Spectral-diagonalization-based matrix exponential integration for efficient and stable solutions of full-Bloch equations in surface NMR
Surface nuclear magnetic resonance (SNMR) is a geophysical extension of nuclear magnetic resonance (NMR) that enables non-invasive mapping of subsurface hydrogeological properties by measuring the relaxation response of groundwater hydrogen nuclei. Accurately modeling the transient spin dynamics in...
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| Veröffentlicht in: | Computers & geosciences Jg. 207; S. 106073 |
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| Abstract | Surface nuclear magnetic resonance (SNMR) is a geophysical extension of nuclear magnetic resonance (NMR) that enables non-invasive mapping of subsurface hydrogeological properties by measuring the relaxation response of groundwater hydrogen nuclei. Accurately modeling the transient spin dynamics in SNMR requires solving the full-Bloch equations under Earth’s geomagnetic field, where magnetic field inhomogeneities, multicomponent relaxation, and nonlinear pulsed excitations introduce significant mathematical and computational challenges. We present a spectral-diagonalization-based matrix exponential integration (SD-MEI) algorithm for efficient and stable solutions of full-Bloch equations in SNMR. Conventional explicit numerical methods exhibit cumulative discretization errors and escalating computational costs due to step-size dependence and finite precision limitations. SD-MEI integrates spectral diagonalization with matrix exponential operations, replacing iterative computations with a single eigendecomposition of the system matrix. This approach achieves parameter-robust computational complexity while maintaining numerical stability across broad B1 field strengths (10−10 T to 10−5 T) and relaxation times (10 ms to 1000 ms). Validated for steady-state free precession (SSFP) dynamics in heterogeneous geomagnetic environments, the method enables high-accuracy modeling of transient magnetization evolution with large time steps. The framework advances SNMR efficient forward modeling and inversion while optimizing protocols by resolving critical limitations in existing numerical and analytical approaches.
•Modeling of Magnetization Dynamics: Accurately describes magnetization vectors over broad excitation fields.•Control of Computational Complexity: Keeps computation stable, improving efficiency by 20–1000x.•Improved Numerical Stability: Solves convergence issues in stiff and highly nonlinear systems.•Temporal Flexibility: Computes magnetization at any time without affecting overall accuracy. |
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| AbstractList | Surface nuclear magnetic resonance (SNMR) is a geophysical extension of nuclear magnetic resonance (NMR) that enables non-invasive mapping of subsurface hydrogeological properties by measuring the relaxation response of groundwater hydrogen nuclei. Accurately modeling the transient spin dynamics in SNMR requires solving the full-Bloch equations under Earth’s geomagnetic field, where magnetic field inhomogeneities, multicomponent relaxation, and nonlinear pulsed excitations introduce significant mathematical and computational challenges. We present a spectral-diagonalization-based matrix exponential integration (SD-MEI) algorithm for efficient and stable solutions of full-Bloch equations in SNMR. Conventional explicit numerical methods exhibit cumulative discretization errors and escalating computational costs due to step-size dependence and finite precision limitations. SD-MEI integrates spectral diagonalization with matrix exponential operations, replacing iterative computations with a single eigendecomposition of the system matrix. This approach achieves parameter-robust computational complexity while maintaining numerical stability across broad B1 field strengths (10−10 T to 10−5 T) and relaxation times (10 ms to 1000 ms). Validated for steady-state free precession (SSFP) dynamics in heterogeneous geomagnetic environments, the method enables high-accuracy modeling of transient magnetization evolution with large time steps. The framework advances SNMR efficient forward modeling and inversion while optimizing protocols by resolving critical limitations in existing numerical and analytical approaches.
•Modeling of Magnetization Dynamics: Accurately describes magnetization vectors over broad excitation fields.•Control of Computational Complexity: Keeps computation stable, improving efficiency by 20–1000x.•Improved Numerical Stability: Solves convergence issues in stiff and highly nonlinear systems.•Temporal Flexibility: Computes magnetization at any time without affecting overall accuracy. |
| ArticleNumber | 106073 |
| Author | Ren, Chunpeng Wang, Qingyue Wang, Liang Lin, Tingting Wang, Yunzhi Jiang, Chuandong |
| Author_xml | – sequence: 1 givenname: Tingting orcidid: 0000-0002-6061-2311 surname: Lin fullname: Lin, Tingting organization: State Key Laboratory of Deep Earth Exploration and Imaging, College of Instrumentation and Electrical Engineering, Jilin University, Changchun, 130026, China – sequence: 2 givenname: Qingyue orcidid: 0000-0003-3057-5094 surname: Wang fullname: Wang, Qingyue organization: State Key Laboratory of Deep Earth Exploration and Imaging, College of Instrumentation and Electrical Engineering, Jilin University, Changchun, 130026, China – sequence: 3 givenname: Chuandong orcidid: 0000-0001-5373-6132 surname: Jiang fullname: Jiang, Chuandong email: jiangchuandong@jlu.edu.cn organization: State Key Laboratory of Deep Earth Exploration and Imaging, College of Instrumentation and Electrical Engineering, Jilin University, Changchun, 130026, China – sequence: 4 givenname: Chunpeng orcidid: 0009-0007-2411-1759 surname: Ren fullname: Ren, Chunpeng organization: State Key Laboratory of Deep Earth Exploration and Imaging, College of Instrumentation and Electrical Engineering, Jilin University, Changchun, 130026, China – sequence: 5 givenname: Yunzhi orcidid: 0000-0003-3301-1921 surname: Wang fullname: Wang, Yunzhi organization: State Key Laboratory of Deep Earth Exploration and Imaging, College of Instrumentation and Electrical Engineering, Jilin University, Changchun, 130026, China – sequence: 6 givenname: Liang orcidid: 0000-0002-7236-786X surname: Wang fullname: Wang, Liang email: wangliang1985@jlu.edu.cn organization: School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, China |
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| Cites_doi | 10.1016/j.mri.2010.07.003 10.1103/PhysRevE.62.1290 10.1103/PhysRev.70.460 10.1190/1.3258342 10.1109/TGRS.2007.903829 10.1007/BF03166553 10.1016/j.jappgeo.2008.05.002 10.1190/geo2013-0452.1 10.1093/gji/ggab321 10.1016/j.jmr.2010.07.012 10.3997/1873-0604.2005013 10.1029/2021GL095381 10.1016/j.pnmrs.2008.01.002 10.1016/j.cageo.2024.105705 10.1119/1.4878621 10.1002/(SICI)1099-0534(1997)9:1<1::AID-CMR1>3.0.CO;2-2 10.1007/s10712-014-9304-0 10.1109/TGRS.2022.3221624 10.1103/PhysRev.69.37 10.3390/app10082850 |
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| References | Hertrich (b10) 2008; 53 Grombacher, Liu, Griffiths, Vang, Larsen (b8) 2021; 48 Bain, Anand, Nie (b1) 2010; 206 Behroozmand, Keating, Auken (b2) 2015; 36 Frimmer, Novotny (b4) 2014; 82 Madhu, Kumar (b15) 1997; 9 Girard, Legchenko, Boucher (b5) 2005; 3 Bloch (b3) 1946; 70 Hertrich, Braun, Gunther, Green, Yaramanci (b11) 2007; 45 Purcell, Torrey, Pound (b19) 1946; 69 Griffiths, Grombacher, Larsen (b6) 2021; 227 Griffiths, Grombacher, Liu, Vang, Larsen (b7) 2022; 60 Legchenko (b14) 2004; 25 Mohnke, Yaramanci (b17) 2008; 66 Murase, Tanki (b18) 2011; 29 Singh, Srivastava (b20) 2020; 10 Weichman, Lavely, Ritzwoller (b21) 2000; 62 Johnston (b13) 2020; 2020 Hertrich, Green, Braun, Yaramanci (b12) 2009; 74 Miao, Wang, Wang, Zheng, He, Ren, Jiang (b16) 2024; 192 Grombacher, Walbrecker, Knight (b9) 2014; 79 Grombacher (10.1016/j.cageo.2025.106073_b9) 2014; 79 Hertrich (10.1016/j.cageo.2025.106073_b10) 2008; 53 Mohnke (10.1016/j.cageo.2025.106073_b17) 2008; 66 Legchenko (10.1016/j.cageo.2025.106073_b14) 2004; 25 Bloch (10.1016/j.cageo.2025.106073_b3) 1946; 70 Frimmer (10.1016/j.cageo.2025.106073_b4) 2014; 82 Miao (10.1016/j.cageo.2025.106073_b16) 2024; 192 Griffiths (10.1016/j.cageo.2025.106073_b7) 2022; 60 Purcell (10.1016/j.cageo.2025.106073_b19) 1946; 69 Bain (10.1016/j.cageo.2025.106073_b1) 2010; 206 Griffiths (10.1016/j.cageo.2025.106073_b6) 2021; 227 Hertrich (10.1016/j.cageo.2025.106073_b11) 2007; 45 Hertrich (10.1016/j.cageo.2025.106073_b12) 2009; 74 Behroozmand (10.1016/j.cageo.2025.106073_b2) 2015; 36 Girard (10.1016/j.cageo.2025.106073_b5) 2005; 3 Weichman (10.1016/j.cageo.2025.106073_b21) 2000; 62 Grombacher (10.1016/j.cageo.2025.106073_b8) 2021; 48 Singh (10.1016/j.cageo.2025.106073_b20) 2020; 10 Murase (10.1016/j.cageo.2025.106073_b18) 2011; 29 Madhu (10.1016/j.cageo.2025.106073_b15) 1997; 9 Johnston (10.1016/j.cageo.2025.106073_b13) 2020; 2020 |
| References_xml | – volume: 25 start-page: 621 year: 2004 end-page: 636 ident: b14 article-title: Magnetic resonance sounding: Enhanced modeling of a phase shift publication-title: Appl. Magn. Reson. – volume: 62 start-page: 1290 year: 2000 ident: b21 article-title: Theory of surface nuclear magnetic resonance with applications to geophysical imaging problems publication-title: Phys. Rev. E – volume: 70 start-page: 460 year: 1946 ident: b3 article-title: Nuclear induction publication-title: Phys. Rev. – volume: 9 start-page: 1 year: 1997 end-page: 12 ident: b15 article-title: Bloch equations revisited: New analytical solutions for the generalized Bloch equations publication-title: Concepts Magn. Reson.: An Educ. J. – volume: 192 year: 2024 ident: b16 article-title: Forward modeling of single-sided magnetic resonance and evaluation of T2 fitting error based on geometric analytical method publication-title: Comput. Geosci. – volume: 206 start-page: 227 year: 2010 end-page: 240 ident: b1 article-title: Exact solution to the Bloch equations and application to the Hahn echo publication-title: J. Magn. Reson. – volume: 60 start-page: 1 year: 2022 end-page: 10 ident: b7 article-title: Forward modeling steady-state free precession in surface NMR publication-title: IEEE Trans. Geosci. Remote Sens. – volume: 36 start-page: 27 year: 2015 end-page: 85 ident: b2 article-title: A review of the principles and applications of the NMR technique for near-surface characterization publication-title: Surv. Geophys. – volume: 82 start-page: 947 year: 2014 end-page: 954 ident: b4 article-title: The classical Bloch equations publication-title: Am. J. Phys. – volume: 2020 year: 2020 ident: b13 article-title: Solution of the Bloch equations including relaxation publication-title: Concepts Magn. Reson. Part A – volume: 29 start-page: 126 year: 2011 end-page: 131 ident: b18 article-title: Numerical solutions to the time-dependent Bloch equations revisited publication-title: Magn. Reson. Imaging – volume: 66 start-page: 73 year: 2008 end-page: 81 ident: b17 article-title: Pore size distributions and hydraulic conductivities of rocks derived from magnetic resonance sounding relaxation data using multi-exponential decay time inversion publication-title: J. Appl. Geophys. – volume: 227 start-page: 1905 year: 2021 end-page: 1916 ident: b6 article-title: Efficient numerical Bloch solutions for multipulse surface NMR publication-title: Geophys. J. Int. – volume: 3 start-page: 187 year: 2005 end-page: 194 ident: b5 article-title: Stability of MRS signal and estimation of data quality publication-title: Near Surf. Geophys. – volume: 79 start-page: E329 year: 2014 end-page: E339 ident: b9 article-title: Imparting a phase during excitation for improved resolution in surface nuclear magnetic resonance publication-title: Geophysics – volume: 74 start-page: G47 year: 2009 end-page: G59 ident: b12 article-title: High-resolution surface NMR tomography of shallow aquifers based on multioffset measurements publication-title: Geophysics – volume: 48 year: 2021 ident: b8 article-title: Steady-state surface NMR for mapping of groundwater publication-title: Geophys. Res. Lett. – volume: 53 start-page: 227 year: 2008 end-page: 248 ident: b10 article-title: Imaging of groundwater with nuclear magnetic resonance publication-title: Prog. Nucl. Magn. Reson. Spectrosc. – volume: 45 start-page: 3752 year: 2007 end-page: 3759 ident: b11 article-title: Surface nuclear magnetic resonance tomography publication-title: IEEE Trans. Geosci. Remote Sens. – volume: 69 start-page: 37 year: 1946 ident: b19 article-title: Resonance absorption by nuclear magnetic moments in a solid publication-title: Phys. Rev. – volume: 10 start-page: 2850 year: 2020 ident: b20 article-title: Numerical simulation for fractional-order Bloch equation arising in nuclear magnetic resonance by using the Jacobi polynomials publication-title: Appl. Sci. – volume: 2020 issue: 1 year: 2020 ident: 10.1016/j.cageo.2025.106073_b13 article-title: Solution of the Bloch equations including relaxation publication-title: Concepts Magn. Reson. Part A – volume: 29 start-page: 126 issue: 1 year: 2011 ident: 10.1016/j.cageo.2025.106073_b18 article-title: Numerical solutions to the time-dependent Bloch equations revisited publication-title: Magn. Reson. Imaging doi: 10.1016/j.mri.2010.07.003 – volume: 62 start-page: 1290 issue: 1 year: 2000 ident: 10.1016/j.cageo.2025.106073_b21 article-title: Theory of surface nuclear magnetic resonance with applications to geophysical imaging problems publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.62.1290 – volume: 70 start-page: 460 issue: 7–8 year: 1946 ident: 10.1016/j.cageo.2025.106073_b3 article-title: Nuclear induction publication-title: Phys. Rev. doi: 10.1103/PhysRev.70.460 – volume: 74 start-page: G47 issue: 6 year: 2009 ident: 10.1016/j.cageo.2025.106073_b12 article-title: High-resolution surface NMR tomography of shallow aquifers based on multioffset measurements publication-title: Geophysics doi: 10.1190/1.3258342 – volume: 45 start-page: 3752 issue: 11 year: 2007 ident: 10.1016/j.cageo.2025.106073_b11 article-title: Surface nuclear magnetic resonance tomography publication-title: IEEE Trans. Geosci. Remote Sens. doi: 10.1109/TGRS.2007.903829 – volume: 25 start-page: 621 issue: 3 year: 2004 ident: 10.1016/j.cageo.2025.106073_b14 article-title: Magnetic resonance sounding: Enhanced modeling of a phase shift publication-title: Appl. Magn. Reson. doi: 10.1007/BF03166553 – volume: 66 start-page: 73 issue: 3–4 year: 2008 ident: 10.1016/j.cageo.2025.106073_b17 article-title: Pore size distributions and hydraulic conductivities of rocks derived from magnetic resonance sounding relaxation data using multi-exponential decay time inversion publication-title: J. Appl. Geophys. doi: 10.1016/j.jappgeo.2008.05.002 – volume: 79 start-page: E329 issue: 6 year: 2014 ident: 10.1016/j.cageo.2025.106073_b9 article-title: Imparting a phase during excitation for improved resolution in surface nuclear magnetic resonance publication-title: Geophysics doi: 10.1190/geo2013-0452.1 – volume: 227 start-page: 1905 issue: 3 year: 2021 ident: 10.1016/j.cageo.2025.106073_b6 article-title: Efficient numerical Bloch solutions for multipulse surface NMR publication-title: Geophys. J. Int. doi: 10.1093/gji/ggab321 – volume: 206 start-page: 227 issue: 2 year: 2010 ident: 10.1016/j.cageo.2025.106073_b1 article-title: Exact solution to the Bloch equations and application to the Hahn echo publication-title: J. Magn. Reson. doi: 10.1016/j.jmr.2010.07.012 – volume: 3 start-page: 187 issue: 3 year: 2005 ident: 10.1016/j.cageo.2025.106073_b5 article-title: Stability of MRS signal and estimation of data quality publication-title: Near Surf. Geophys. doi: 10.3997/1873-0604.2005013 – volume: 48 issue: 23 year: 2021 ident: 10.1016/j.cageo.2025.106073_b8 article-title: Steady-state surface NMR for mapping of groundwater publication-title: Geophys. Res. Lett. doi: 10.1029/2021GL095381 – volume: 53 start-page: 227 issue: 4 year: 2008 ident: 10.1016/j.cageo.2025.106073_b10 article-title: Imaging of groundwater with nuclear magnetic resonance publication-title: Prog. Nucl. Magn. Reson. Spectrosc. doi: 10.1016/j.pnmrs.2008.01.002 – volume: 192 year: 2024 ident: 10.1016/j.cageo.2025.106073_b16 article-title: Forward modeling of single-sided magnetic resonance and evaluation of T2 fitting error based on geometric analytical method publication-title: Comput. Geosci. doi: 10.1016/j.cageo.2024.105705 – volume: 82 start-page: 947 issue: 10 year: 2014 ident: 10.1016/j.cageo.2025.106073_b4 article-title: The classical Bloch equations publication-title: Am. J. Phys. doi: 10.1119/1.4878621 – volume: 9 start-page: 1 issue: 1 year: 1997 ident: 10.1016/j.cageo.2025.106073_b15 article-title: Bloch equations revisited: New analytical solutions for the generalized Bloch equations publication-title: Concepts Magn. Reson.: An Educ. J. doi: 10.1002/(SICI)1099-0534(1997)9:1<1::AID-CMR1>3.0.CO;2-2 – volume: 36 start-page: 27 year: 2015 ident: 10.1016/j.cageo.2025.106073_b2 article-title: A review of the principles and applications of the NMR technique for near-surface characterization publication-title: Surv. Geophys. doi: 10.1007/s10712-014-9304-0 – volume: 60 start-page: 1 year: 2022 ident: 10.1016/j.cageo.2025.106073_b7 article-title: Forward modeling steady-state free precession in surface NMR publication-title: IEEE Trans. Geosci. Remote Sens. doi: 10.1109/TGRS.2022.3221624 – volume: 69 start-page: 37 issue: 1–2 year: 1946 ident: 10.1016/j.cageo.2025.106073_b19 article-title: Resonance absorption by nuclear magnetic moments in a solid publication-title: Phys. Rev. doi: 10.1103/PhysRev.69.37 – volume: 10 start-page: 2850 issue: 8 year: 2020 ident: 10.1016/j.cageo.2025.106073_b20 article-title: Numerical simulation for fractional-order Bloch equation arising in nuclear magnetic resonance by using the Jacobi polynomials publication-title: Appl. Sci. doi: 10.3390/app10082850 |
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| Title | Spectral-diagonalization-based matrix exponential integration for efficient and stable solutions of full-Bloch equations in surface NMR |
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