绝热脉冲磁共振地下水探测技术数值模拟及影响分析

杨玉晶; 赵汗青; 王鹏飞; 林婷婷

doi:10.7498/aps.69.20200015

摘要

磁共振测深技术能够定性、定量探测地下水, 且信息量丰富, 成本较低, 在水资源探测领域有较好的发展前景. 传统磁共振探测主磁场为地磁场, 信号仅为纳伏级, 极易被环境噪声淹没. 绝热脉冲等信号增强方法是当前国际磁共振领域关注的研究热点. 通过满足绝热条件的连续变幅、变频发射方式, 能够有效增大磁共振信号幅度, 改善探测信噪比. 但绝热技术激发原理复杂、建模实现困难且计算量极大, 相关理论报道较少. 针对以上问题, 本文从基本磁共振原理及绝热条件公式出发, 推导了基于绝热脉冲技术的磁共振横向磁化强度及灵敏度核函数计算方式, 通过插值实现了绝热脉冲的高效正演建模, 并比较了几种不通发射参数对信号幅度的影响, 为磁共振绝热脉冲仪器的研发提供理论支撑. 相比于传统技术, 在相同激发电流条件下, 匹配80 ms发射时间, 绝热技术能够在深部达到最大16.56倍信号增强效果. 本文的研究结果, 将为磁共振技术在城镇等复杂噪声环境地区的应用提供有力支撑.

关键词:

Abstract

Magnetic resonance sounding (MRS) technology used to detect groundwater directly and quantificationally, which owns the advantages of rich information and low cost. In these years, it has shown significant potential applications in hydrological detections. Considering the traditional measurements with the geomagnetic field, the nano-valt MRS signals are easy to suppress to environmental noise. As one of the MRS signal enhancement methods, the adiabatic pulse was quite popular recently. It is transmitted with variable frequency and amplitude pulse satisfying the adiabatic condition, which can enhance the signal amplitude and signal-to-noise ratio several times. However, there are only a few reports about this method, especially its geophysical modeling. Thus, we introduce the calculating progress of transverse magnetization and kernel function for this method. By employing the interpolation, the computation cost of forward modeling is obviously reduced. Moreover, several different settings of adiabatic transmitting factors are also proceeded to obtain certain results. In conclusion, a pulse moment with 80 ms transmitting duration and 30 quality factor produces a maximum signal amplitude that is enhanced 16.56 times for deep areas. The research in this paper could provide powerful support for MRS method used in noisy environments.

Keywords:

作者及机构信息

1.
吉林大学仪器科学与电气工程学院, 长春　130061

2.
吉林大学, 地球信息探测仪器教育部重点实验室, 长春　130061

通信作者: 林婷婷, ttlin@jlu.edu.cn

基金项目: 国家级-国家自然科学基金优秀青年基金项目(41722405)

Authors and contacts

1.
College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130061, China

2.
Key Laboratory of Geophysical Exploration Equipment, Ministry of Education, Jilin University, Changchun 130061, China

Corresponding author: Lin Ting-Ting, ttlin@jlu.edu.cn

文章全文 : translate this paragraph

参考文献

[1]	吴璐苹, 石昆法, 李荫槐, 李松浩 1996 地球物理学报 39 712 Google Scholar Wu L P, Shi K F, Li Y H, Li S H 1996 Chin. J. Geophys. 39 712 Google Scholar
[2]	Di Q Y, Xue G Q, Fu C M, Wang R 2020 Sci. Bull. 65 611 Google Scholar
[3]	Di Q Y, Wang M Y 2010 Bull. Eng. Geol. Environ. 69 105 Google Scholar
[4]	Di Q Y, Xue G Q, Lei D, Wang Z X, Zhang Y M, Wang S, Zhang Q M 2018 J. Appl. Geophys. 158 65 Google Scholar
[5]	侯彦威 2012 地球物理学进展 27 2698 Google Scholar Hou Y W 2012 Prog. Geophys. 27 2698 Google Scholar
[6]	傅良魁, 孟海东, 宋宇辰 1993 物探与化探 6 435 Fu L K, Meng H D, Song Y C 1993 Geophys. Geochem. Explor. 6 435
[7]	Behroozmand A A, Keating K, Auken E 2015 Surv. Geophys. 36 27 Google Scholar
[8]	林君, 段清明, 王应吉 2010 核磁共振找水仪原理与应用 (北京: 科学出版社) 第7—13页 Lin J, Duan Q M, Wang Y J 2010 Theory and Design of Magnetic Resonance Sounding Instrument for Groundwater Detection and Its Applications (Beijing: Science Press) pp7－13 (in Chinese)
[9]	Hertrich M, Braun M, Gunther T 2007 IEEE Trans. Geosci. Remote Sens. 45 3752 Google Scholar
[10]	潘玉玲, 张昌达 2000 地面核磁共振找水理论和方法 (北京: 中国地质大学出版社) 第1—5页 Pan Y L, Zhang C D 2000 Theory and Method of Surface Nuclear Magnetic Resonance Instrument for Groundwater Detection (Beijing: China University of Geosciences Press) pp1－5 (in Chinese)
[11]	孙淑琴, 林君, 张庆文, 嵇艳鞠 2005 物探与化探 29 153 Google Scholar Sun S Q, Lin J, Zhang Q W, Ji Y J 2005 Geophys. Geochem. Explor. 29 153 Google Scholar
[12]	Davis A C, Dlugosch R, Queitsch M, Macnae J C, Stolz R, Mueller-Petke M 2014 Geophys. Res. Lett. 41 4222 Google Scholar
[13]	Lin T T, Zhang Y, Lee Y H, Krause H J, Lin J 2014 Rev. Sci. Instrum. 85 114708 Google Scholar
[14]	Jiang C D, Lin J, Duan Q M, Sun S Q, Tian B F 2011 Near Surf. Geophys. 9 459 Google Scholar
[15]	Costabel S, Mueller-Petke M 2014 Near Surf. Geophys. 12 185 Google Scholar
[16]	Larsen J J 2016 Geophysics 81 WB1 Google Scholar
[17]	Legchenko A, Valla P 2003 J. Appl. Geophys. 53 103 Google Scholar
[18]	Larsen J J, Dalgaard E, Auken E 2014 Geophys. J. Int. 196 828 Google Scholar
[19]	Walsh D O 2008 J. Appl. Geophys. 66 140 Google Scholar
[20]	Mueller-Petke M, Costabel S 2014 Near Surf. Geophys. 12 199 Google Scholar
[21]	Lin T T, Zhang Y, Yi X F, Fan T H, Wan L 2018 Geophys. J. Int. 213 727 Google Scholar
[22]	林婷婷, 张扬, 杨莹, 杨莹, 滕飞, 万玲 2018 地球物理学报 61 3812 Google Scholar Lin T T, Zhang Y, Yang Y, Yang Y J, Teng F, Wan L 2018 Chin. J. Geophys. 61 3812 Google Scholar
[23]	Grombacher D, Knight R 2015 Geophysics 80 E329 Google Scholar
[24]	Lin T T, Yang Y J, Teng F, Wan L 2017 Geophys. J. Int. 212 1463 Google Scholar
[25]	Grunewald E, Grombacher D, Walsh D 2016 Geophysics 81 WB85 Google Scholar
[26]	Tannus A, Garwood M 1997 NMR Biomed. 10 423 Google Scholar
[27]	Garwood M, DelaBarre L 2002 J. Magn. Reson. 153 155 Google Scholar
[28]	Wi S, Kim C, Schurko R, Frydman L 2017 J. Magn. Reson. 277 131 Google Scholar
[29]	Levitt M H 2002 Spin Dynamics-Basics of Nuclear Magnetic Resonance (Chichester: John Wiley & Sons, LTD) pp1–6
[30]	Callaghan P 2007 Principles of Nuclear Magnetic Resonance Microscopy (New Zealand: Oxford University Press) pp1–8
[31]	Hertrich M 2008 Prog. Nucl. Magn. Reson. Spectrosc. 53 227 Google Scholar
[32]	Weichman P B, Lavely E M, Ritzwoller M H 2000 Phys. Rev. E 62 1290 Google Scholar
[33]	Walbrecker J O, Hertrich M, Green A G 2011 Geophysics 76 G1 Google Scholar
[34]	Grombacher D, Walbrecker J O, Knight R 2014 Geophysics 79 E329 Google Scholar
[35]	Bloch F 1946 Phys. Rev. 70 460 Google Scholar
[36]	Baum J, Tycko R, Pines A 1985 Phys. Rev. A 32 3435 Google Scholar
[37]	Behroozmand A A, Auken E, Fiandaca G, Rejkjaer S 2016 Geophys. J. Int. 205 243 Google Scholar

施引文献

图 1 磁共振激发原理图　(a) 传统方式; (b) 绝热方式

Fig. 1. Principle of excitation dynamics of magnetic resonance sounding: (a) Traditional type; (b) adiabatic type.

下载: 全尺寸图片幻灯片

图 2 绝热磁共振激发过程　(a) 发射时序, 红色曲线为发射电流, 蓝色曲线为FID信号; (b) 激发磁场与磁化强度示意图, 深红箭头和蓝色线分别表示激发磁场与磁化强度

Fig. 2. Excitation process of the adiabatic pulses: (a) The sequence diagram of the transmitting current (red) and FID signal (blue); (b) the relationship of the excitation magnetic field (dark red arrow) and magnetization (blue line).

下载: 全尺寸图片幻灯片

图 3 双曲正切绝热半波横向磁化强度与有效激发磁场关系图(品质因数Q = 30, 脉冲持续时间τ = 80 ms)　(a)发射波形实时幅值; (b)频率调制函数; (c)磁化强度x分量、y分量及模值

Fig. 3. The relationship of transverse magnetization and exciting magnetic based on hyperbolic tangent AHP pulse: (a) The waveform of transmitting current amplitude; (b) its frequency vs. time; (c) magnetization x-component, y-component and real value.

下载: 全尺寸图片幻灯片

图 4 相同激发电流分布(1—600 A)情况下, 脉冲持续时间τ不同时, 绝热半波对应的灵敏度核函数实部(品质因数Q = 30)　(a) τ = 20 ms; (b) τ = 40 ms; (c) τ = 60 ms; (d) τ = 80 ms; (e) τ = 100 ms; (f) τ = 120 ms; (g) τ = 140 ms; (h) τ = 160 ms

Fig. 4. The real kernel function of adiabatic half-passage pulses for the same excitation current (1–600 A) corresponding to different τ, with quality factor Q = 30: (a) τ = 20 ms; (b) τ = 40 ms; (c) τ = 60 ms; (d) τ = 80 ms; (e) τ = 100 ms; (f) τ = 120 ms; (g) τ = 140 ms; (h) τ = 160 ms.

下载: 全尺寸图片幻灯片

图 5 相同激发电流分布情况下, 脉冲持续时间τ不同时绝热半波对应的灵敏度核函数虚部(品质因数Q = 30)　(a) τ = 20 ms; (b) τ = 40 ms; (c) τ = 60 ms; (d) τ = 80 ms; (e) τ = 100 ms; (f) τ = 120 ms; (g) τ = 140 ms; (h) τ = 160 ms

Fig. 5. The imaginary kernel function of adiabatic half-passage pulses for the same excitation current (1–600 A) corresponding to different τ, with quality factor Q = 30: (a) τ = 20 ms; (b) τ = 40 ms; (c) τ = 60 ms; (d) τ = 80 ms; (e) τ = 100 ms; (f) τ = 120 ms; (g) τ = 140 ms; (h) τ = 160 ms.

下载: 全尺寸图片幻灯片

图 6 相同脉冲矩(0.01—7.3 A·s)情况下, 脉冲持续时间τ不同时绝热半波对应的灵敏度核函数实部(品质因数Q = 30)　(a) τ = 20 ms, 最大600 A电流; (b) τ = 40 ms, 最大300 A电流; (c) τ = 60 ms, 最大200 A电流; (d) τ = 80 ms, 最大150 A电流; (e) τ = 100 ms, 最大120 A电流; (f) τ = 120 ms, 最大100 A电流; (g) τ = 140 ms, 最大85.7 A电流; (h) τ = 160 ms, 最大75 A电流

Fig. 6. The real kernel function of adiabatic half-passage pulses for the same pulse moment corresponding to different τ, with quality factor Q = 30: (a) τ = 20 ms with maximum current 600 A; (b) τ = 40 ms with maximum current 300 A; (c) τ = 60 ms with maximum current 200 A; (d) τ = 80 ms with maximum current 150 A; (e) τ = 100 ms with maximum current 120 A; (f) τ = 120 ms with maximum current 100 A; (g) τ = 140 ms with maximum current 85.7 A; (h) τ = 160 ms with maximum current 75 A.

下载: 全尺寸图片幻灯片

图 7 相同脉冲矩(0.01—7.3 A.s)情况下, 脉冲持续时间τ不同时绝热半波对应的灵敏度核函数虚部(品质因数Q = 30)　(a) τ = 20 ms, 最大600 A电流; (b) τ = 40 ms, 最大300 A电流; (c) τ = 60 ms, 最大200 A电流; (d) τ = 80 ms, 最大150 A电流; (e) τ = 100 ms, 最大120 A电流; (f) τ = 120 ms, 最大100 A电流; (g) τ = 140 ms, 最大85.7 A电流; (h) τ = 160 ms, 最大75 A电流

Fig. 7. The imaginary kernel function of adiabatic half-passage pulses for the same pulse moment corresponding to different τ, with quality factor Q = 30: (a) τ = 20 ms with maximum current 600 A; (b) τ = 40 ms with maximum current 300 A; (c) τ = 60 ms with maximum current 200 A; (d) τ = 80 ms with maximum current 150 A; (e) τ = 100 ms with maximum current 120 A; (f) τ = 120 ms with maximum current 100 A; (g) τ = 140 ms with maximum current 85.7 A; (h) τ = 160 ms with maximum current 75 A.

下载: 全尺寸图片幻灯片

图 8 相同脉冲矩(0.01—7.3 A·s)情况下, 在不同脉冲持续时间及电流条件时绝热半波对应的正演响应(假设地下半空间内存在10%均匀的含水量, 发射线圈的品质因数Q = 30)

Fig. 8. The forward modeling of adiabatic half-passage pulse for the same pulse moment (0.01–7.3 A·s) with different τ and current. The modeling assume a homogeneous aquifer subsurface with 10% water content, the quality factor Q = 30.

下载: 全尺寸图片幻灯片

图 9 脉冲持续时间τ = 80 ms, 品质因数Q不同时绝热半波对应的灵敏度核函数的(a), (b), (c), (d)实部和(e), (f), (g), (h)虚部　(a), (e) Q = 10; (b), (f) Q = 20; (c), (g) Q = 30; (d), (h) Q = 40

Fig. 9. The (a), (b), (c), (d) real and (e), (f), (g), (h) imaginary part of the kernel function of adiabatic half-passage pulses for different quality factor Q with τ = 80 ms: (a), (e) Q = 10; (b), (f) Q = 20; (c), (g) Q = 30; (d), (h) Q = 40.

下载: 全尺寸图片幻灯片

图 10 相同绝热脉冲电流(1—600 A)条件下, 品质因数Q不同时绝热半波对应的正演响应(灰色虚线为传统激发方式信号响应, 假设地下半空间内存在10%均匀的含水量, 发射脉冲持续时间为80 ms)

Fig. 10. The forward modeling of adiabatic half-passage pulse for the same pulse current (1–600 A) with different quality factor Q (The gray dotted line is the initial amplitude of traditional nuclear magnetic resonance responses). The modeling assume a homogeneous aquifer subsurface with 10% water content with τ = 80 ms.

下载: 全尺寸图片幻灯片

[1]	吴璐苹, 石昆法, 李荫槐, 李松浩 1996 地球物理学报 39 712 Google Scholar Wu L P, Shi K F, Li Y H, Li S H 1996 Chin. J. Geophys. 39 712 Google Scholar
[2]	Di Q Y, Xue G Q, Fu C M, Wang R 2020 Sci. Bull. 65 611 Google Scholar
[3]	Di Q Y, Wang M Y 2010 Bull. Eng. Geol. Environ. 69 105 Google Scholar
[4]	Di Q Y, Xue G Q, Lei D, Wang Z X, Zhang Y M, Wang S, Zhang Q M 2018 J. Appl. Geophys. 158 65 Google Scholar
[5]	侯彦威 2012 地球物理学进展 27 2698 Google Scholar Hou Y W 2012 Prog. Geophys. 27 2698 Google Scholar
[6]	傅良魁, 孟海东, 宋宇辰 1993 物探与化探 6 435 Fu L K, Meng H D, Song Y C 1993 Geophys. Geochem. Explor. 6 435
[7]	Behroozmand A A, Keating K, Auken E 2015 Surv. Geophys. 36 27 Google Scholar
[8]	林君, 段清明, 王应吉 2010 核磁共振找水仪原理与应用 (北京: 科学出版社) 第7—13页 Lin J, Duan Q M, Wang Y J 2010 Theory and Design of Magnetic Resonance Sounding Instrument for Groundwater Detection and Its Applications (Beijing: Science Press) pp7－13 (in Chinese)
[9]	Hertrich M, Braun M, Gunther T 2007 IEEE Trans. Geosci. Remote Sens. 45 3752 Google Scholar
[10]	潘玉玲, 张昌达 2000 地面核磁共振找水理论和方法 (北京: 中国地质大学出版社) 第1—5页 Pan Y L, Zhang C D 2000 Theory and Method of Surface Nuclear Magnetic Resonance Instrument for Groundwater Detection (Beijing: China University of Geosciences Press) pp1－5 (in Chinese)
[11]	孙淑琴, 林君, 张庆文, 嵇艳鞠 2005 物探与化探 29 153 Google Scholar Sun S Q, Lin J, Zhang Q W, Ji Y J 2005 Geophys. Geochem. Explor. 29 153 Google Scholar
[12]	Davis A C, Dlugosch R, Queitsch M, Macnae J C, Stolz R, Mueller-Petke M 2014 Geophys. Res. Lett. 41 4222 Google Scholar
[13]	Lin T T, Zhang Y, Lee Y H, Krause H J, Lin J 2014 Rev. Sci. Instrum. 85 114708 Google Scholar
[14]	Jiang C D, Lin J, Duan Q M, Sun S Q, Tian B F 2011 Near Surf. Geophys. 9 459 Google Scholar
[15]	Costabel S, Mueller-Petke M 2014 Near Surf. Geophys. 12 185 Google Scholar
[16]	Larsen J J 2016 Geophysics 81 WB1 Google Scholar
[17]	Legchenko A, Valla P 2003 J. Appl. Geophys. 53 103 Google Scholar
[18]	Larsen J J, Dalgaard E, Auken E 2014 Geophys. J. Int. 196 828 Google Scholar
[19]	Walsh D O 2008 J. Appl. Geophys. 66 140 Google Scholar
[20]	Mueller-Petke M, Costabel S 2014 Near Surf. Geophys. 12 199 Google Scholar
[21]	Lin T T, Zhang Y, Yi X F, Fan T H, Wan L 2018 Geophys. J. Int. 213 727 Google Scholar
[22]	林婷婷, 张扬, 杨莹, 杨莹, 滕飞, 万玲 2018 地球物理学报 61 3812 Google Scholar Lin T T, Zhang Y, Yang Y, Yang Y J, Teng F, Wan L 2018 Chin. J. Geophys. 61 3812 Google Scholar
[23]	Grombacher D, Knight R 2015 Geophysics 80 E329 Google Scholar
[24]	Lin T T, Yang Y J, Teng F, Wan L 2017 Geophys. J. Int. 212 1463 Google Scholar
[25]	Grunewald E, Grombacher D, Walsh D 2016 Geophysics 81 WB85 Google Scholar
[26]	Tannus A, Garwood M 1997 NMR Biomed. 10 423 Google Scholar
[27]	Garwood M, DelaBarre L 2002 J. Magn. Reson. 153 155 Google Scholar
[28]	Wi S, Kim C, Schurko R, Frydman L 2017 J. Magn. Reson. 277 131 Google Scholar
[29]	Levitt M H 2002 Spin Dynamics-Basics of Nuclear Magnetic Resonance (Chichester: John Wiley & Sons, LTD) pp1–6
[30]	Callaghan P 2007 Principles of Nuclear Magnetic Resonance Microscopy (New Zealand: Oxford University Press) pp1–8
[31]	Hertrich M 2008 Prog. Nucl. Magn. Reson. Spectrosc. 53 227 Google Scholar
[32]	Weichman P B, Lavely E M, Ritzwoller M H 2000 Phys. Rev. E 62 1290 Google Scholar
[33]	Walbrecker J O, Hertrich M, Green A G 2011 Geophysics 76 G1 Google Scholar
[34]	Grombacher D, Walbrecker J O, Knight R 2014 Geophysics 79 E329 Google Scholar
[35]	Bloch F 1946 Phys. Rev. 70 460 Google Scholar
[36]	Baum J, Tycko R, Pines A 1985 Phys. Rev. A 32 3435 Google Scholar
[37]	Behroozmand A A, Auken E, Fiandaca G, Rejkjaer S 2016 Geophys. J. Int. 205 243 Google Scholar

[1]	于家成, 仲佳勇, 安维明, 平永利. 短脉冲强激光驱动磁重联过程的靶后电势分布特征. 物理学报, 2021, 70(6): 065201. doi: 10.7498/aps.70.20201339
[2]	左娟莉, 杨泓, 魏炳乾, 侯精明, 张凯. 气力提升系统气液两相流数值模拟分析. 物理学报, 2020, 69(6): 064705. doi: 10.7498/aps.69.20191755
[3]	成玉国, 夏广庆. 感应式脉冲推力器中等离子体加速数值研究. 物理学报, 2017, 66(7): 075204. doi: 10.7498/aps.66.075204
[4]	刘扬, 韩燕龙, 贾富国, 姚丽娜, 王会, 史宇菲. 椭球颗粒搅拌运动及混合特性的数值模拟研究. 物理学报, 2015, 64(11): 114501. doi: 10.7498/aps.64.114501
[5]	王新鑫, 樊丁, 黄健康, 黄勇. 双钨极耦合电弧数值模拟. 物理学报, 2013, 62(22): 228101. doi: 10.7498/aps.62.228101
[6]	陈石, 王辉, 沈胜强, 梁刚涛. 液滴振荡模型及与数值模拟的对比. 物理学报, 2013, 62(20): 204702. doi: 10.7498/aps.62.204702
[7]	黄培培, 刘大刚, 刘腊群, 王辉辉, 夏梦局, 陈颖. 单路脉冲功率真空装置的三维数值模拟研究. 物理学报, 2013, 62(19): 192901. doi: 10.7498/aps.62.192901
[8]	刘智, 刁文婷, 王杰英, 梁强兵, 杨保东, 何军, 张天才, 王军民. 铯原子气室中相干布居俘获的参数依赖关系研究. 物理学报, 2012, 61(23): 233201. doi: 10.7498/aps.61.233201
[9]	石玗, 郭朝博, 黄健康, 樊丁. 脉冲电流作用下TIG电弧的数值分析. 物理学报, 2011, 60(4): 048102. doi: 10.7498/aps.60.048102
[10]	赵啦啦, 刘初升, 闫俊霞, 蒋小伟, 朱艳. 不同振动模式下颗粒分离行为的数值模拟. 物理学报, 2010, 59(4): 2582-2588. doi: 10.7498/aps.59.2582
[11]	蔡利兵, 王建国. 介质表面高功率微波击穿的数值模拟. 物理学报, 2009, 58(5): 3268-3273. doi: 10.7498/aps.58.3268
[12]	邓一鑫, 涂成厚, 吕福云. 非线性偏振旋转锁模自相似脉冲光纤激光器的研究. 物理学报, 2009, 58(5): 3173-3178. doi: 10.7498/aps.58.3173
[13]	朱昌盛, 王智平, 荆涛, 肖荣振. 二元合金微观偏析的相场法数值模拟. 物理学报, 2006, 55(3): 1502-1507. doi: 10.7498/aps.55.1502
[14]	郭文琼, 周晓军, 张雄军, 隋展, 吴登生. 等离子体电极普克尔盒电光开关单脉冲过程数值模拟. 物理学报, 2006, 55(7): 3519-3523. doi: 10.7498/aps.55.3519
[15]	张远涛, 王德真, 王艳辉. 大气压介质阻挡丝状放电时空演化数值模拟. 物理学报, 2005, 54(10): 4808-4815. doi: 10.7498/aps.54.4808
[16]	王艳辉, 王德真. 大气压下多脉冲均匀介质阻挡放电的研究. 物理学报, 2005, 54(3): 1295-1300. doi: 10.7498/aps.54.1295
[17]	朱鹏飞, 钱列加, 薛绍林, 林尊琪. 基于“神光-Ⅱ”装置的飞秒拍瓦级光学参量啁啾脉冲放大的特性分析与系统设计. 物理学报, 2003, 52(3): 587-594. doi: 10.7498/aps.52.587
[18]	秦颖, 王晓钢, 董闯, 郝胜智, 刘悦, 邹建新, 吴爱民, 关庆丰. 强流脉冲电子束诱发温度场及表面熔坑的形成. 物理学报, 2003, 52(12): 3043-3048. doi: 10.7498/aps.52.3043
[19]	訾炳涛, 姚可夫, 许光明, 崔建忠. 脉冲磁场下金属熔体凝固流场的数值模拟. 物理学报, 2003, 52(1): 115-119. doi: 10.7498/aps.52.115
[20]	丁伯江, 匡光力, 刘岳修, 沈慰慈, 俞家文, 石跃江. 低杂波电流驱动的数值模拟. 物理学报, 2002, 51(11): 2556-2561. doi: 10.7498/aps.51.2556

计量

文章访问数: 7225
PDF下载量: 82
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

绝热脉冲磁共振地下水探测技术数值模拟及影响分析