Tomography and Inverse Theory References

 

I have compiled a list of references pertaining to travel time and electrical resistivity tomography and the inverse problem. Some of these references are for developing the forward model, for example, Vidale, 1990. Others look at different methods to solve the tomography problem. Several references are about developing resolution matrices from solvers that do not compute the matrix inverse. I hope that these references will provide a fairly comprehensive list for people who wish to learn about tomography and inverse theory using a geophysical approach. At the very least, this list provides a starting point.

 

Caveat Emptor:

I do not distribute tomography software. The codes that I use are commercial or I have permission to use specific tomography codes by arrangement with the authors. I suggest that you contact the authors of the listed papers to determine the availability of their codes. Daryl Tweeton of GeoTom, LLC, has several tomography packages available, such as GeoTomCG. You can contact him through e-mail or via telephone at (612) 423-3838.

 

 

Aki, K. and P. G. Richards, Quantitative Seismology: Theory and practice, W. H. Freeman, New York, chap. 12, 1980.

Aki, K. and W. H. K. Lee, Determination of three-dimensional velocity anomalies under a seismic array using first P arrival times from local earthquakes, I, A homogeneous initial model, Journal of Geophysical Research, 81, 4381-4399-296, 1976.

Aki, K., A. Christoffersson, and E. S. Huesbye, Determination of the three-dimensional structure of the lithosphere, Journal of Geophysical Research, 82, 277-296, 1977.

Aldridge, D. F., and D. W., Oldenburg, D. W., Two-dimensional tomographic inversion with finite-difference traveltimes, Journal of Seismic Exploration, 2, 257-274, 1993.

Alumbaugh, D. L., and G. A. Newman, Image appraisal for 2-D and 3-D electromagnetic inversion, Geophysics, 65: 1455-1467, 2000.

Ammon, C. J., and J. E. Vidale, Tomography without rays, Seismological Society of America Bulletin, 83, 509-528, 1993.

Backus, G. E. and J. F. Gilbert, Numerical application of a formalism for geophysical inverse problems, Geophysical Journal of the Royal Astronomical Society, 13, 247-276, 1967.

Backus, G. E. and J. F. Gilbert, The resolving power of gross earth data, Geophysical Journal of the Royal Astronomical Society, 16, 169-205, 1968.

Backus, G. E. and J. F. Gilbert, Uniqueness in the inversion of gross Earth data, Philosophical Transactions of the Royal Society of London, Series A, 266, 123-192, 1970.

Benz, J. M., B. A. Chouet, P. B. Dawson, J. C. Lahr, R. A. Page, and J. A. Hole, Three-dimensional P and S wave velocity structure of Redoubt Volcano, Alaska, Journal of Geophysical Research, 101, 8111-8128, 1996.

Berryman, J. G., Fermat's principle and nonlinear traveltime tomography, Physical Review Letters, 62, 2953-2956, 1989.

Berryman, J. G., Tomographic resolution without singular value decomposition, in S. Hassanzadeh (ed.), Mathematical Methods in Geophysical Imaging II, Proceedings of SPIE, The International Society for Optical Engineering, 2301, 2-13, 1994.

Berryman, J. G., Computing tomographic resolution matrices using Arnoldi's iterative inversion algorithm, Stanford Exploration Project, 52, 173-185, 1997.

Berryman, J. G., Resolution for Lanczos and Paige-Saunders inverses in tomography, Stanford Exploration Project, 12 p., 1993.

Berryman, J. G., Fermat's Principle and nonlinear traveltime tomography, Physical Review Letters, 62, 2953-2956, 1989.

Berryman, J. G., Constraints on minimum model variance for seismic traveltime tomography, Geophysical Journal International, 119, 689-692, 1994.

Berryman, J. G., Weighted least-squares criteria for seismic traveltime tomography, IEEE Transactions on Geoscience and Remote Sensing, 27, 302-309, 1989.

Berryman, J. G., Nonlinear least squares and regularization, Stanford Exploration Project, 7 p., 1996.

Berryman, J. G., Resolution of iterative inversion methods using partial renormalization, Lecture Notes.

Berryman, J. G., Lecture Notes on Nonlinear Inversion and Tomography, 1991.

Binley, A., P. Winship, R. Middleton, M. Pokar, and J. West, High-resolution characterization of vadose zone dynamics using cross-borehole radar, Water Resources Research, 37, 2639-2652, 2001.

Bishop, T. N., K. P. Bube, R. T. Cutler, R. T. Langan, P. L. Love, J. R. Resnick, R. T. Shuey, D. A. Spindler, and H. W. Wyld, Tomographic determination of velocity and depth in laterally varying media, Geophysics, 50, 903-923, 1985.

Bois, P., M. L. Porte, M. Lavergne, and G. Thomas, Well-to-well seismic measurements, Geophysics, 37, 471-480, 1972.

Bording, R. P., A. Gersztenkorn, L. R. Lines, J. A. Scales, and S. Treitel, Applications of seismic travel-time tomography, Geophysical Journal of the Royal Astronomical Society, 90, 285-303, 1987.

Bregman, N. D., R. C. Bailey, and C. H. Chapman, Crosshole seismic tomography, Geophysics, 54, 200-215, 1989.

Bregman, N. D., C. H. Chapman, and R. C. Bailey, Travel time and amplitude analysis in seismic tomography, Journal of Geophysical Research, 94, 7577-7587, 1989.

Bube, K. P., and R. T. Langan, Hybrid l1/l2 minimization with applications to tomography, Geophysics, 62, 1183-1195, 1997.

Chen, J., S. Hubbard, and Y. Rubin, Estimating the hydraulic conductivity at the South Oyster Site from geophysical tomographic data using Bayesian techniques based on the normal linear regression model, Water Resource Research, 37, 1603-1613, 2001.

Claerbout, J. and F. Muir, Robust modeling with erratic data, Geophysics, 38, 826-844, 1973.

Constable, S., R. Parker, and C. Constable, Occam's inversion: a practical algorithm for generating smooth models from electromagnetic sounding data, Geophysics, 52, 289-300, 1987.

Daily, W., Underground oil-shale retort monitoring using geotomography, Geophysics, 49, 1701-1707, 1984.

Daily, W. and J. Lytle, Geophysical tomography, Journal of Geomagnetism and Geoelectricity, 35, 423-442, 1983.

Daily, W. and E. Owen, Cross-borehole resistivity tomography, Geophysics, 56, 1228-1235, 1991.

Daily, W. D., A. L. Ramirez, In situ porosity distribution using geophysical tomography, Geophysical Research Letters, 11, 614-616, 1984.

Daily, W. D., A. L. Ramirez, D. J. LaBrecque, and J. Nitao, Electrical resistivity tomography of vadose water movement, Water Resource Research, 28, 1429-1442, 1992.

Daily, W., A. Ramirez, and R. Johnson, Electrical impedance tomography of a perchloroethelyne release, Journal of Environmental and Engineering Geophysics, 2, 189-201, 1998.

Day-Lewis, F. D., J. M. Harris, and S. M. Gorelick, Time-lapse inversion of crosswell radar data, Geophysics, 67, 1740-1752, 2002.

Deal, M. M. and G. Nolet, Comment on "Estimation of resolution and covariance for large matrix inversions" by J. Zhang and G. A. McMechan, Geophysical Journal International, 127, 245-250, 1996.

Deal, M. M. and G. Nolet, Nullspace shuttles, Geophysical Journal International, 124, 372-380, 1996.

Delprat-Jannaud, F. and P. Lailly, Ill-posed and well-posed formulations of the reflection traveltime tomography problem, Journal of Geophysical Research, 97, 19827-19844, 1992.

Devaney, A. J., Geophysical diffraction tomography, IEEE Transactions on Geoscience and Remote Sensing, 22, 3-13, 1984.

Dines, K. A. and R. J. Lytle, Computerized geophysical tomography, Proceedings of the IEEE, 67, 1065-01073, 1979.

Dobroka, M., L. Dresen, C. Gelbke, and H. Rueter, Tomographic inversion of normalized data: double-trace tomography algorithms, Geophysical Prospecting, 40, 1-14, 1992.

Efron, B., Bootstrap methods: Another look at the jackknife, The Annals of Statistics, 7, 1-26, 1979.

Efron, B., The Jackknife, the Bootstrap, and Other Resampling Plans, SIAM monograph, 38, 1982.

Efron, B. and G. Gong, A leisurely look at the Bootstrap, the Jackknife, and Cross-Validation, The American Statistician, 37, 36-48, 1983.

Ellefsen, K. J., J. E. Kibler, P. A. Hsieh, and A. M. Shapiro, Crosswell seismic tomography t the USGS Fractured Rock Research Site - Data collection, data processing and tomograms, U. S. Geological Survey Open-File Report 98-510, 1998.

Ellefsen, K. J., P. A. Hsieh, and A. M. Shapiro, Crosswell seismic investigation of hydraulically conductive, fractured bedrock near Mirror Lake, New Hampshire, Journal of Applied Geophysics, 50, 299-317, 2002.

Eppstein, M. J. and D. E. Dougherty, Simultaneous estimation of transmissivity values and zonation, Water Resources Research, 32, 3321-3336, 1996.

Eppstein, M. J. and D. E. Dougherty, Efficient three-dimensional data inversion: Soil characterization and moisture monitoring from cross-well ground-penetrating radar at a Vermont test site, Water Resources Research, 34, 1889-1900, 1998.

Eppstein, M. J. and D. E. Dougherty, Optimal 3-d traveltime tomography, Geophysics, 63, 1053-1061, 1998.

Friedel, M. J., D. R. Tweeton, J. J. Jackson, J. A. Jessop, and C. L. Cumerlato, Mining applications of seismic tomography, Proceedings of Society of Exploration Geophysicists, New Orleans, LA, 1992.

Gelbke, C., F. Miranda, and G. Sattel, Results of a seismic transmission tomography survey at the Grimsel Rock Laboratory, Log Analyst, 30, 243-260, 1986.

Gersztenkorn, A., J. B. Bednar, and L. R. Lines, Robust iterative inversion for the one-dimensional acoustic wave equation, Geophysics, 51, 357-368, 1986.

Gersztenkorn, A. and J. A. Scales, Smoothing seismic tomograms with alpha-trimmed means, Geophysical Journal, 92, 67-72, 1988.

Gheshlagni, F. and J. C. Santamarina, Data pre-processing in cross-hole geotomography, Journal of Environmental and Engineering Geophysics, 3, 41-47, 1998.

Gouveia, W. and J. A. Scales, Resolution of seismic waveform inversion: Bayes versus Occam, Inverse Problems, 13, 323-349, 1997.

Gouveia, W. and J. A. Scales, Bayesian seismic waveform inversion: Parameter estimation and uncertainty analysis, Journal of Geophysical Research, 103, 2759-2779, 1998.

Hansen, P. C., Regularization tools, Numerical Algorithms, 6, 1-35, 1994.

Hole, J. A., Nonlinear high-resolution three-dimensional seismic travel time tomography, Journal of Geophysical Research, 97, 6553-6562, 1992.

Hole, J. A., R. M. Clowes, and R, M. Ellis, Interface inversion using broadside seismic refraction data and three-dimensional travel time calculations, Journal of Geophysical Research, 97, 3417-3429, 1992.

Hole, J. A. and B. C. Zelt, 3-D finite-difference reflection traveltimes, Geophysical Journal International, 121, 427-434, 1995.

Honjo, Y. and N. Kashiwagi, On the optimum design of a smoothing filter for geophysical tomography, Soils and Foundations, 31, 131-144, 1991.

Hubbard, S. S., Y. Rubin, and E. Majer, Spatial correlation structure estimation using geophysical and hydrogeological data, Water Resources Research, 35, 1809-1825, 1999.

Hubbard, S. S., J. Peterson, E. Majer, P. T. Zawislanski, K.H. Williams, J. Roberts, and F. Wobber, Estimation of permeable pathways and water content using tomographic radar data, The Leading Edge, 16, 1623-1628, 1997.

Hubbard, S. S., J. Chen, J. Peterson, E. Majer, K.H. Williams, D. J. Swift, B. Mailloux, and Y. Rubin, hydrogeological characterization of the South Oyster Bacterial Transport Site using geophysical data, Water Resource Research, 37, 2431-2456, 2001.

Hyndman, D. W. and S. M. Gorelick, Estimating lithologic and transport properties in three dimensions using seismic and tracer data, Water Resources Research, 32, 2659-2670, 1996.

Hyndman, D. W., and J. M. Harris, Traveltime inversion for the geometry of aquifer lithologies, Geophysics, 61, 1728-1737, 1996.

Hyndman, D. W., J. M. Harris, and S. M. Gorelick, Inferring the relation between seismic slowness and hydraulic conductivity in heterogeneous aquifers, Water Resources Research, 36, 2121-2132, 2000.

Hyndman, D. W., J. M. Harris, and S. M. Gorelick, Coupled seismic and tracer test inversion for aquifer property characterization, Water Resources Research, 30, 1965-1977, 1994.

Hyndman, D. W., Geophysical and tracer characterization methods, in The Handbook of Groundwater Engineering, J. W. Delleur (ed.), Boston: CRC Press, 11-1-11-30, 1998.

Iyer, H. M. and K. Hirahara, (eds.) Seismic Tomography: Theory and Practice, London: Chapman and Hall Co., 842 p., 1993.

Jackson, D. D., Interpretation of inaccurate, insufficient and inconsistent data, Geophysical Journal of the Royal Astronomical Society, 28, 97-110, 1972.

Jackson, D. D., The use of a priori data to resolve non-uniqueness in linear inversion, Geophysical Journal of the Royal Astronomical Society, 57, 137-157, 1979.

Jackson, M. J., and D. R. Tweeton, Migratom-Geophysical tomography using wavefront migration and fuzzy constraints, U.S. Bureau of Mines Report of Investigations, 9497, 1993. (see also: Tweeton, D. R., Program MIGRATOM for Crosswell Radar and Seismic Tomography, U.S. Geological Survey Open-File Report 00-0457 <http://geology.cr.usgs.gov/pub/open-file-reports/ofr-00-0457>).

Jackson, M. J., and Tweeton, D. R., 3DTOM - Three-dimensional geophysical tomography: USBM Report of Investigation 9617, 52 p., 1996. (see also: Tweeton, D., Program 3DTOM for Crosswell Radar and Seismic Tomography U.S. Geological Survey Open-File Report 00-0456 <http://geology.cr.usgs.gov/pub/open-file-reports/ofr-00-0456/index.html>).

LaBrecque, M. Miletto, W. Daily, A. Ramirez, and E. Owen, The effects of noise on Occam's inversion of resistivity tomography data, Geophysics, 61, 538-548, 1996.

LaBrecque, A. Ramirez, W. Daily, A. Binley, and S. Schima, ERT monitoring of environmental remediation processes, Meas. Sci. Technol., 7 375-383, 1996.

Langan, R. T., I. Lerche, and R. T. Cutler, Tracing of rays through heterogeneous media: An accurate and efficient procedure, Geophysics, 50, 1456-1465, 1985.

Lanz, E, H. Maurer, and A. G. Green, Refraction tomography over a buried waste disposal site, Geophysics, 63, 1414-1433, 1998.

Lees, J. M. and R. S. Crosson, Tomographic inversion for three-dimensional velocity structure at Mount St. Helens using earthquake data, Journal of Geophysical Research, 94, 5716-5728, 1989.

Lévêque, J.-J., L. Rivera, and G. Wittlinger, On the use of the checker-board test to assess the resolution of tomographic inversions, Geophysical Journal International, 115, 313-318, 1993.

Liao, Q. and G. A. McMechan, Tomographic imaging of velocity and Q, with application to crosswell seismic data from the Gypsy Pilot Site, Oklahoma, Geophysics, 62, 1804-1811, 1997.

Lines, L. and S. Treitel, A review of least-squares inversion and its application to geophysical problems, Geophysical Prospecting, 32, 159-186, 1984.

Liu, L, J.W. Lane, and Y. Quan, 1998, Radar attenuation tomography using the centroid frequency downshift method: J. Applied Geophysics, 40, 105-116.

Lutter, W. J. and R. L. Nowack, Inversion for crustal structure using reflections from the PASSCAL Ouachita experiment, Journal of Geophysical Research, 95, 4633-4646, 1990.

Lytle, R. J. and K. A. Dines, An impedance camera: A system for determining the spatial variation of electrical conductivity, Lawrence Livermore Laboratory, Livermore, CA, UCRL-52413, 1978.

Maurer, H, and A. G. Green, Potential coordinate mislocations in crosshole tomography: Results from the Grimsel test site, Switzerland, Geophysics, 62, 1696-1709, 1997.

McMechan, G. A., Seismic tomography in boreholes Geophysical Journal of the Royal Astronomical Society, 74, 601-612, 1983.

Menke, W., Geophysical Data Analysis: Discrete Inverse Theory, Academic Press, 1989.

Menke, W., The resolving power of cross borehole tomography, Geophysical Research Letters, 11, 105-108, 1984.

Meju, M. A., Geophysical Data Analysis: Understanding Inverse Problem Theory and Practice, Society of Exploration Geophysicists, Course Notes Series, 6, 296 p., 1994.

Meyerholtz, K. A., G. L. Pavlis, and S. A Szpakowski, Convolutional quelling in seismic tomography, Geophysics, 54, 570-580, 1989.

Michelena, R., Singular-value decomposition for crosswell tomography, Geophysics, 58, 1655-1661, 1993.

Michelena, R. J., and J. M. Harris, Tomographic traveltime inversion using natural pixels, Geophysics, 56, 635-644, 1991.

Minkoff, S. E., A computationally feasible approximate resolution matrix for seismic inverse problems, Geophysical Journal International, 126, 345-359, 1996.

Moraes, F. S. and J. A. Scales, Local Bayesian inversion: theoretical developments, Geophysical Journal International, 141, 713-723, 2000.

Mosegaard, K., Resolution analysis of general inverse problems through inverse Monte Carlo sampling, Inverse Problems, 14, 405-426, 1998.

Moser, T. J., Shortest path calculation of seismic rays, Geophysics, 56, 59-67, 1991.

Nemeth, T., E. Normark, and F. Qin, Dynamic smoothing in crosswell traveltime tomography, Geophysics, 62, 168-176, 1997.

Nercessian, A. A. Hirn, and A. Tarantola, Three-dimensional seismic transmission prospecting of the Montdore volcano, France, Geophysical Journal of the Royal Astronomical Society, 76, 307-315, 1984.

Newmark, R. L., W. D. Daily, D. R. Kyle, and A. L. Ramirez, Monitoring DNAPL pumping using integrated geophysical techniques, Journal of Environmental and Engineering Geophysics, 3, 7-13, 1998.

Nolet, G., (ed.) Seismic Tomography: with applications in global seismology and exploration geophysics, Dordrecht, Holland: D. Reidel Publishing Co., 386 p., 1987.

Nolet, G., Solving large linearized tomographic problems, in Iyer, H. M. and K. Hirahara (eds.), Seismic Tomography: Theory and practice, London: Chapman & Hall, 227-247, 1993.

Nolet, G., R. Montelli, and J. Virieux, Explicit, approximate expressions for the resolution and a posteriori covariance of massive tomographic systems, Geophysical Journal International, 138, 36-44, 1999.

Nolet, G., R. Montelli, and J. Virieux, Reply to comment by Z. S. Yao, R. G. Roberts, and A. Tryggvason on "Explicit, approximate expressions for the resolution and a posteriori covariance of massive tomography systems", Geophysical Journal International, 145, 315, 2001.

Nowack, R. L., and W. J. Lutter, A note on the calculation of covariance and resolution, Geophysical Journal, 95, 205-207, 1988.

Oldenburg, D. W., P. R. McGillivray, and R. G. Ellis, Generalized subspace methods for large-scale inverse problems, Geophysical Journal International, 114, 12-20, 1993.

Olsson, O., L. Falk, O. Forslund, L. Lundmark, and E. Sandberg, Borehole radar applied to the characterization of hydraulically conductive fracture zones in crystalline rock, Geophysical Prospecting, 40, 109-142, 1992.

Paige, C. and M. Saunders, LSQR: An algorithm for sparse linear equations and sparse least squares, Assn. Comp. Math. Transactions on Mathematical Software, 8, 43-71, 1982.

Parker, R. L., Understanding inverse theory, Annual reviews of Earth and Planetary Science, 5, 35-64, 1977.

Parker, R. L., Geophysical Inverse Theory, Princeton University Press, 386 p., 1994.

Peterson, J. E. Jr., Pre-inversion corrections and analysis of radar tomographic data, Journal of Environmental and Engineering Geophysics, 6, 1-18, 2001.

Peterson, J. E. Jr., B. N. P. Paulsson, and T. V. McEvilly, Applications of algebraic reconstruction techniques to crosshole seismic data, Geophysics, 50, 1566-1580, 1985.

Peterson, J. E. Jr., and A. Davey, Crossvalidation method for crosswell seismic tomography, Geophysics, 56, 385-389, 1991.

Phillips, W. S., and M. C. Fehler, Traveltime tomography: A comparison of popular methods, Geophysics, 56, 1639-1649, 1991.

Pilkington, M. and J. P. Todoeschuck, Natural smoothness constraints in cross-hole seismic tomography, Geophysical Prospecting, 40, 227-242, 1992.

Podvin, P. and I. Lecomte, Finite difference computation of travel times in very contrasted velocity models: A massively parallel approach and its associated tools, Geophysical Journal International, 105, 271-284, 1991.

Ramirez, A., W. Daily, and R. Newmark, Electrical resistance tomography for steam injection and process control, Journal of Environmental and Engineering Geophysics, 0, 39-51, 1995.

Ramirez, A., W. Daily, A. Binley, D. LaBrecque, and D. Roelant, Detection of leaks in underground storage tanks using electrical resistance methods, Journal of Environmental and Engineering Geophysics, 1, 189-203, 1996.

Ramirez, A., W. Daily, A. Binley, and D. LaBrecque, Electrical impedance tomography of known targets, Journal of Environmental and Engineering Geophysics, 4, 11-26, 1999.

Sambridge, M., Exploring multidimensional landscapes without a map, Inverse Problems, 14, 427-440, 1998.

Santamarina, J. C. and D. Fratta, Introduction to Discrete Signals and Inverse Problems in Civil Engineering, ASCE Press, Reston, VA, 327 p., 1998.

Sasaki, Y., Resolution of resistivity tomography inferred from numerical simulation, Geophysical Prospecting, 40, 453-463, 1992.

Scales, J. A. and A. Gersztenkorn, Robust methods in inverse theory, Inverse Problems, 4, 1071-1091, 1988.

Scales, J. A., A. Gersztenkorn, and S. Treitel, Fast lp solution of large, sparse, linear systems: Application to seismic travel time tomography Journal of Computational Physics, 75, 314-333, 1988.

Scales, J. A., P. Docherty, and A. Gersztenkorn, Regularization of nonlinear inverse problems: imaging the near-surface weathering layer, Inverse Problems, 6, 115-131, 1990.

Scales, J. A., and M. L. Smith, Introductory Geophysical Inverse Theory, Samizdat Press, 1998.

Scales, J. A., Tomographic inversion via the conjugate gradient method, Geophysics, 52, 179-185, 1987.

Scales, J. A., On the use of conjugate gradient to calculate the eigenvalues and singular values of large, spare matrices, Geophysical Journal, 97, 179-183, 1989.

Scales, J. A. and R. Snieder, To Bayes or not to Bayes, Geophysics, 62, 1045-1046, 1997.

Scales, J. A. and R. Snieder, Humility and Nonlinearity, Geophysics, 62, 1355-1358, 1997.

Scales, J. A. and R. Snieder, What is noise?, Geophysics, 63, 1122-1124, 1998.

Scales, J. A. and R. Snieder, Modes of Survival, Geophysics, 63, 1845-1846, 1998.

Scales, J. A. and R. Snieder, What is a wave?, Nature, 401, 739-740, 1999.

Scales, J. A. and R. Snieder, Computers and Creativity, Geophysics, 64, 1347-1348, 1999.

Schueller, W., I. B. Morozov, and S. B. Smithson, Crustal and uppermost mantle velocity structure of northern Eurasia along Profile Quartz, Bulletin of the Seismological Society of America, 87, 414-426, 1997.

Schuster, G. T., Resolution limits for crosswell migration and traveltime tomography, Geophysical Journal International, 127, 427-440, 1996.

Sen, M. K. and P. L. Stoffa, Global optimization methods in geophysical inversion, Elsevier, Amsterdam, 281 p., 1995.

Sena, A. G. and M. N. Toksov, Simultaneous reconstruction of permittivity and conductivity for crosshole geometries: Geophysics, 55, 1302-1311, 1990.

Singh, R. P. and Y. P. Singh, RATPT: A new inversion technique for geotomographic data, Geophysics, 56, 1215-1227, 1991.

Sivia, D. S., Data Analysis: A Bayesian Tutorial, Clarendon Press, Oxford, U.K., 189 p., 1996.

Slater, L., A. Binley, W. Daily, and R. Johnson, Cross-hole electrical imaging of a controlled saline tracer injection, Journal of Applied Geophysics, 44, 85-102, 2000.

Snieder, R., An extension of Backus-Gilbert theory to nonlinear inverse problems, Inverse Problems, 7, 409-433, 1991.

Snieder, R., The role of nonlinearity in inverse problems, Inverse Problems, 14, 387-404, 1998.

Snieder, R. and J. Trampert, Inverse Problems in Geophysics, Samizdat Press, 1999.

Spakman, W., and G. Nolet, Imaging algorithms, accuracy and resolution in delay-time tomography, in Vlaar, N. J., G. Nolet, M. J. R. Wortel, et al. (eds.), Mathematical Geophysics, Hingham, MA: Reidel, 155-187, 1988.

Squires, L. J., S. M. Blakeslee, and P. L. Stoffa, The effects of statics on tomographic velocity reconstructions, Geophysics, 57, 353-362, 1992.

Squires, L. J., P. L. Stoffa, and G. Cambois, Borehole transmission tomography for velocity plus statics, Geophysics, 59, 1028-1036, 1994.

Stefani, J. P., Turning-ray tomography, Geophysics, 60, 1917-1929, 1995.

Stewart, R. R., Exploration Seismic Tomography: Fundamentals, Society of Exploration Geophysicists, Course Notes Series, 3, 140 p., 1991.

Tarantola, A., Inverse Problem Theory, Elsevier Press, New York, 1987.

Tarantola, A. and B. Valette, Generalized non-linear inverse problems solved using the least squares criterion, Review of Geophysics and Space Physics, 20, 219-232, 1982.

Tarantola, A. and B. Valette, Inverse problems = quest for information, Journal of Geophysics, 50, 159-170, 1982.

Thill, R. E., D. R. Tweeton, J. A. Jessop, and K. S. Roessler, Developments in seismic tomography for minesite investigation, Rock Mechanics, 1093-1102, 1992.

Thurber, C. and D. Eberhart-Phillips, Local earthquake tomography with flexible gridding, Computers and Geosciences, 25, 809-818, 1999.

Tichelaar, B. W. and L. R. Ruff, How good are our best models?, EOS, 70, 593-606, 1989.

Trampert, J., Global seismic tomography: the inverse problem and beyond, Inverse Problems, 14, 371-385, 1998.

Trampert, J. and J.-J. Lévêque, Simultaneous iterative reconstruction technique: Physical interpretation based on the generalized least squares solution, Journal of Geophysical Research, 95, 12,553-12,559, 1990.

Tronicke, J. D. R. Tweeton, P. Dietrich, and E. Appel, Improved crosshole radar tomography by using direct and reflected arrival times, Journal of Applied Geophysics, 97-105, 2001.

Tweeton, D. R., A Tomographic computer program with constraints to improve reconstructions for monitoring in situ mining leachate, Bureau of Mines Report of Investigations, 9159, 70 p., 1988.

Tweeton, D. R., K. S. Roessler, and M. J. Jackson, Tomographic computer programs with constraints to improve the reliability of reconstructions with crosshole data, Proceedings of APCOM'92, Tuscon, AZ, 63-71, 1992.

Tweeton, D. R., GeoTomCG <http://www.giscogeo.com/pages/seixgotm.html>.

Vasco, D. W., J. E. Peterson, Jr., and E. L. Majer, Beyond ray tomography: Wavepaths and Fresnel volumes, Geophysics, 60, 1790-1804, 1995.

Vasco, D. W., J. E. Peterson, Jr., and E. L. Majer, Nonuniqueness in traveltime tomography: Ensemble inference and cluster analysis, Geophysics, 61, 1209-1227, 1996.

Vasco, D. W., and E. L. Majer, Wavepath traveltime tomography, Geophysical Journal International, 115, 1055-1069, 1993.

Vasco, D. W., J. E. Peterson, Jr., and K. H. Lee, Ground-penetrating radar velocity tomography in heterogeneous and anisotropic media, Geophysics, 62, 1758-1773, 1997.

Vidale, J., Finite-difference calculation of traveltimes in three dimensions, Geophysics, 55, 521-526, 1990.

van der Sluis, A. and H. A. van der Vorst, Numerical solution of large, sparse linear algebraic systems arising from tomographic problems, in Nolet, G., (ed.) Seismic Tomography: with applications in global seismology and exploration geophysics, Dordrecht, Holland: D. Reidel Publishing Co., 49-83, 1987.

van Wijk, K., J. A. Scales, W. Navidi, and L. Tenorio, Data and model uncertainty estimation for linear inversion, Geophysical Journal International, 149, 625-632, 2002.

Washbourne, J. K., J. W. Rector, and K. P. Bube, Crosswell traveltime tomography in three dimensions, Geophysics, 67, 853-871, 2002.

Wexler, A., B. Fry, and M. R. Neuman, Impedance-computed tomography algorithm and system, Applied Optics, 24, 3985-3992, 1985.

White, D. J., Two-dimensional seismic refraction tomography, Geophysical Journal, 97, 223-245, 1989.

White, D. J. and A. V. Boland, A comparison of forward modeling and inversion of seismic first arrivals over the Kapuskasing uplift. Bulletin of the Seismological Society of America, 82, 304-322, 1992.

Wiggins, R. A., The general linear inverse problem: implication of surface waves and free oscillations for Earth structure, Reviews of Geophysics and Space Sciences, 10, 251-285, 1972.

Witten, A. J., Exploring Earth's shallow subsurface with geophysical diffraction tomography, Geotimes, 40, 14-17, 1995.

Worthington, M. H., An introduction to geophysical tomography, First Break, 2, 20-26, 1984.

Wu, C. F. J., Jackknife, bootstrap and other resampling methods in regression analysis, The Annals of Statistics, 14, 1261-1295, 1986.

Wu, R. S. and M. N. Toksoz, Diffraction tomography and multisource holography applied to seismic imaging, Geophysics, 52, 11-25, 1987.

Yao, Z. S., R. G. Roberts, and A. Tryggvason, Calculating resolution and covariance matrices for seismic tomography with the LSQR method, Geophysical Journal International, 138, 886-894, 1999.

Yao, Z. S. and R. G. Roberts, A practical regularization for seismic tomography, Geophysical Journal International, 138, 293-299, 1999.

Yao, Z. S., R. G. Roberts, and A. Tryggvason, Comment on "Explicit, approximate expressions for the resolution and a posteriori covariance of massive tomography systems" by G. Nolet, R. Montelli and J. Virieux, Geophysical Journal International, 145, 307-314, 2001

Zelt, C. A. and R. B. Smith, Seismic travel time inversion for 2-D crustal velocity structure, Geophysical Journal International, 108, 16-34, 1992.

Zelt, C. A., and P. J. Barton, Three-dimensional seismic refraction seismic tomography: A comparison of two methods applied to data from the Faeroe Basin, Journal of Geophysical Research, 103, 7187-7210, 1998.

Zhang, J. and G. A. McMechan, 3-D transmission tomography using wide aperture data for velocity estimation of irregular salt bodies, Geophysics, 59, 1620-1630, 1994.

Zhang, J. and G. A. McMechan, Estimation of resolution and covariance for large matrix inversions, Geophysical Journal International, 127, 409-426, 1995.

Zhang, J. and G. A. McMechan, Reply to comment by M. M. Deal and G. Nolet on "Estimation of resolution and covariance for large matrix inversions", Geophysical Journal International, 127, 251-252, 1996.

Zhang, J. and Toksoz, M. N., Nonlinear refraction traveltime tomography, Geophysics, 63, 1726-1737, 1998.

Zhang, J., Mackie, R. L., and T. R. Madden, 3-D resistivity forward modeling and inversion using conjugate gradients, Geophysics, 60, 1313-1325, 1995.

Zhou, C., and L. Liu, Diffraction tomography using the modified quasi-linear approximation: IEEE Trans. on Geoscience and Remote Sensing, 38, 404-415, 2000.

Zhou, C., L. Liu, and J. W. Lane, Jr., Simultaneous inversion for velocity and attenuation, Journal of Applied Geophysics, 47, 199-215, 2001.

Zhu, X., D. P. Sixta, and B. G. Angstman, Tomostatics: Turning-ray tomography + static corrections, The Leading Edge, 11, 15-23, 1992.