Grantee Research Project Results
1997 Progress Report: Geophysical Sensing in Environmental Applications: Efficient Numerical Simulations
EPA Grant Number: R825225Title: Geophysical Sensing in Environmental Applications: Efficient Numerical Simulations
Investigators: Liu, Qing-Huo
Institution: New Mexico State University - Main Campus
EPA Project Officer: Hahn, Intaek
Project Period: November 21, 1996 through September 20, 2001
Project Period Covered by this Report: November 21, 1996 through September 20, 1997
Project Amount: $500,000
RFA: Exploratory Research - Early Career Awards (1996) RFA Text | Recipients Lists
Research Category: Early Career Awards
Objective:
The objective of this research is to develop efficient forward and inverse techniques to model electromagnetic and acoustic problems in environmental geophysical sensing. Specifically, fast forward and inverse computer models will be developed for electrical resistance tomography (ERT), electromagnetic induction (EMI), radio imaging methods (RIM), ground-penetrating radar (GPR), surface seismic reflection, and borehole seismic imaging measurements in three-dimensional inhomogeneous media.Progress Summary:
During the past 18 months, much progress has been made toward the full 3-D modeling for transient electromagnetic and acoustic measurements and for electrical resistance tomography. Our accomplishments in this research can be summarized as follows.1. We have completed the development of the new perfectly matched layer (PML) absorbing boundary condition for electromagnetic and acoustic waves in lossy media. A perfectly matched interface is an interface between two half spaces (one is the regular medium and the other the artificial lossy PML medium) that does not reflect a plane wave for any frequencies and any angles of incidence. The attenuation of the wave in the lossy PML half space is in the direction normal to the interface. As a consequence, layers of such material can be designed at the edge of a computer simulation region to absorb outgoing waves. Previously, the PML absorbing boundary condition has been formulated only for lossless media, and hence cannot be applied to the lossy earth. Our new formulation allows this new absorbing boundary condition to be used in lossy media which are common in the environmental applications.
2. We have developed finite-difference time-domain (FDTD) methods with the PML absorbing boundary condition, with both uniform and nonuniform grids, for electromagnetic and acoustic waves in lossy media. For environmental applications such as the characterization of waste sites, nonuniform grids become very useful for modeling buried tanks whose shapes are not conformal with Cartesian coordinates. An accurate material averaging scheme is designed to further improve the FDTD algorithm. The new FDTD algorithm thus significantly increases the efficiency for computer memory and computation time.
Since the perfectly matched interface is a material absorbing boundary condition, only one set of computer code is needed to simulate an open region. Hence, it is easy to parallelize such programs on multiprocessor computers. This absorbing boundary condition has been implemented to solve 2-D, 2.5-D, and 3-D Maxwell's equations and acoustic wave equations. The computer programs are stable even when inhomogeneous medium interfaces intersect with the edge of the simulation region. The resulting algorithm has been implemented and validated using previous analytical and numerical results. These computer programs are considered fully validated and are ready to be used to simulate realistic waste sites and compare the results with the measurements. Computer programs developed are:
a) 2-D FDTD code for electromagnetic waves, uniform Cartesian grid.
b)
2.5-D FDTD code for electromagnetic waves, uniform Cartesian grid.
c) 3-D
FDTD code for electromagnetic waves, uniform Cartesian grid.
d) 2-D FDTD
code for electromagnetic waves, nonuniform cylindrical grid.
e) 2.5-D FDTD
code for electromagnetic waves, nonuniform cylindrical grid.
f) 3-D FDTD code
for electromagnetic waves, nonuniform cylindrical grid.
g) 2-D FDTD code for
scalar acoustic waves, uniform Cartesian grid.
h) 3-D FDTD code for scalar
acoustic waves, uniform Cartesian grid.
3. The numerical mode-matching (NMM) method for the three-dimensional simulations of electrical resistance tomography (ERT) has been developed. Previously the NMM method has been demonstrated to be a very efficient numerical method for 2-D problems. This is the first NMM method applied to 3-D problems, where the advantages of the method over the conventional finite-element method is even more profound than the 2-D problems. The 3-D problem is solved through the eigenmode expansion of a series of 2-D problems. The expansion coefficients, expressed in terms of the local and global reflection and transmission matrices, are then efficiently obtained by a recursive scheme. The computer software is already developed and is being validated.
4. In addition to fulfilling our commitment to the planned tasks, we have made some fundamental advances in the development of a new algorithm, the pseudospectral time-domain (PSTD) method, for transient wave propagation in heterogeneous media. We have applied this method to both electromagnetic and acoustic waves, and shown that this new method can be three orders of magnitude more efficient than the conventional FDTD methods. The key idea of the PSTD algorithm is to use the fast Fourier transform (FFT) to approximate the spatial derivatives in the partial differential equations, and to use the PML medium to eliminate the wraparound effect from the periodicity in the FFT. Computer programs developed include:
a) 2-D FDTD code for electromagnetic waves, uniform Cartesian grids.
b)
2.5-D FDTD code for electromagnetic waves, uniform Cartesian grids.
c) 3-D
FDTD code for electromagnetic waves, uniform Cartesian grids.
d) 2-D FDTD
code for electromagnetic waves, uniform cylindrical grids.
e) 3-D FDTD code
for electromagnetic waves, uniform cylindrical grids.
f) 2-D FDTD code for
scalar acoustic waves, uniform Cartesian grids.
g) 3-D FDTD code for scalar
acoustic waves, uniform Cartesian grids.
5. We have developed new, more accurate algorithms for the fast Fourier transform of nonuniformly sampled data (NUFFT). Conventional fast Fourier transform (FFT) algorithms apply only to uniformly sampled data. However, many applications involve nonuniformly sampled data. The NUFFT algorithms have far-reaching applications in computational electromagnetics, acoustics, and signal processing.
6. We have also developed PML and FDTD algorithms for dispersive media. Traditionally, the FDTD methods are applied to regular non-dispersive media. However, it is well known that the soil is an electrically dispersive medium, i.e., the conductivity and dielectric constant of the soil are functions of the frequency used in the electromagnetic measurements. To account for this dispersion, we develop an FDTD algorithm to model an arbitrary dispersive, heterogeneous medium. A full 3-D FDTD code for electromagnetic waves in a uniform Cartesian grid has been developed.
Future Activities:
Continue our research in the development of computer programs for modeling ERT, EMI, RIM, and Seismic measurements. Validation of the computer models. Comparison with field measurements. Attend conferences to present information about this research project.Journal Articles on this Report : 12 Displayed | Download in RIS Format
Other project views: | All 54 publications | 24 publications in selected types | All 24 journal articles |
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Type | Citation | ||
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Chang C, Liu Q-H. Inversion of source-time functions using borehole array sonic waveforms. Journal of the Acoustical Society of America 1998;103(6):3163-3168. |
R825225 (1997) R825225 (1999) |
Exit |
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Chen Y-H, Chew WC, Liu Q-H. A three-dimensional finite difference code for the modeling of sonic logging tools. Journal of the Acoustical Society of America 1998;103(2):702-712. |
R825225 (1997) R825225 (1999) |
Exit |
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Fan G-X, Liu QH. A PML-FDTD algorithm for simulating plasma-covered cavity-backed slot antennas. Microwave and Optical Technology Letters 1998;19(4):258-262. |
R825225 (1997) R825225 (1999) |
Exit |
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Liu QH. An FDTD algorithm with perfectly matched layers for conductive media. Microwave and Optical Technology Letters 1997;14(2):134-137. |
R825225 (1997) R825225 (1999) |
Exit |
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Liu QH. The PSTD algorithm: a time-domain method requiring only two cells per wavelength. Microwave and Optical Technology Letters 1997;15(3):158-165. |
R825225 (1997) |
not available |
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Liu QH, Tao J. The perfectly matched layer (PML) for acoustic waves in absorptive media. Journal of the Acoustical Society of America 1997;102(4):2072-2082. |
R825225 (1997) |
not available |
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Liu QH, Nguyen N. An accurate algorithm for nonuniform fast Fourier transforms (NUFFT's). IEEE Microwave and Guided Wave Letters 1998;8(1):18-20. |
R825225 (1997) R825225 (1999) |
Exit |
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Liu QH. The pseudospectral time-domain (PSTD) algorithm for acoustic waves in absorptive media. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 1998;45(4):1044-1055. |
R825225 (1997) R825225 (1999) |
Exit |
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Liu QH, He JQ. Quasi-PML for waves in cylindrical coordinates. Microwave and Optical Technology Letters 1998;19(2):107-111. |
R825225 (1997) R825225 (1999) |
Exit |
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Liu QH, Tang XY. Iterative algorithm for nonuniform inverse fast Fourier transform (NU-IFFT). Electronics Letters 1998;34(20):1913-1914. |
R825225 (1997) R825225 (1999) |
Exit |
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Liu QH. Some current trends in numerical methods for transient acoustic and elastic waves in multidimensional inhomogeneous media. Current Topics in Acoustical Research 1998;2:31-42. |
R825225 (1997) R825225 (1999) |
Exit |
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Nguyen N, Liu QH. The regular Fourier matrices and nonuniform fast-Fourier transforms. SIAM Journal of Scientific Computing 1999;21(1):283-293. |
R825225 (1997) |
not available |
Supplemental Keywords:
Assessment, remediation, cleanup, restoration, engineering, modeling, monitoring, remote sensing., Scientific Discipline, Waste, Remediation, Physics, Geology, Engineering, Environmental Engineering, nonlinear inverse problems, surface seismic reflection, electromagnetic induction, electromagnetic sensors, acoustic sensors, numerical simulations, electrical resistance tomography, assessment methods, computer modeling programs, ecology assessment models, geophysical sensingRelevant Websites:
http://gauss.nmsu.edu:8000/~qhliuProgress and Final Reports:
Original AbstractThe perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Conclusions drawn by the principal investigators have not been reviewed by the Agency.