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10.1 Magnitude sensitivity for homogeneous model: test case 10#
This is an example of computing magnitude sensitivity for a homogeneous model.
Test case 10:
Geometry: a single station above the DAS cable in a deep vertical borehole
Data: Noise level at the station: 5e-9 m/s, for DAS - noise level decreasing with depth (from 5e-7 to 8.87e-12)
Velocity model: homogeneous, Vp = 4300 m/s, Vp/Vs = 1.73, Qp = 100, Qs = 50, rho = 2300 kg/m^3
Processing: magnitude sensitivity computation for all stations (for grid slices only).
Load all necessary packages#
Input#
Read geometry#
### Read geometry
station_geometry_file_path = '../data/homo/test_10/TMPL_net_geometry_Single.txt'
station_geometry_df = pndmod.io.read_geometry(station_geometry_file_path)
print(station_geometry_df)
print(station_geometry_df.attrs)
das_geometry_file_path = '../data/homo/test_10/TMPL_net_geometry_Noise_Decreasing.txt'
das_geometry_df = pndmod.io.read_geometry(das_geometry_file_path)
print(das_geometry_df)
print(das_geometry_df.attrs)
### Show
print("\nStation geometry:")
print(station_geometry_df.head())
print(station_geometry_df.attrs)
print("\nDAS geometry:")
print(das_geometry_df.head())
print(das_geometry_df.attrs)
Name Y X Z NoiseLevel
0 ST1 0.0 0.0 -0.0 5.000000e-09
{'file_path': '../data/homo/test_10/TMPL_net_geometry_Single.txt', 'original_coord_units': 'm', 'coordinate_system': 'local', 'noise_type': 'velocity', 'noise_unit': 'm/s', '_is_combined': False}
Y X Z NoiseLevel
0 0.0 0.0 10.0 5.000000e-07
1 0.0 0.0 60.0 4.170000e-07
2 0.0 0.0 110.0 3.470000e-07
3 0.0 0.0 160.0 2.890000e-07
4 0.0 0.0 210.0 2.410000e-07
.. ... ... ... ...
56 0.0 0.0 2810.0 1.840000e-11
57 0.0 0.0 2860.0 1.530000e-11
58 0.0 0.0 2910.0 1.280000e-11
59 0.0 0.0 2960.0 1.060000e-11
60 0.0 0.0 3010.0 8.870000e-12
[61 rows x 4 columns]
{'file_path': '../data/homo/test_10/TMPL_net_geometry_Noise_Decreasing.txt', 'original_coord_units': 'm', 'coordinate_system': 'local', 'noise_type': 'strain', 'noise_unit': 'ε', 'gauge_length': 10.0, '_is_combined': False}
Station geometry:
Name Y X Z NoiseLevel
0 ST1 0.0 0.0 -0.0 5.000000e-09
{'file_path': '../data/homo/test_10/TMPL_net_geometry_Single.txt', 'original_coord_units': 'm', 'coordinate_system': 'local', 'noise_type': 'velocity', 'noise_unit': 'm/s', '_is_combined': False}
DAS geometry:
Y X Z NoiseLevel
0 0.0 0.0 10.0 5.000000e-07
1 0.0 0.0 60.0 4.170000e-07
2 0.0 0.0 110.0 3.470000e-07
3 0.0 0.0 160.0 2.890000e-07
4 0.0 0.0 210.0 2.410000e-07
{'file_path': '../data/homo/test_10/TMPL_net_geometry_Noise_Decreasing.txt', 'original_coord_units': 'm', 'coordinate_system': 'local', 'noise_type': 'strain', 'noise_unit': 'ε', 'gauge_length': 10.0, '_is_combined': False}
Combine geometry#
combined_geometry_df = pndmod.io.combine_geometry(station_geometry_df,
das_geometry_df,
names=['Stations',
'DAS'])
### Show combined
print("\nCombined geometry:")
print(combined_geometry_df)
print(combined_geometry_df.attrs)
print("\nGeometry names:")
print(combined_geometry_df.get_names())
print("\nCombined status:",
pndmod.io.is_combined_geometry(combined_geometry_df))
### Show recovered
print("\nStation geometry (recovered):")
print(combined_geometry_df.recover('Stations').head())
print("\nCombined status:",
pndmod.io.is_combined_geometry(combined_geometry_df.recover('Stations')))
print("\nDAS geometry (recovered):")
print(combined_geometry_df.recover('DAS').head())
print("\nCombined status:",
pndmod.io.is_combined_geometry(combined_geometry_df.recover('DAS')))
print("\nAttributes of DAS (recovered):")
print(combined_geometry_df.recover('DAS').attrs)
Combined geometry:
Name Y X Z NoiseLevel
source
Stations 0 ST1 0.0 0.0 -0.0 5.000000e-09
DAS 0 NaN 0.0 0.0 10.0 5.000000e-07
1 NaN 0.0 0.0 60.0 4.170000e-07
2 NaN 0.0 0.0 110.0 3.470000e-07
3 NaN 0.0 0.0 160.0 2.890000e-07
... ... ... ... ... ...
56 NaN 0.0 0.0 2810.0 1.840000e-11
57 NaN 0.0 0.0 2860.0 1.530000e-11
58 NaN 0.0 0.0 2910.0 1.280000e-11
59 NaN 0.0 0.0 2960.0 1.060000e-11
60 NaN 0.0 0.0 3010.0 8.870000e-12
[62 rows x 5 columns]
{'original_attributes': {'Stations': {'file_path': '../data/homo/test_10/TMPL_net_geometry_Single.txt', 'original_coord_units': 'm', 'coordinate_system': 'local', 'noise_type': 'velocity', 'noise_unit': 'm/s', '_is_combined': False}, 'DAS': {'file_path': '../data/homo/test_10/TMPL_net_geometry_Noise_Decreasing.txt', 'original_coord_units': 'm', 'coordinate_system': 'local', 'noise_type': 'strain', 'noise_unit': 'ε', 'gauge_length': 10.0, '_is_combined': False}}, '_is_combined': True}
Geometry names:
['Stations', 'DAS']
Combined status: True
Station geometry (recovered):
Name Y X Z NoiseLevel
0 ST1 0.0 0.0 -0.0 5.000000e-09
Combined status: False
DAS geometry (recovered):
Y X Z NoiseLevel
0 0.0 0.0 10.0 5.000000e-07
1 0.0 0.0 60.0 4.170000e-07
2 0.0 0.0 110.0 3.470000e-07
3 0.0 0.0 160.0 2.890000e-07
4 0.0 0.0 210.0 2.410000e-07
Combined status: False
Attributes of DAS (recovered):
{'file_path': '../data/homo/test_10/TMPL_net_geometry_Noise_Decreasing.txt', 'original_coord_units': 'm', 'coordinate_system': 'local', 'noise_type': 'strain', 'noise_unit': 'ε', 'gauge_length': 10.0, '_is_combined': False}
Read velocity model#
velocity_file_path = '../data/homo/test_10/TMPL_velocity_model.txt'
velocity_df = pndmod.io.read_velocity(velocity_file_path)
print(velocity_df)
print(velocity_df.attrs)
Depth Vp VpVsRatio Qp Qs Rho Ep Dt Gm
0 40000 4300 1.73 100 50 2300 0.0 0.0 0.0
{'model_type': 'homo', 'model_anisotropy': 'isotropic', 'parameter_descriptions': {'Depth': 'Depth', 'Vp': 'P-wave velocity', 'Vs': 'S-wave velocity', 'VpVsRatio': 'Vp/Vs', 'Qp': 'P-wave quality factor', 'Qs': 'S-wave quality factor', 'Rho': 'density', 'Ep': 'Thomsen epsilon parameter', 'Dt': 'Thomsen delta parameter', 'Gm': 'Thomsen gamma parameter'}, 'parameter_units': {'Depth': 'm', 'Vp': 'm/s', 'Vs': 'm/s', 'VpVsRatio': '', 'Qp': '', 'Qs': '', 'Rho': 'kg/m^3', 'Ep': '', 'Dt': '', 'Gm': ''}}
Set imaging grid parameters#
# Imaging grid parameters
gx = np.arange(-7000, 7000 + 100, 100)
gy = np.arange(-7000, 7000 + 100, 100)
gz = np.arange(0, 10000 + 100, 100)
# Generate grid points
grid_points = pndmod.utils.generate_grid(x=gx,y=gy,z=gz)
print("Number of grid points:",grid_points.size)
print("Number of grid points in x:",gx.size)
print("Number of grid points in y:",gy.size)
print("Number of grid points in z:",gz.size)
print("grid_points.shape:",grid_points.shape)
Number of grid points: 6023943
Number of grid points in x: 141
Number of grid points in y: 141
Number of grid points in z: 101
grid_points.shape: (2007981, 3)
Plot geometry and imaging grid#
_ = pndvis.geometry.plot_stations_view(df=combined_geometry_df,
grid_points=grid_points,
plot_names=False,
grid_marker_size = 1,
station_marker_size=100)
_ = pndvis.geometry.plot_stations_view(df=combined_geometry_df,
grid_points=grid_points,
plot_names=False,
grid_marker_size = 1,
station_marker_size=1,
view = 'xz')
_ = pndvis.geometry.plot_stations_view(df=combined_geometry_df,
grid_points=grid_points,
plot_names=False,
grid_marker_size = 1,
station_marker_size=1,
view = 'yz')
Prepare to compute magnitude sensitivity#
# Get medium parameters
density = velocity_df.at[0,'Rho']
v_p = velocity_df.at[0,'Vp']
Q_p = velocity_df.at[0,'Qp']
v_s = velocity_df.at[0,'Vp']/velocity_df.at[0,'VpVsRatio']
Q_s = velocity_df.at[0,'Qs']
print("density, v_p, Q_p, v_s, Q_s:",density,v_p,Q_p,v_s,Q_s)
# Specify source parameters
frequency = 10 # Hz
# Minimum S/N for detection on individual channel
min_SNR_p = 2
min_SNR_s = 2
# Minimum stations on which an event must be detected
min_stations_p = 3
min_stations_s = 3
# Save parameters
params = pndmod.classes.DetectionParameters(
f_p=frequency,
f_s=frequency,
min_SNR_p=min_SNR_p,
min_SNR_s=min_SNR_s,
min_stations_p=min_stations_p,
min_stations_s=min_stations_s,
)
# Define slices to use
slice_X = 0
slice_Y = 0
slice_Z = 2400
# Get slice planes
X_plane_points, X_plane_indices = pndmod.utils.get_slice_coordinates(grid_points=grid_points,slice_dimension=0,slice_coordinate=slice_X)
Y_plane_points, Y_plane_indices = pndmod.utils.get_slice_coordinates(grid_points=grid_points,slice_dimension=1,slice_coordinate=slice_Y)
Z_plane_points, Z_plane_indices = pndmod.utils.get_slice_coordinates(grid_points=grid_points,slice_dimension=2,slice_coordinate=slice_Z)
density, v_p, Q_p, v_s, Q_s: 2300 4300 100 2485.549132947977 50
Compute magnitude sensitivity#
print("Computing magnitude sensitivity...")
start_time = time()
X_slice_mag_sens_p = pndmod.core.get_mag_sensitivity(grid_coords=X_plane_points,
geometry_df=combined_geometry_df,
velocity_df=velocity_df,
params=params,
wave_mode='P')
X_slice_mag_sens_s = pndmod.core.get_mag_sensitivity(grid_coords=X_plane_points,
geometry_df=combined_geometry_df,
velocity_df=velocity_df,
params=params,
wave_mode='S')
X_slice_mag_sens_ps = pndmod.core.get_mag_sensitivity(grid_coords=X_plane_points,
geometry_df=combined_geometry_df,
velocity_df=velocity_df,
params=params,
wave_mode='PS')
Y_slice_mag_sens_p = pndmod.core.get_mag_sensitivity(grid_coords=Y_plane_points,
geometry_df=combined_geometry_df,
velocity_df=velocity_df,
params=params,
wave_mode='P')
Y_slice_mag_sens_s = pndmod.core.get_mag_sensitivity(grid_coords=Y_plane_points,
geometry_df=combined_geometry_df,
velocity_df=velocity_df,
params=params,
wave_mode='S')
Y_slice_mag_sens_ps = pndmod.core.get_mag_sensitivity(grid_coords=Y_plane_points,
geometry_df=combined_geometry_df,
velocity_df=velocity_df,
params=params,
wave_mode='PS')
Z_slice_mag_sens_p = pndmod.core.get_mag_sensitivity(grid_coords=Z_plane_points,
geometry_df=combined_geometry_df,
velocity_df=velocity_df,
params=params,
wave_mode='P')
Z_slice_mag_sens_s = pndmod.core.get_mag_sensitivity(grid_coords=Z_plane_points,
geometry_df=combined_geometry_df,
velocity_df=velocity_df,
params=params,
wave_mode='S')
Z_slice_mag_sens_ps = pndmod.core.get_mag_sensitivity(grid_coords=Z_plane_points,
geometry_df=combined_geometry_df,
velocity_df=velocity_df,
params=params,
wave_mode='PS')
end_time = time()
print(f"Computation time: {end_time - start_time} seconds")
Computing magnitude sensitivity...
Computation time: 3.068803310394287 seconds
Plot magnitude sensitivity#
Plot magnitude sensitivity for P wave#
station_marker_size = 25
clb_range = None
plt_levels = None
_ = pndvis.sensitivity.plot_sensitivity_slice(sens_data= X_slice_mag_sens_p, yi=gy, zi=gz,
plot_title=f"Magnitude sensitivity at X={slice_X} m: YZ view, P-waves",
clb_title="$M_w$",
geometry_df=combined_geometry_df,
plot_names = False,
station_marker_size = station_marker_size,
clb_range=clb_range,
plt_levels=plt_levels)
_ = pndvis.sensitivity.plot_sensitivity_slice(sens_data= Y_slice_mag_sens_p, xi=gx, zi=gz,
plot_title=f"Magnitude sensitivity at Y={slice_Y} m: XZ view, P-waves",
clb_title="$M_w$",
geometry_df=combined_geometry_df,
plot_names = False,
station_marker_size = station_marker_size,
clb_range=clb_range,
plt_levels=plt_levels)
_ = pndvis.sensitivity.plot_sensitivity_slice(sens_data= Z_slice_mag_sens_p, xi=gx, yi=gy,
plot_title=f"Magnitude sensitivity at Z={slice_Z} m: XY view, P-waves",
clb_title="$M_w$",
geometry_df=combined_geometry_df,
plot_names = False,
station_marker_size = station_marker_size,
clb_range=clb_range,
plt_levels=plt_levels)
Plot magnitude sensitivity for S wave#
_ = pndvis.sensitivity.plot_sensitivity_slice(sens_data= X_slice_mag_sens_s, yi=gy, zi=gz,
plot_title=f"Magnitude sensitivity at X={slice_X} m: YZ view, S-waves",
clb_title="$M_w$",
geometry_df=combined_geometry_df,
plot_names = False,
station_marker_size = station_marker_size,
clb_range=clb_range,
plt_levels=plt_levels)
_ = pndvis.sensitivity.plot_sensitivity_slice(sens_data= Y_slice_mag_sens_s, xi=gx, zi=gz,
plot_title=f"Magnitude sensitivity at Y={slice_Y} m: XZ view, S-waves",
clb_title="$M_w$",
geometry_df=combined_geometry_df,
plot_names = False,
station_marker_size = station_marker_size,
clb_range=clb_range,
plt_levels=plt_levels)
_ = pndvis.sensitivity.plot_sensitivity_slice(sens_data= Z_slice_mag_sens_s, xi=gx, yi=gy,
plot_title=f"Magnitude sensitivity at Z={slice_Z} m: XY view, S-waves",
clb_title="$M_w$",
geometry_df=combined_geometry_df,
plot_names = False,
station_marker_size = station_marker_size,
clb_range=clb_range,
plt_levels=plt_levels)
Plot magnitude sensitivity for P and S waves#
_ = pndvis.sensitivity.plot_sensitivity_slice(sens_data= X_slice_mag_sens_ps, yi=gy, zi=gz,
plot_title=f"Magnitude sensitivity at X={slice_X} m: YZ view, P- and S-waves",
clb_title="$M_w$",
geometry_df=combined_geometry_df,
plot_names = False,
station_marker_size = station_marker_size,
clb_range=clb_range,
plt_levels=plt_levels)
_ = pndvis.sensitivity.plot_sensitivity_slice(sens_data= Y_slice_mag_sens_ps, xi=gx, zi=gz,
plot_title=f"Magnitude sensitivity at Y={slice_Y} m: XZ view, P- and S-waves",
clb_title="$M_w$",
geometry_df=combined_geometry_df,
plot_names = False,
station_marker_size = station_marker_size,
clb_range=clb_range,
plt_levels=plt_levels)
_ = pndvis.sensitivity.plot_sensitivity_slice(sens_data= Z_slice_mag_sens_ps, xi=gx, yi=gy,
plot_title=f"Magnitude sensitivity at Z={slice_Z} m: XY view, P- and S-waves",
clb_title="$M_w$",
geometry_df=combined_geometry_df,
plot_names = False,
station_marker_size = station_marker_size,
clb_range=clb_range,
plt_levels=plt_levels)
Total running time of the script: (0 minutes 8.346 seconds)