April), pp. 674-700.
Hunt, R.J., J. Doherty, and M.J. Tonkin, 2007. Are Models too Simple? Arguments for Increased Parameterization. Ground Water, v. 45, no. 3, pp. 254–262.
Eddebarh, A.-A, S.C. James, J. Doherty, G.A. Zyvoloski, and B.W. Arnold, 2007. A New Saturated Zone Site-Scale Model for Yucca Mountain. EOS Transactions, American Geophysical Union, v. 88, no. 52, H21C-0706.
Gallagher, M. and J. Doherty, 2007. Predictive Error Analysis for a Water Resource Management Model. Journal of Hydrology, v/ 34, no. 3-4, pp. 513-533.
Gallagher, M.R., and J. Doherty, 2007. Parameter Interdependence and Uncertainty Induced by Lumping in a Hydrologic Model. Water Resources Research. v.43, W05421. doi: 10.1029/2006WR005347
Kim, S.M., B.L. Benham, K.M. Brannan, R.W. Zeckoski, and J. Doherty, 2007. Comparison of Hydrologic Calibration of HSPF Using Automatic and Manual Methods. Water Resources Research, v. 43, W01402. doi: 10.1029/2006WR004883
Tonkin, M., J. Doherty, and C. Moore, 2007. Efficient Nonlinear Predictive Error Variance for Highly Parameterized Models. Water Resources Research, v. 43, W07429. doi: 10.1029/2006WR005348
Doherty, J. and B. Skahill, 2006. An Advanced Regularization Methodology for use in Watershed Model Calibration. Journal of Hydrology, v. 327, no. 3-4, pp. 564-577.
Banta, E.R., E.P. Poeter, J. Doherty, and M.C. Hill, 2006. JUPITER: Joint Universal Parameter Identification and Evaluation of Reliability — An Application Programming Interface (API) for Model Analysis. Techniques and Methods 6-E1. U.S. Geological Survey, Denver, CO.
Gallagher, M.R. and J. Doherty, 2006. Parameter Estimation and Uncertainty Analysis for a Watershed Model. Environmental Modelling and Software, v. 22, 1000-1020.
Moore, C. and J. Doherty, 2006. The Cost of Uniqueness in Groundwater Model Calibration. Advances in Water Resources, v. 29, Issue 4 (April), pp. 605–623.
Skahill, B. and J. Doherty, 2006. Efficient Accommodation of Local Minima in Watershed Model Calibration. Journal of Hydrology, v. 329, no. 1-2, pp122-139.
Moore, C. and J. Doherty, 2005. The Role of the Calibration Process in Reducing Model Predictive Error. Water Resources Research, v. 41, no 5, W05050.
Tonkin, M. and J. Doherty, 2005. A Hybrid Regularized Inversion Methodology for Highly Parameterized Models. Water Resources Research, v. 41, W10412. doi: 10.1029/2005WR003995
Doherty, J., 2003. Groundwater Model Calibration Using Pilot Points and Regularization. Ground Water, v. 41, no. 2, pp. 170-177.
Doherty, J. and J.M. Johnston, 2003. Methodologies for Calibration and Predictive Analysis of a Watershed Model. Journal of the American Water Resources Association, v. 39, no. 2, pp. 251-265.
McKenna, S.A., J. Doherty, and D.B. Hart, 2003. Non-Uniqueness of Inverse Transmissivity Field Calibration and Predictive Transport Modeling. Journal of Hydrology, v. 281, no. 4, pp. 265-282.
Tonkin, M.J., M.C. Hill, and J. Doherty, 2003. MODFLOW-2000, the U.S. Geological Survey Modular Ground-Water Model — Documentation of MOD-PREDICT for Predictions, Prediction Sensitivity Analysis, and Enhanced Analysis of Model Fit. U.S. Geological Survey Open-File Report 03-385, 69 p.
Doherty, J., 2001. A Methodology for Preventing the Occurrence of Dry Cells in a Three-Dimensional MODFLOW Model. Ground Water, v. 39.
Doherty, J., 1990. The Interpretation of Pump-Test Data from a Disused Underground Mine. Journal of Hydrology, v. 114, pp. 109-123.
Doherty, J., 1988. EM modelling Using Surface Integral Equations. Geophysical Prospecting, v. 36, no. 6.
Doherty, J., 1987. The Use of Surface Integral Equations in Modelling for Electrical Prospecting. PhD Thesis, University of Queensland, Australia.
Dixon, O. and J. Doherty, 1977. New Interpretation Methods for IP Soundings. ASEG Bulletin, v. 8, no. 3, pp. 65-74.