Simple in operation, rich in information and unique in solution, the surface nuclear magnetic resonance is a geophysical technique specifically developed for hydrogeological investigations. Along with its unintermittent growth and its exploration, this technique has been applied successfully to the detection of groundwater, archaeological work, test of shallow groundwater quality, etc. And detection of these targets can be derived from the inversion of the surface nuclear magnetic resonance data.
For horizontally layered conductivity and water content distributions, the existing inversion algorithms are all based on the assumption that the prior information about the resistivity distributions is objective and reliable. This certainly results in low inversion precision.
Researchers from the State Key Laboratory of Acoustics of Institute of Acoustics, the Chinese Academy of Sciences and School of Information and Communication Engineering, Guilin University of Electronic Technology have recently proposed a regularization-total least square (R-TLS) model to improve the stability and accuracy of the surface nuclear magnetic resonance inversion result.
The inversion for surface nuclear magnetic resonance data in layered electrically conductive media can be concluded as the problem to solving a matrix equation An=E, where A is a kernel function matrix, E is an initial amplitude sequence of the measured data and n is the unknown water content distributions sequence. The precision of A mainly depends on the estimation to the special resistivity distributions. Because of the intrinsic error existing in both A and E and the big condition number of A, the regularization-total least square model of the surface nuclear magnetic resonance inversion arises to address the problem.
This newly proposed model is then transformed into a constrained nonlinear optimization problem, and the solution to the optimization problem is obtained by using a proposed improved particle swarm optimization algorithm. This inversion algorithm has many advantages such as low dependence to initial model, stable result, and strong anti-noise ability.
Although An=E is generally an ill-conditioned and highly underdetermined equation, the proposed algorithm still works effectively. The whole proposed approach is examined by using synthetic data and practical field data, which well demonstrates the capability of the approach.
The results of the synthetic data example demonstrate that proposed approach can well derive the construction information of the hypothesis model under poor relative error of the resistivity distributions (ERRORlayer=17.7%) and poor SNR (SNR=5dB) at the root mean square (RMS) 5.11%, while all existing approaches are useless at all in this example.
And the inversion results of the practical field example show that both the new algorithm (RMS=2.92%) and the inversion software Samovar v6.2 (RMS=3.65%) agree well the construction information from an in-site borehole, and the former algorithm has slightly higher precision than the posterior one.
Funding for this research came from the National Natural Science Foundation of China (Nos. 11434012, 61362020 and 61371186) and the Joint NSFC-ISF Research Program, jointly from the National Natural Science Foundation of China and the Israel Science Foundation (No. 41561144006).
Reference:
ZHANG Hairu, WANG Guofu, and ZHANG Faquan. Non-linear Inversion for Surface Nuclear Magnetic Resonance Data in Layered Electrically Conductive Media. Electronic Journal of Geotechnical Engineering (Vol. 14, No. 21, 2016, pp. 4445-4457). Available at ejge.com (EI: 20163202691493)
Contact:
ZHANG Hairu
State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences
Email: zhanghairu@mail.ioa.ac.cn