pygrt.utils

file:

utils.py

author:

Zhu Dengda (zhudengda@mail.iggcas.ac.cn)

date:

2024-07-24

该文件包含一些数据处理操作上的补充:

1、剪切源、张裂源、单力源、爆炸源、矩张量源 通过格林函数合成理论地震图的函数

2、Stream类型的时域卷积、微分、积分 (基于numpy和scipy)

3、Stream类型写到本地sac文件，自定义名称

4、读取波数积分和峰谷平均法过程文件

5、其它辅助函数

pygrt.utils.gen_syn_from_gf_DC(st: Stream | dict, M0: float, strike: float, dip: float, rake: float, az: float = -999, ZNE=False, calc_upar: bool = False, **kwargs)

Shear source, the unit of angles is all degrees(°)

参数:

• st – Green’s functions in a obspy.Stream (dynamic-case) or a dict (static-case)

• M0 – scalar seismic moment (dyne*cm)

• strike – 0 <= strike <= 360 (north=0, clockwise as positive)

• dip – 0 <= dip <= 90

• rake – -180 <= rake <= 180 (on the fault plane, counterclockwise as positive)

• az – azimuth, 0 <= az <= 360 (not used for static case)

• ZNE – whether output in ‘ZNE’-coord, default is ‘ZRT’

• calc_upar – whether calculate the spatial derivatives of displacements.

• kwargs – For static rsults, you can set “xarr” and “yarr” to define a new XY grid, the program will automatically find the nearest Green’s functions for each node.

返回:

• stream - obspy.Stream

pygrt.utils.gen_syn_from_gf_SF(st: Stream | dict, S: float, fN: float, fE: float, fZ: float, az: float = -999, ZNE=False, calc_upar: bool = False, **kwargs)

Single-force source (dyne)

参数:

• st – Green’s functions in a obspy.Stream (dynamic-case) or a dict (static-case)

• S – scaling factor (dyne)

• fN – coefficient of Northward force

• fE – coefficient of Eastward force

• fZ – coefficient of Vertical(Downward) force

• az – azimuth, 0 <= az <= 360 (not used for static case)

• ZNE – whether output in ‘ZNE’-coord, default is ‘ZRT’

• calc_upar – whether calculate the spatial derivatives of displacements.

• kwargs – For static rsults, you can set “xarr” and “yarr” to define a new XY grid, the program will automatically find the nearest Green’s functions for each node.

返回:

• stream - obspy.Stream

pygrt.utils.gen_syn_from_gf_EX(st: Stream | dict, M0: float, az: float = -999, ZNE=False, calc_upar: bool = False, **kwargs)

Explosion

参数:

• st – Green’s functions in a obspy.Stream (dynamic-case) or a dict (static-case)

• M0 – scalar seismic moment (dyne*cm)

• az – azimuth, 0 <= az <= 360 (not used for static case)

• ZNE – whether output in ‘ZNE’-coord, default is ‘ZRT’

• calc_upar – whether calculate the spatial derivatives of displacements.

• kwargs – For static rsults, you can set “xarr” and “yarr” to define a new XY grid, the program will automatically find the nearest Green’s functions for each node.

返回:

• stream - obspy.Stream

pygrt.utils.gen_syn_from_gf_MT(st: Stream | dict, M0: float, MT: _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], az: float = -999, ZNE=False, calc_upar: bool = False, **kwargs)

Moment tensor

参数:

• st – Green’s functions in a obspy.Stream (dynamic-case) or a dict (static-case)

• M0 – scalar seismic moment (dyne*cm)

• MT – coefficient of Moment tensor (M11, M12, M13, M22, M23, M33), subscripts 1,2,3 denote Northward,Eastward,Downward

• az – azimuth, 0 <= az <= 360 (not used for static case)

• ZNE – whether output in ‘ZNE’-coord, default is ‘ZRT’

• calc_upar – whether calculate the spatial derivatives of displacements.

• kwargs – For static rsults, you can set “xarr” and “yarr” to define a new XY grid, the program will automatically find the nearest Green’s functions for each node.

返回:

• stream - obspy.Stream

pygrt.utils.compute_strain(st: Stream | dict)

Compute dynamic/static strain tensor from synthetic spatial derivatives.

参数:

st – synthetic spatial derivatives obspy.Stream class for dynamic case, dict class for static case.

返回:

• stres - dynamic/static strain tensor, in obspy.Stream class or dict class.

pygrt.utils.compute_rotation(st: Stream | dict)

Compute dynamic/static rotation tensor from synthetic spatial derivatives.

参数:

st – synthetic spatial derivatives obspy.Stream class for dynamic case, dict class for static case.

返回:

• stres - dynamic/static rotation tensor, in obspy.Stream class or dict class.

pygrt.utils.compute_stress(st: Stream | dict)

Compute dynamic/static stress tensor from synthetic spatial derivatives.

参数:

st – synthetic spatial derivatives obspy.Stream class for dynamic case, dict class for static case.

返回:

• stres - dynamic/static stress tensor (unit: dyne/cm^2 = 0.1 Pa), in obspy.Stream class or dict class.

pygrt.utils.stream_convolve(st0: Stream, signal0: ndarray, inplace=True)

convolve each trace with a signal

参数:

• st0 – obspy.Stream

• signal0 – convolution signal

• inplace – whether change in-place

返回:

• stream - convolution result, obspy.Stream

pygrt.utils.stream_integral(st0: Stream, inplace=True)

Perform integration on each trace

参数:

• st0 – obspy.Stream

• inplace – whether change in-place

返回:

• stream - integration result, obspy.Stream

pygrt.utils.stream_diff(st0: Stream, inplace=True)

Perform central difference on each trace

参数:

• st0 – obspy.Stream

• inplace – whether change in-place

返回:

• stream - difference result, obspy.Stream

pygrt.utils.stream_write_sac(st: Stream, dir: str)

save each trace to “dir/{channel}.sac”

参数:

• st – obspy.Stream

• dir – saving directory

pygrt.utils.read_kernels_freqs(statsdir: str, vels: ndarray | None = None, ktypes: List[str] | None = None)

read all statsfiles in statsdir (except that of 0 frequency). If record wavenumber, interpolate to the phase velocity.

参数:

• statsdir – directory path

• vels – When a positive-order vels (km/s) is specified, files starting with K_ are read and linear interpolation from wavenumber to phase velocity is performed. Otherwise read the files starting with C_

• ktype – Specify the return of a series of kernel function names, such as EX_q, DS_w, etc. By default, all are returned

返回:

• kerDct - kernel functions in a dict

pygrt.utils.read_statsfile(statsfile: str)

read a statsfile

参数:

statsfile – File path (Wildcards can be used to simplify input)

返回:

• data - numpy.ndarray custom type array

pygrt.utils.read_statsfile_ptam(statsfile: str)

read a statsfile from PTAM process

参数:

statsfile – File path (Wildcards can be used to simplify input)

返回:

• data1 - numpy.ndarray custom type array, during DCM or (SA)FIM

• data2 - numpy.ndarray custom type array, during PTAM

• ptam_data - numpy.ndarray custom type array, record the peak/trough from PTAM

• dist - epicentral distance from the filename (km)

pygrt.utils.plot_statsdata(statsdata: ndarray, dist: float, srctype: str, ptype: str, RorI: bool | int = True, fig: Figure | None = None, axs: Axes | None = None)

Based on the data read by the read_statsfile function, plot the kernel function \(F(k,\omega)\), the integrand \(F(k,\omega)J_m(kr)k\), and calculate the cumulative integral \(\sum F(k,\omega)J_m(kr)k\) .

备注

Not every source type corresponds to every order and every integration type, see 格林函数分类 for details.

参数:

• statsdata – return value of read_statsfile function

• dist – epicentral distance (km)

• srctype – abbreviation of source type, including EX, VF, HF, DD, DS, SS

• ptype – integration type (0,1,2,3)

• RorI – whether to plot real or imaginary part, default is real part, pass 2 to plot both

• fig – user-defined matplotlib.Figure object, default is None

• axs – user-defined matplotlib.Axes object array (three elements), default is None

返回:

• fig - matplotlib.Figure object

• (ax1,ax2,ax3) - matplotlib.Axes object array

pygrt.utils.plot_statsdata_ptam(statsdata1: ndarray, statsdata2: ndarray, statsdata_ptam: ndarray, dist: float, srctype: str, ptype: str, RorI: bool | int = True, fig: Figure | None = None, axs: Axes | None = None)

Based on data read by the read_statsfile_ptam function, simply calculate and plot the cumulative integral as well as the peak/trough positions used by PTAM.

备注

Not every source type corresponds to every order and every integration type, see 格林函数分类 for details.

参数:

• statsdata1 – integral process data during DWM or FIM

• statsdata2 – integral process data during PTAM

• statsdata_ptam – peak/trough positions and amplitudes from PTAM

• dist – epicentral distance (km)

• srctype – abbreviation of source type, including EX, VF, HF, DD, DS, SS

• ptype – integration type (0, 1, 2, 3)

• RorI – whether to plot real or imaginary part, default is real part, pass 2 to plot both

• fig – user-defined matplotlib.Figure object, default is None

• axs – user-defined matplotlib.Axes object array (three elements), default is None

返回:

• fig - matplotlib.Figure object

• (ax1, ax2, ax3) - matplotlib.Axes object array

pygrt.utils.solve_lamb1(nu: float, ts: ndarray, azimuth: float)

solve the first-kind Lamb’s problem using the generalized closed-form solution, see：

张海明, 冯禧 著. 2024. 地震学中的 Lamb 问题（下）. 科学出版社

参数:

• nu – possion ratio in (0, 0.5)

• ts – dimensionless time \(\bar{t}\) ，\(\bar{t}=\dfrac{t}{r/\beta}\)

• azimuth – azimuth in degree

返回:

Normalized solution with shape (nt, 3, 3). To get the physical solution, divide by \(\pi^2 \mu r\)