تحلیل وابستگی و همبستگی پارامترهای مدل کول-کول در توموگرافی قطبش القایی طیفی با استفاده از استنباط بیزین

Bérubé, C. L., Chouteau, M., Shamsipou, M., Enkin, P., & Olivo, G. R. (2017). Bayesian inference of spectral induced polarization parameters for laboratory complex resistivity measurements of rocks and soils. Computers and Geosciences, 105, 51-64.

Binley, A., & Slater, L. (2020). Resistivity and induced polarization: Theory and applications to the near-surface earth. Cambridge University Press.

Binley, A., Slater, L. D., Fukes, M., & Cassiani, G. (2005). Relationship between spectral induced polarization and hydraulic properties of saturated and unsaturated sandstone. Water Resources Research, 41(12), W12417.

Blaschek, R., Hördt, A., & Kemna, A. (2008). A new sensitivity-controlled focusing regularization scheme for the inversion of induced polarization data based on the minimum gradient support. Geophysics, 73(2), F45–F54.

Boadu, F. K., & Seabrook, B. (2000). Estimating hydraulic conductivity and porosity of soils from spectral electrical response measurements. Journal of Environmental and Engineering Geophysics, 5(1), 1–9.

Chen, J., Kemna, A., & Hubbard, S. (2008). A comparison between Gauss-Newton and Markov-chain Monte Carlo-based methods for inverting spectral induced-polarization data for Cole-Cole parameters. Geophysics, 73, F247-F259.

Chib, S., & Greenberg, E. (1995). Understanding the Metropolis-Hastings Algorithm. The American Statistician, 49 (4), 327–335.

Cole, Kenneth S., Cole, & Robert H. (1941). Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics. The Journal of Chemical Physics, 9(4), 341-351.

De Pasquale, G., & Linde, N., (2017). On Structure-Based Priors in Bayesian Geophysical Inversion. Geophysical Journal International, 208, 1342–1358.

Dey, A., & Morrison, M. F. (1979). Resistivity modeling for arbitrarily shaped two-dimensional structures. Geophysical Prospecting, 27, 106-136.

Fiandaca, G., Auken, E., Gazoty, A., & Christiansen, A. V. (2012). Time-domain induced polarization: Full-decay forward modeling and 1D laterally constrained inversion of Cole-Cole parameters. Geophysics, 77, E213-E225.

Fiandaca, G., Madsen, L., & Maurya, P. (2017). Re-parameterization of the Cole-Cole Model for Improved Spectral Inversion of Induced Polarization Data. Near Surface Geophysics. 2018, 16, 385–399.

Fiandaca, G., Ramm, J., Binley, A., Gazoty, A., Christiansen, A. V., & Auken, E. (2013). Resolving spectral information from time domain induced polarization data through 2-D inversion. Geophysical Journal International, 192, 631-646.

Foreman-Mackey, D., Farr, W. M., Sinha, M., Archibald, A. M., Hogg, D. W., Sanders, J. S., Zuntz, J., Williams, P. K. G., Nelson, A. R. J., de Val-Borro, M., Erhardt, T., Pashchenko, I., & Abril Pla, O. A. (2019). emcee v3: A Python ensemble sampling toolkit for affine-invariant MCMC. Journal of Open Source Software, 4(43), 1864.

Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. (2013). emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific, 125(925), 306.

Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2014). Bayesian data analysis. 3rd ed. Chapman and Hall.

Gelman, A., Roberts, G. O., & Gilks, W. R. (1994). Bayesian Statistics 5, Oxford University Press, 599–607.

Ghanati, R., & Müller-Petke, M. (2021). A homotopy continuation inversion of geoelectrical sounding data. Journal of Applied Geophysics, 191, p.104356.

Ghorbani, A., Camerlynck, C., Florsch, N., Cosenza, P., & Revil, A. (2007). Bayesian inference of the Cole-Cole parameters from time-and frequency-domain induced polarization. Geophysical Prospecting, 55, 589–605.

Goodman, J., & Weare, J. (2010). Ensemble samplers with affine invariance. Communications in Applied Mathematics and Computational Science, 5, 65–80.

Günther, T., & Martin, T. (2016). Spectral two-dimensional inversion of frequency-domain induced polarisation data from a mining slag heap. Journal of Applied Geophysics, 135, 436-448.

Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97–109.

Hoffman, M. D., & Gelman, A. (2014). The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15(1), 1593–1623.

Jaggar, S. R., & Fell, P. A. (1988). Forward and inverse Cole–Cole modelling in the analysis of frequency domain electrical impedance data. Exploration Geophysics, 19, 463–470.

Jardani, A., Revil, A., & Dupont, J. P. (2013). Stochastic joint inversion of hydrogeophysical data for salt tracer test monitoring and hydraulic conductivity imaging. Advances in Water Resources, 52, 62-77.

Johnson, T. C., & Thomle, J. (2018). 3-D decoupled inversion of complex conductivity data in the real number domain. Geophysical Journal International, 212, 284–296.

Keery, J., Binley, A., Elshenawy, A., & Clifford, J. (2012). Markov-chain Monte Carlo estimation of distributed Debye relaxations in spectral induced polarization. Geophysics, 77(2), E159-E170.

Kemna, A., Binley, A., & Slater, L. (2004). Crosshole IP imaging for engineering and environmental applications. Geophysics, 69, 97–107.

Luo, Y., & Zhang, G., (1998). Theory and application of spectral induced polarization. SEG, Geophysical Monograph Series, no. 8.

MacKay, D. (2003). Information Theory, Inference, and Learning Algorithms. Cambridge University Press, Cambridge.

Madsen, L. M., Fiandaca, G., Auken, E., & Christiansen, A. V. (2017). Time-domain induced polarization – an analysis of Cole–Cole parameter resolution and correlation using Markov Chain Monte Carlo inversion. Geophysical Journal International, 211, 1341-1353.

Metropolis, N., Rosenbluth, M. N., Rosenbluth, A. W., & Teller, A. H. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1987–1092.

Mosegaard, K., & Tarantola, A. (1995). Monte Carlo sampling of solutions to inverse problems. Journal of Geophysical Research, Atmospheres, 100, 12431–12448.

Pelton, W. H., Ward, S. H., Hallof, P. G., Sill, W. R., & Nelson, P. H. (1978). Mineral discrimination and removal of inductive coupling with multifrequency IP. Geophysics, 43(3), 588–609.

Roudsari, M. S., Ghanati, R., & Bérubé, C. L. (2024). Spectral induced polarization tomography inversion: Hybridizing homotopic continuation with Bayesian inversion. Geophysics, 89(5), 1-63.

Rücker, C., Günther, T., & Spitzer, K. (2006). Three-dimensional modeling and inversion of DC resistivity data incorporating topography—part I: modeling. Geophysical Journal International, 166, 495–505.

Rücker, C., Günther, T., & Wagner, F. M. (2017). pyGIMLi: An open-source library for modelling and inversion in geophysics. Computers & Geosciences, 109, 106–123.

Sambridge, M., & Mosegaard, K. (2002) Monte Carlo methods in geophysical inverse problems. Reviews of Geophysics, 40(3), 3.13.29

Tarantola, A. (2004). Inverse Problem Theory and Methods for Model Parameter Estimation. Society for Industrial and Applied Mathematics, USA.

Vanhala, H. (1997). Mapping oil-contaminated sand and till with the spectral induced polarization (SIP) method. Geophysical Prospecting, 45(2), 303326.

Vrügt, J. A. (2016). Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation. Environmental Modelling and Software, 75, 273316.

Weller, A., & Slater, L. (2023). Ambiguity in induced polarization time constants and the advantage of the Pelton model, Geophysics, 87(6), E393E399.

Weller, A., M. Seichter, & Kampke, A. (1996). Induced-polarization modelling using complex electrical conductivities, Geophysical Journal International, 127, 387398,

Wohling, T., & Vrügt, J. A. (2011). Multiresponse multilayer vadose zone model calibration using Markov chain Monte Carlo simulation and field water retention data. Water Resources Research, 47, 19.