1.
K. Aki and P. G. Richards. Quantitative Seismology. Freeman and Sons, 1980.
2.
A. M. Anile, J. K. Hunter, P. Pantano, and G. Russo. Ray Methods for Nonlinear Waves in Fluids and Plasmas. Longman Scientific and Technical, 1993.
3.
J. Bear. Dynamics of Fluids in Porous Media. Dover Publications, 1972.
4.
R. N. Bracewell.
The Fourier Transform and Its Applications. McGraw-Hill, New York, 1978.
MATH5.
J. Carrera. State of the art of the inverse problem applied to the flow and solute transport problems. In Groundwater Flow and Quality Modeling, pages 549–585. NATO ASI Ser., 1987.
6.
H. S. Carslaw and J. C. Jaeger. Conduction of Heat in Solids. Oxford University Press, Oxford, 1959.
7.
H. Cheng, A. Datta-Gupta, and Z. He. A comparison of travel-time and amplitude matching for field-scale production data integration: Sensitivity, non-linearity, and practical implications. SPE Annual Meeting, 84570:1–15, 2003.
8.
R. Courant and D. Hilbert.
Methods of Mathematical Physics. Interscience, New York, 1962.
MATH9.
M. J. Crane and M. J. Blunt. Streamline-based simulation of solute transport.
Water Resour. Res., 35:3061–3078, 1999.
CrossRef10.
A. Datta-Gupta and M. J. King. A semianalytic approach to tracer flow modeling in heterogeneous permeable media.
Advan. Water Resour., 18:9–24, 1995.
CrossRef11.
A. Datta-Gupta, L. W. Lake, G. A. Pope, K. Sepehrnoori, and M. J. King. High-resolution monotonic schemes for reservoir fluid flow simulation. In Situ, 15:289–317, 1991.
12.
A. Datta-Gupta, D. W. Vasco, J. C. S. Long, P. S. D’Onfro, and W. D. Rizer. Detailed characterization of a fractured limestone formation by use of stochastic inverse approaches. SPE Form. Eval., 10:133–140, 1995.
13.
G. de Marsily. Quantitative Hydrogeology. Academic Press, San Diego, 1986.
14.
S. N. Domenico. Effect of water saturation on seismic reflectivity of sand reservoirs encased in shale.
Geophysics, 39:759–769, 1974.
CrossRef15.
F. G. Friedlander and J. B. Keller. Asymptotic expansions of solutions of (∇
^{2} +
k
^{2})
u = 0.
Comm. Pure Appl. Math., 8:387, 1955.
MATHCrossRefMathSciNet16.
C. S. Gardner and G. K. Morikawa. Similarity in the asymptotic behavior of collision-free hydromagnetic waves and water waves. Courant Inst. Math. Sci. Rep., 90:9082, 1960.
17.
F. Gassmann. Elastic waves through a packing of spheres.
Geophysics, 16:673–685, 1951.
CrossRef18.
L. W. Gelhar and M. A. Collins. General analysis of longitudinal dispersion in nonuniform flow. Water Resour. Res., pages 1511–1521, 1971.
19.
R. E. Grundy, C. J. van Duijn, and Dawson C. N. Asymptotic profiles with finite mass in one-dimensional contaminant transport through porous media: The fast reaction case.
Q. J. Mech. Appl. Math., 47:69–106, 1994.
MATHCrossRef20.
Z. He, A. Datta-Gupta, and D. W. Vasco. Rapid inverse modeling of pressure interference tests using trajectory-based traveltime and amplitude sensitivities. Water Resources Research, 42:1–15, 2006.
21.
G. M. Hoversten, R. Gritto, J. Washbourne, and T. Daley. Pressure and fluid saturation prediction in a multicomponent reservoir using combined seismic and electromagnetic imaging.
Geophysics, 68:1580–1591, 2003.
CrossRef22.
U. Jaekel, A. Georgescu, and H. Vereecken. Asymptotic analysis of nonlinear equilibrium solute transport in porous media.
Water Resour. Res., 32:3093–3098, 1996.
CrossRef23.
K. Karasaki, B. Freifeld, A. Cohen, K. Grossenbacher, P. Cook, and D. Vasco. A multidisciplinary fractured rock characterization study at the Raymond field site, Raymond, California.
J. Hydrol., 236:17–34, 2000.
CrossRef24.
J. B. Keller and R. M. Lewis. Asymptotic methods for partial differential equations: The reduced wave equation, and Maxwell’s equations. In J. P. Keller, D. W. McLaughlin, and G. C. Papanicolaou, editors, Surveys in Applied Mathematics, volume 1, chapter 1. Plenum Press, 1995.
25.
M. J. King and A. Datta-Gupta. Streamline simulation: A current perspective. In Situ, 22:91–140, 1998.
26.
M. Kline and I. W. Kay. Electromagnetic Theory and Geometrical Optics. Robert E. Krieger Publishing, Huntington, NY, 1979.
27.
S. Korsunsky.
Nonlinear Waves in Dispersive and Dissipative Systems with Coupled Fields. Addison Wesley Longman Ltd., Essex, 1997.
MATH28.
Y. A. Kravtsov and Y. I. Orlov. Geometrical Optics of Inhomogeneous Media. Springer-Verlag, 1990.
29.
M. Landro. Discrimination between pressure and fluid saturation changes from time-lapse seismic data.
Geophysics, 66:836–844, 2001.
CrossRef30.
R. K. Luneburg. Mathematical Theory of Optics. University of California Press, Berkeley, 1966.
31.
T. N. Narasimhan and P. A. Witherspoon. An integrated finite difference method for analyzing fluid flow in porous media.
Water Resour. Res., 12:57–64, 1976.
CrossRef32.
B. Noble and J. W. Daniel.
Applied Linear Algebra. Prentice-Hall, Englewood Cliffs, NJ, 1977.
MATH33.
A. Nur. Four-dimensional seismology and (true) direct detection of hydrocarbon: The petrophysical basis.
The Leading Edge, 8:30–36, 1989.
CrossRef34.
C. C. Paige and M. A. Saunders. LSQR: An algorithm for sparse linear equations and sparse linear systems.
ACM Trans. Math. Software, 8:195–209, 1982.
CrossRefMathSciNet35.
R. L. Parker.
Geophysical Inverse Theory. Princeton University Press, Princeton, 1994.
MATH36.
D. W. Peaceman. Fundamentals of Numerical Reservoir Simulation. Elsevier Scientific Publishing, 1977.
37.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes. Cambridge University Press, Cambridge, 1992.
38.
K. Pruess, C. Oldenburg, and G. Moridis. Tough2 user’s guide, version 2.0. LBNL Report, Berkeley, 43134, 1999.
39.
J. R. Rice and M. P. Cleary. Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents.
Rev. Geophys. Space. Phys., 14:227–241, 1976.
CrossRef40.
P. Segall. Stress and subsidence resulting from subsurface fluid withdrawal in the epicentral region of the 1983 Coalinga earthquake.
J. Geophys. Res., 90:6801–6816, 1985.
CrossRef41.
J. A. Sethian.
Level Set and Fast Marching Methods. Cambridge University Press, Cambridge, 1999.
MATH42.
N.-Z. Sun and W.-G. Yeh. Coupled inverse problems in groundwater modeling, 1, sensitivity analysis and parameter identification. Water Resour. Res., 26:2507–2525, 1990.
43.
T. Taniuti and Nishihara K.
Nonlinear Waves. Pitman Publishing Inc., Marshfield, MA, 1983.
MATH44.
A. Tarantola. Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier Sci., 1987.
45.
A. Tura and D. E. Lumley. Estimating pressure and saturation changes from time-lapse avo data. 61st Ann. Conf. Eur. Assoc. Geosci. Eng., Extended Abstracts:1–38, 1999.
46.
S. E. van der Zee. Analytical traveling wave solutions for transport with nonlinear and nonequilibrium adsorption. Water Resour. Res., 26:2563–2578, 1990.
47.
C. J. van Duijn and P. Knabner. Traveling waves in the transport of reactive solutes through porous media: Adsorption and binary ion exchange, 1.
Trans. Porous. Media, 8:167–194, 1992.
CrossRef48.
D. W. Vasco, S. Yoon, and A. Datta-Gupta. Integrating dynamic data into high-resolution reservoir models using streamline-based analytic sensitivity coefficients.
SPE Journal, 4:389–399, 1999.
CrossRef49.
D. W. Vasco. An asymptotic solution for two-phase flow in the presence of capillary forces.
Water Resources Research, 40:W12407, 2004.
CrossRef50.
D. W. Vasco. Estimation of flow properties using surface deformation and head data: A trajectory-based approach. Water Resources Research, 40:1–14, 2004.
51.
D. W. Vasco. Trajectory-based modeling of broadband electromagnetic wavefields.
Geophysical Journal International, 168:949–963, 2007.
CrossRef52.
D. W. Vasco and A. Datta-Gupta. Asymptotic solutions for solute transport: A formalism for tracer tomography.
Water Resources Research, 35:1–16, 1999.
CrossRef53.
D. W. Vasco and A. Datta-Gupta. Asymptotics, saturation fronts, and high resolution reservoir characterization.
Transport in Porous Media, 42:315–350, 2001.
CrossRefMathSciNet54.
D. W. Vasco, A. Datta-Gupta, R. Behrens, P. Condon, and J. Rickett. Seismic imaging of reservoir flow properties: Time-lapse amplitude changes.
Geophsics, 69:1425–1442, 2004.
CrossRef55.
D. W. Vasco and S. Finsterle. Numerical trajectory calculations for the efficient inversion of transient flow and tracer observations.
Water Resources Research, 40:W01507, 2004.
CrossRef56.
D. W. Vasco, K. Karasaki, and H. Keers. Estimation of reservoir properties using transient pressure: An asymptotic approach.
Water Resources Research, 36:3447–3465, 2000.
CrossRef57.
D. W. Vasco, K. Karasaki, and K. Kishida. A coupled inversion of pressure and surface displacement.
Water Resources Research, 37:3071–3089, 2001.
CrossRef58.
J. Virieux, C. Flores-Luna, and D. Gibert. Asymptotic theory for diffusive electromagnetic imaging.
Geophys. J. Int., 119:857–868, 1994.
CrossRef59.
G. B. Whitham.
Linear and Nonlinear Waves. Wiley, New York, 1974.
MATH60.
W.-G. Yeh. Review of parameter identification procedures in groundwater hydrology: The inverse problem.
Water Resour. Res., 22:95–108, 1986.
CrossRef