From 5fa0d36da669757ca76a83933d33dcab4150abf2 Mon Sep 17 00:00:00 2001 From: Dengda98 Date: Fri, 18 Apr 2025 14:24:04 +0800 Subject: [PATCH 1/5] DOC: add `grt.b2a` example in Tutorial --- docs/source/Tutorial/dynamic/gfunc.rst | 12 ++++++++++++ docs/source/Tutorial/dynamic/run/HFZ_head | 11 +++++++++++ docs/source/Tutorial/dynamic/run/run.sh | 6 ++++++ 3 files changed, 29 insertions(+) create mode 100644 docs/source/Tutorial/dynamic/run/HFZ_head diff --git a/docs/source/Tutorial/dynamic/gfunc.rst b/docs/source/Tutorial/dynamic/gfunc.rst index e7b07087..64808f7a 100644 --- a/docs/source/Tutorial/dynamic/gfunc.rst +++ b/docs/source/Tutorial/dynamic/gfunc.rst @@ -40,6 +40,18 @@ Python中计算动态格林函数的主函数为 :func:`compute_grn() HFZ +# END grt.b2a +head -n 10 HFZ > HFZ_head +echo "..." >> HFZ_head + # BEGIN SYN EXP # 合成结果在 syn_exp/ 目录下,以SAC格式保存。 grt.syn -GGRN/milrow_2_0_10 -S1e24 -A30 -Osyn_exp From 351d0d9b0a521d3ad0b18740869be1d0921c5054 Mon Sep 17 00:00:00 2001 From: Dengda98 Date: Fri, 18 Apr 2025 14:56:48 +0800 Subject: [PATCH 2/5] DOC: add some formulas for synthetic seismograms in Tutorial --- docs/source/Tutorial/dynamic/gfunc.rst | 2 +- docs/source/Tutorial/dynamic/syn.rst | 22 ++++++++++++++++++++++ 2 files changed, 23 insertions(+), 1 deletion(-) diff --git a/docs/source/Tutorial/dynamic/gfunc.rst b/docs/source/Tutorial/dynamic/gfunc.rst index 64808f7a..6309324d 100644 --- a/docs/source/Tutorial/dynamic/gfunc.rst +++ b/docs/source/Tutorial/dynamic/gfunc.rst @@ -107,7 +107,7 @@ Python中计算动态格林函数的主函数为 :func:`compute_grn() ` (\*表示对不同震源) ,C程序为 :command:`grt.syn`。 使用上节计算的格林函数,合成动态位移(理论地震图)。方便起见,这里统一使用milrow模型,震源深度2km,场点位于地表,震中距10km的格林函数,方位角30°。 +在已知三分量格林函数 :math:`W_m(t), Q_m(t), V_m(t)` 后,合成三分量位移 :math:`U_Z(t), U_R(t), U_T(t)` 的公式为 + +.. math:: + + \left\{ + \begin{aligned} + U_Z(t) &= D(t) * \left[ \sum_{m=0}^{m=2} A_m W_m(t) \right] \\ + U_R(t) &= D(t) * \left[ \sum_{m=0}^{m=2} A_m Q_m(t) \right] \\ + U_T(t) &= D(t) * \left[ \sum_{m=1}^{m=2} A_{m+3} V_m(t) \right] + \end{aligned} + \right. + +其中 :math:`D(t)` 为震源时间函数,:math:`*` 表示卷积,:math:`A_m` 为与方位角和震源机制相关的方向因子,其中 :math:`U_Z, U_R` 的方向因子相同,而 :math:`U_T` 的方向因子满足 + +.. math:: + + A_{m+3} = \frac{d A_m}{d (m\theta)}, m=1,2 + +其中 :math:`m` 为阶数,:math:`\theta` 为方位角。 + + .. note:: 合成位移的结果单位为 :math:`\text{cm}`。 From 9627429f8efab87850cf2b428aa2412d96a6ab0b Mon Sep 17 00:00:00 2001 From: Dengda98 Date: Fri, 18 Apr 2025 15:23:48 +0800 Subject: [PATCH 3/5] DOC: remove some typo --- docs/source/Tutorial/dynamic/gfunc.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/Tutorial/dynamic/gfunc.rst b/docs/source/Tutorial/dynamic/gfunc.rst index 6309324d..7adc37ce 100644 --- a/docs/source/Tutorial/dynamic/gfunc.rst +++ b/docs/source/Tutorial/dynamic/gfunc.rst @@ -36,7 +36,7 @@ Python中计算动态格林函数的主函数为 :func:`compute_grn() Date: Fri, 18 Apr 2025 17:55:25 +0800 Subject: [PATCH 4/5] DOC: add `docs/` reference --- docs/source/index.rst | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/source/index.rst b/docs/source/index.rst index 426ade16..00fe3a0d 100755 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -58,6 +58,8 @@ 以下包括 **Python** 和 **C** 两部分的API介绍。如果只关心程序的使用,可以只查看 **Python** 部分;若对具体实现过程感兴趣,尤其是在学习 **广义反射透射系数矩阵、离散波数法、线性Filon积分法、峰谷平均法** 等内容感到迷惑难解时,可以在运行程序的同时结合阅读相关 **C代码**,我在C代码中给出了 **明确的中文注释以及相关公式索引** ,希望能帮助你在学习相关内容时解答一些疑惑。 +本文档页面源码位于 Github主页的 `docs/ `_,可查看示例代码和画图脚本。 + .. toctree:: From 1cc45353d8aff8071758b14d357763ce4e4e1c8c Mon Sep 17 00:00:00 2001 From: Dengda98 Date: Fri, 18 Apr 2025 17:56:23 +0800 Subject: [PATCH 5/5] DOC: add "strain and stress calculation" in Tutorial --- docs/source/Tutorial/dynamic/run_upar/milrow | 9 + docs/source/Tutorial/dynamic/run_upar/run.py | 173 +++++++++++++++++ docs/source/Tutorial/dynamic/run_upar/run.sh | 28 +++ .../Tutorial/dynamic/run_upar/strain.png | Bin 0 -> 58325 bytes .../Tutorial/dynamic/run_upar/stress.png | Bin 0 -> 49978 bytes .../source/Tutorial/dynamic/strain_stress.rst | 183 +++++++++++++++++- docs/source/Tutorial/dynamic/syn.rst | 12 +- docs/source/Tutorial/static/run_upar/milrow | 9 + docs/source/Tutorial/static/run_upar/run.py | 62 ++++++ docs/source/Tutorial/static/run_upar/run.sh | 23 +++ .../static/run_upar/static_strain.png | Bin 0 -> 50882 bytes .../static/run_upar/static_stress.png | Bin 0 -> 44340 bytes .../Tutorial/static/static_strain_stress.rst | 29 ++- docs/source/Tutorial/static/static_syn.rst | 2 + 14 files changed, 523 insertions(+), 7 deletions(-) create mode 100644 docs/source/Tutorial/dynamic/run_upar/milrow create mode 100644 docs/source/Tutorial/dynamic/run_upar/run.py create mode 100755 docs/source/Tutorial/dynamic/run_upar/run.sh create mode 100644 docs/source/Tutorial/dynamic/run_upar/strain.png create mode 100644 docs/source/Tutorial/dynamic/run_upar/stress.png create mode 100644 docs/source/Tutorial/static/run_upar/milrow create mode 100644 docs/source/Tutorial/static/run_upar/run.py create mode 100755 docs/source/Tutorial/static/run_upar/run.sh create mode 100644 docs/source/Tutorial/static/run_upar/static_strain.png create mode 100644 docs/source/Tutorial/static/run_upar/static_stress.png diff --git a/docs/source/Tutorial/dynamic/run_upar/milrow b/docs/source/Tutorial/dynamic/run_upar/milrow new file mode 100644 index 00000000..a99f4912 --- /dev/null +++ b/docs/source/Tutorial/dynamic/run_upar/milrow @@ -0,0 +1,9 @@ +0.2 3.4 1.7 2.3 9e10 9e10 +0.6 3.7 1.9 2.4 9e10 9e10 +0.5 4.2 2.1 2.4 9e10 9e10 +0.5 4.6 2.3 2.5 9e10 9e10 +0.7 4.9 2.8 2.6 9e10 9e10 +0.5 5.1 2.9 2.7 9e10 9e10 +6.0 5.9 3.3 2.7 9e10 9e10 +1. 6.9 4.0 2.8 9e10 9e10 +0.0 8.2 4.7 3.2 9e10 9e10 \ No newline at end of file diff --git a/docs/source/Tutorial/dynamic/run_upar/run.py b/docs/source/Tutorial/dynamic/run_upar/run.py new file mode 100644 index 00000000..a648f2fd --- /dev/null +++ b/docs/source/Tutorial/dynamic/run_upar/run.py @@ -0,0 +1,173 @@ +# BEGIN GRN +import numpy as np +import pygrt + +modarr = np.loadtxt("milrow") + +pymod = pygrt.PyModel1D(modarr, depsrc=2.0, deprcv=0.0) + +# 传入calc_upar=True计算空间导数 +stgrn = pymod.compute_grn(distarr=[10], nt=500, dt=0.02, calc_upar=True)[0] +print(stgrn.__str__(extended=True)) +# 45 Trace(s) in Stream: +# .SYN..EXZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..VFZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..DDZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..HFZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..DSZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..SSZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zEXZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rEXZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zVFZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rVFZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zDDZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rDDZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zHFZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rHFZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zDSZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rDSZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zSSZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rSSZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..EXR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..VFR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..DDR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..HFR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..DSR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..SSR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zEXR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rEXR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zVFR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rVFR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zDDR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rDDR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zHFR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rHFR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zDSR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rDSR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zSSR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rSSR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..HFT | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..DST | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..SST | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zHFT | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rHFT | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zDST | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rDST | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zSST | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rSST | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# END GRN + + + +# BEGIN SYN DC +# 传入calc_upar=True计算空间导数 +stsyn = pygrt.utils.gen_syn_from_gf_DC(stgrn, M0=1e24, strike=33, dip=50, rake=120, az=30, calc_upar=True) +print(stsyn) +# 12 Trace(s) in Stream: +# .SYN..DCZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..DCR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..DCT | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zDCZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zDCR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zDCT | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rDCZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rDCR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..rDCT | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..tDCZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..tDCR | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..tDCT | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# END SYN DC + + +# BEGIN ZNE +# 传入ZNE=True可返回ZNE分量 +stsyn = pygrt.utils.gen_syn_from_gf_DC(stgrn, M0=1e24, strike=33, dip=50, rake=120, az=30, calc_upar=True, ZNE=True) +print(stsyn) +# 12 Trace(s) in Stream: +# .SYN..DCZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..DCN | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..DCE | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zDCZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zDCN | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..zDCE | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..nDCZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..nDCN | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..nDCE | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..eDCZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..eDCN | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..eDCE | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# END ZNE + +from obspy import * +import matplotlib.pyplot as plt + +def plot6(st6:Stream, title:str, out:str|None=None): + nt = st6[0].stats.npts + dt = st6[0].stats.delta + t = np.arange(nt)*dt + + MAX, MIN = 0, 9e30 + for tr in st6: + d = np.abs(tr.data) + if MAX < np.max(d): + MAX = np.max(d) + if MIN > np.min(d): + MIN = np.min(d) + + travtP = stsyn[0].stats.sac['t0'] + travtS = stsyn[0].stats.sac['t1'] + + fig, axs = plt.subplots(6, 1, figsize=(10, 7), gridspec_kw=dict(hspace=0.0), sharex=True) + for i in range(6): + tr = st6[i] + ax = axs[i] + + ax.plot(t, tr.data, c='k', lw=0.5, label=tr.stats.channel) + ax.legend(loc='upper left') + + ylims = ax.get_ylim() + if np.max(np.abs(np.array(ylims)))/MAX < 1e-5: + ylims = [-1, 1] + ax.set_ylim(ylims) + + # 绘制到时 + ax.vlines(travtP, *ylims, colors='b') + ax.text(travtP, ylims[1], "P", ha='left', va='top', color='b') + ax.vlines(travtS, *ylims, colors='r') + ax.text(travtS, ylims[1], "S", ha='left', va='top', color='r') + + ax.set_xlim([t[0], t[-1]]) + ax.set_ylim(np.array(ylims)*1.2) + + axs[0].set_title(title) + + if out is not None: + fig.savefig(out, dpi=100) + + + +# BEGIN STRAIN +st_strain = pygrt.utils.compute_strain(stsyn) +print(st_strain) +# 6 Trace(s) in Stream: +# .SYN..ZZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..ZN | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..ZE | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..NN | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..NE | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..EE | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# END STRAIN +plot6(st_strain, "Strain", "strain.png") + +# BEGIN STRESS +st_stress = pygrt.utils.compute_stress(stsyn) +print(st_stress) +# 6 Trace(s) in Stream: +# .SYN..ZZ | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..ZN | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..ZE | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..NN | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..NE | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# .SYN..EE | 1970-01-01T00:00:00.000000Z - 1970-01-01T00:00:09.980000Z | 50.0 Hz, 500 samples +# END STRESS +plot6(st_stress, "Stress", "stress.png") diff --git a/docs/source/Tutorial/dynamic/run_upar/run.sh b/docs/source/Tutorial/dynamic/run_upar/run.sh new file mode 100755 index 00000000..8e86afd4 --- /dev/null +++ b/docs/source/Tutorial/dynamic/run_upar/run.sh @@ -0,0 +1,28 @@ +#!/bin/bash + + +# BEGIN GRN +# -e 表示计算空间导数 +grt -Mmilrow -D2/0 -N500/0.02 -OGRN -R10 -e +# END GRN + +# BEGIN SYN DC +# -e 表示计算空间导数 +grt.syn -GGRN/milrow_2_0_10 -S1e24 -A30 -M33/50/120 -Osyn_dc -e +# END SYN DC + +# BEGIN ZNE +# -N 表示输出ZNE分量 +grt.syn -GGRN/milrow_2_0_10 -S1e24 -A30 -M33/50/120 -Osyn_dc_zne -e -N +# END ZNE + + +# BEGIN STRAIN +# 指定文件夹以及中间名,会在原文件夹内输出SAC格式的应变 +grt.strain syn_dc_zne/out +# END STRAIN + +# BEGIN STRESS +# 指定文件夹以及中间名,会在原文件夹内输出SAC格式的应变 +grt.stress syn_dc_zne/out +# END STRESS \ No newline at end of file diff --git a/docs/source/Tutorial/dynamic/run_upar/strain.png b/docs/source/Tutorial/dynamic/run_upar/strain.png new file mode 100644 index 0000000000000000000000000000000000000000..8cc34bd2e46ee82eb6f3553c7be9140d9da29330 GIT binary patch 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zk~$O(tRb$7+eszoJJe4eUAI@hLb{>Ez@ijs(80Q(QC2&{^&YLevv<>#0N&ngXuH$f z&l}@Pvt{enf=&@=J3!BEb$PbawIU1-aj=dv)D$A58ck6Pnf?K|FWXBFL>w!Bd3sE( zH6-3>ml2EBP!Ow;OpW^d?YuF!j_w0co?4;>9~>#><69Lc@FwIc505ZpFCNEo9jwO6z)EL z+(*s|NQN!PDYVlL=XwzTvnse>Y+YSllN$|K6hL6V^;kc(A+TIDp~vOx<0c{!p{x3U z^A_ax?|5|v;z)#%B_zAmp$Q{>ai**07Z<;b=%tK!C>g?kLgBN1|JML0mn(nbG^#FX zxsXu8h>%bIG_KMNN~ru&?SH)0|GG)4G97v4{~lHU|2O^r?wUqds>QW#erKcQl?<8v OGGyRLo8bOV8~z{gJoiZe literal 0 HcmV?d00001 diff --git a/docs/source/Tutorial/dynamic/strain_stress.rst b/docs/source/Tutorial/dynamic/strain_stress.rst index fc6815ec..7d5a811d 100644 --- a/docs/source/Tutorial/dynamic/strain_stress.rst +++ b/docs/source/Tutorial/dynamic/strain_stress.rst @@ -1,3 +1,5 @@ +.. _strain_stress_rst: + 计算动态应变和应力 =================== @@ -6,4 +8,183 @@ ----------------------------------------------------------- -TODO + +计算应变张量与应力张量需要计算位移的空间导数 :math:`\partial z,\partial r,\partial \theta` [#]_ 。 从前文关于格林函数的计算 ( :ref:`gfunc_rst` ) 和位移合成的公式 ( :ref:`syn_rst` ) 出发,位移空间导数分两个步骤计算,再根据几何方程和本构方程合成应变和应力。 + +.. [#] :math:`\partial z,\partial r,\partial \theta` 为 :math:`\dfrac{\partial}{\partial z},\dfrac{\partial}{\partial r},\dfrac{\partial}{\partial \theta}` 的简写。 + +计算格林函数阶段,求出 :math:`\partial z,\partial r` +----------------------------------------------------------------------------------------------- + +假设在 :file:`milrow` 模型中,震源深度2km,接收点位于地表,震中距为10km,计算格林函数及其空间导数,要求采样点数500个点,采样间隔0.02s。 + +.. tabs:: + + .. tab:: C + + .. literalinclude:: run_upar/run.sh + :language: bash + :start-after: BEGIN GRN + :end-before: END GRN + + 在 :rst:dir:`GRN/milrow_{depsrc}_{deprcv}_{dist}/` 路径下,文件名开头有"r"和"z"就代表 :math:`\partial r` 和 :math:`\partial z`。 + + .. tab:: Python + + .. literalinclude:: run_upar/run.py + :language: python + :start-after: BEGIN GRN + :end-before: END GRN + + 通道名开头有"r"和"z"就代表 :math:`\partial r` 和 :math:`\partial z`。 + + +.. note:: + + 计算格林函数阶段求出的空间导数的单位: + + + 爆炸源: :math:`10^{-25} \, /\text{dyne} \cdot \text{cm}` + + 单力源: :math:`10^{-20} \, /\text{dyne}` + + 剪切源: :math:`10^{-25} \, /\text{dyne} \cdot \text{cm}` + + 矩张量源: :math:`10^{-25} \, /\text{dyne} \cdot \text{cm}` + + + +合成位移阶段,求出 :math:`\partial \theta / r` 并合成位移空间导数 +----------------------------------------------------------------------------- + +假设震源为剪切源,断层走向33°,倾角50°,滑动角120°,标量矩 1e24 dyne·cm,方位角30°。待求项中有 :math:`r` 是为了保证量纲统一。 + +.. tabs:: + + .. tab:: C + + .. literalinclude:: run_upar/run.sh + :language: bash + :start-after: BEGIN SYN DC + :end-before: END SYN DC + + 在 :rst:dir:`syn_dc/` 路径下,文件名开头有"r","z","t"分别代表 :math:`\partial r`, :math:`\partial z`,:math:`\partial \theta / r`。 + + .. tab:: Python + + .. literalinclude:: run_upar/run.py + :language: python + :start-after: BEGIN SYN DC + :end-before: END SYN DC + + 通道名开头有"r","z","t"分别代表 :math:`\partial r`, :math:`\partial z`,:math:`\partial \theta / r`。 + + +以上计算的空间导数在柱坐标系下,即 :math:`\dfrac{\partial u(z,r,\theta)}{\partial(z,r,\theta)}`。如果需要 :math:`\dfrac{\partial u(z,x,y)}{\partial(z,x,y)}` ( :math:`x` 表示北向, :math:`y` 表示东向),传入适当参数即可,则输出结果开头的标识符从"z/r/t"变为"z/x/y"。 + +.. tabs:: + + .. tab:: C + + .. literalinclude:: run_upar/run.sh + :language: bash + :start-after: BEGIN ZNE + :end-before: END ZNE + + 在 :rst:dir:`syn_dc_zne/` 路径下,文件名开头有"z","n","e"分别代表 :math:`\partial z`, :math:`\partial x`,:math:`\partial y`。 + + .. tab:: Python + + .. literalinclude:: run_upar/run.py + :language: python + :start-after: BEGIN ZNE + :end-before: END ZNE + + 通道名开头有"z","n","e"分别代表 :math:`\partial z`, :math:`\partial x`,:math:`\partial y`。 + + .. warning:: + + 不可以使用ObsPy库中提供的Stream.rotate()函数进行位移空间导数的旋转。 + + +.. note:: + + 合成的位移空间导数单位为1。 + + +合成应变和应力 +----------------------- +应变和应力均为二阶对称张量,故将输出6个独立分量。程序选择应变应力的坐标系的依据是——根据文件名/通道名判断是否存在 :math:`\dfrac{\partial u_x}{\partial x}`,如果有则使用ZNE坐标系,否则使用ZRT坐标系。 **所以建议保存结果的文件夹中只使用同种坐标系**,就像上面分为 :rst:dir:`syn_dc/` 和 :rst:dir:`syn_dc_zne/` 两个文件夹保存。 + +应变张量 +~~~~~~~~~~~~~~ +根据几何方程 [#]_ + +.. math:: + + e_{ji} = \dfrac{1}{2} \left( u_{i,j} + u_{j,i} \right) = \dfrac{1}{2} \left( \dfrac{\partial u_i}{\partial x_j} + \dfrac{\partial u_j}{\partial x_i} \right) + + +.. [#] 这只适用于ZNE坐标系,对于ZRT坐标系需考虑协变导数。程序中已考虑,这里不再做公式介绍。 + +.. tabs:: + + .. tab:: C + + .. literalinclude:: run_upar/run.sh + :language: bash + :start-after: BEGIN STRAIN + :end-before: END STRAIN + + 在 :rst:dir:`syn_dc_zne/` 原路径下,生成 :file:`*.strain.??.sac`,文件名中包括分量名,如ZZ、ZN等。 + + .. tab:: Python + + .. literalinclude:: run_upar/run.py + :language: python + :start-after: BEGIN STRAIN + :end-before: END STRAIN + + 返回的 |Stream| 通道名即为分量名,如ZZ、ZN等。 + +.. image:: run_upar/strain.png + :align: center + + +应力张量 +~~~~~~~~~~~~~~ +根据各向同性介质的本构方程 [#]_ + +.. math:: + + \sigma_{ji} = \lambda \delta_{ij} e_{kk} + 2 \mu e_{ij} = \lambda \delta_{ij} u_{kk} + \mu \left( u_{i,j} + u_{j,i} \right) + + +.. [#] 这只适用于ZNE坐标系,对于ZRT坐标系需考虑协变导数。程序中已考虑,这里不再做公式介绍。 + +.. tabs:: + + .. tab:: C + + .. literalinclude:: run_upar/run.sh + :language: bash + :start-after: BEGIN STRESS + :end-before: END STRESS + + 在 :rst:dir:`syn_dc_zne/` 原路径下,生成 :file:`*.stress.??.sac`,文件名中包括分量名,如ZZ、ZN等。 + + .. tab:: Python + + .. literalinclude:: run_upar/run.py + :language: python + :start-after: BEGIN STRESS + :end-before: END STRESS + + 返回的 |Stream| 通道名即为分量名,如ZZ、ZN等。 + +.. image:: run_upar/stress.png + :align: center + + +.. note:: + + 计算得到的应力的单位为 :math:`\frac{\text{dyne}}{\text{cm}^2} = 0.1 \text{Pa}`。 + + +由于场点位于地表(自由表面),过Z平面的应力均为0(由于浮点数计算误差,呈极小非零数),结果和理论保持一致。 \ No newline at end of file diff --git a/docs/source/Tutorial/dynamic/syn.rst b/docs/source/Tutorial/dynamic/syn.rst index 31ffd488..0eea0ea5 100644 --- a/docs/source/Tutorial/dynamic/syn.rst +++ b/docs/source/Tutorial/dynamic/syn.rst @@ -1,3 +1,5 @@ +.. _syn_rst: + 合成动态位移 ================= @@ -10,19 +12,19 @@ Python中合成动态位移的主函数为 :func:`gen_syn_from_gf_*() MAX: + MAX = m + + for i in range(6): + ax = axs[i] + ch = chs[i] + vmin = vmax = None + if np.max(np.abs(data[ch]))/MAX < 1e-5: + vmin = -1 + vmax = 1 + + pcm = ax.pcolormesh(yarr, xarr, data[ch], shading='nearest', vmin=vmin, vmax=vmax) + ax.set_title(ch) + cbar = fig.colorbar(pcm, ax=ax) + cbar.formatter.set_powerlimits((0, 0)) + cbar.update_normal(pcm) + + fig.suptitle(title) + + if out is not None: + fig.tight_layout() + fig.savefig(out, dpi=100) + +plot6(static_strain, "Strain", 'static_strain.png') +plot6(static_stress, "Stress", 'static_stress.png') \ No newline at end of file diff --git a/docs/source/Tutorial/static/run_upar/run.sh b/docs/source/Tutorial/static/run_upar/run.sh new file mode 100755 index 00000000..09a15ff1 --- /dev/null +++ b/docs/source/Tutorial/static/run_upar/run.sh @@ -0,0 +1,23 @@ +#!/bin/bash + +depsrc=2 +deprcv=0 + +x1=-3 +x2=3 +nx=41 + +y1=-2.5 +y2=2.5 +ny=33 +# -e 表示计算空间导数 +stgrt -Mmilrow -D${depsrc}/${deprcv} -X$x1/$x2/$nx -Y$y1/$y2/$ny -e > grn + +# 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