forward package

Submodules

forward.ert_forward module

Forward modeling utilities for Electrical Resistivity Tomography (ERT).

class forward.ert_forward.ERTForwardModeling(mesh: pygimli.Mesh, data: pygimli.DataContainer | None = None)

Bases: object

Class for forward modeling of Electrical Resistivity Tomography (ERT) data.

create_synthetic_data(xpos: ndarray, ypos: ndarray | None = None, mesh: pygimli.Mesh | None = None, res_models: ndarray | None = None, schemeName: str = 'wa', noise_level: float = 0.05, absolute_error: float = 0.0, relative_error: float = 0.05, save_path: str | None = None, show_data: bool = False, seed: int | None = None, xbound: float = 100, ybound: float = 100) → Tuple[pygimli.DataContainer, pygimli.Mesh]

Create synthetic ERT data using forward modeling.

This method simulates an ERT survey by placing electrodes, creating a measurement scheme, performing forward modeling to generate synthetic data, and adding noise.

Parameters:

• xpos – X-coordinates of electrodes

• ypos – Y-coordinates of electrodes (if None, uses flat surface)

• mesh – Mesh for forward modeling

• res_models – Resistivity model values

• schemeName – Name of measurement scheme (‘wa’, ‘dd’, etc.)

• noise_level – Level of Gaussian noise to add

• absolute_error – Absolute error for data estimation

• relative_error – Relative error for data estimation

• save_path – Path to save synthetic data (if None, does not save)

• show_data – Whether to display data after creation

• seed – Random seed for noise generation

• xbound – X boundary extension for mesh

• ybound – Y boundary extension for mesh

Returns:

Tuple of (synthetic ERT data container, simulation mesh)

forward(resistivity_model: ndarray, log_transform: bool = True) → ndarray

Compute forward response for a given resistivity model.

Parameters:

• resistivity_model – Resistivity model values

• log_transform – Whether resistivity_model is log-transformed

Returns:

Forward response (apparent resistivity)

forward_and_jacobian(resistivity_model: ndarray, log_transform: bool = True) → Tuple[ndarray, ndarray]

Compute forward response and Jacobian matrix.

Parameters:

• resistivity_model – Resistivity model values

• log_transform – Whether resistivity_model is log-transformed

Returns:

Tuple of (forward response, Jacobian matrix)

get_coverage(resistivity_model: ndarray, log_transform: bool = True) → ndarray

Compute coverage (resolution) for a given resistivity model.

Parameters:

• resistivity_model – Resistivity model values

• log_transform – Whether resistivity_model is log-transformed

Returns:

Coverage values for each cell

set_data(data: pygimli.DataContainer) → None

Set ERT data for forward modeling.

Parameters:

data – ERT data container

set_mesh(mesh: pygimli.Mesh) → None

Set mesh for forward modeling.

Parameters:

mesh – PyGIMLI mesh

forward.ert_forward.ertforandjac(fob, rhomodel, xr)

Forward model and Jacobian for ERT.

Parameters:

• fob (pygimli.ERTModelling) – ERT forward operator.

• rhomodel (pg.RVector) – Resistivity model.

• xr (np.ndarray) – Log-transformed model parameter.

Returns:

Log-transformed forward response. J (np.ndarray): Jacobian matrix.

Return type:

dr (np.ndarray)

forward.ert_forward.ertforandjac2(fob, xr, mesh)

Alternative ERT forward model and Jacobian using log-resistivity values.

Parameters:

• fob (pygimli.ERTModelling) – ERT forward operator.

• xr (np.ndarray) – Log-transformed model parameter.

• mesh (pg.Mesh) – Mesh for the forward model.

Returns:

Log-transformed forward response. J (np.ndarray): Jacobian matrix.

Return type:

dr (np.ndarray)

forward.ert_forward.ertforward(fob, mesh, rhomodel, xr)

Forward model for ERT.

Parameters:

• fob (pygimli.ERTModelling) – ERT forward operator.

• mesh (pg.Mesh) – Mesh for the forward model.

• rhomodel (pg.RVector) – Resistivity model vector.

• xr (np.ndarray) – Log-transformed model parameter (resistivity).

Returns:

Log-transformed forward response. rhomodel (pg.RVector): Updated resistivity model.

Return type:

dr (np.ndarray)

forward.ert_forward.ertforward2(fob, xr, mesh)

Simplified ERT forward model.

Parameters:

• fob (pygimli.ERTModelling) – ERT forward operator.

• xr (np.ndarray) – Log-transformed model parameter.

• mesh (pg.Mesh) – Mesh for the forward model.

Returns:

Log-transformed forward response.

Return type:

dr (np.ndarray)

forward.srt_forward module

Forward modeling utilities for Seismic Refraction Tomography (SRT).

class forward.srt_forward.SeismicForwardModeling(mesh: pygimli.Mesh, scheme: pygimli.DataContainer | None = None)

Bases: object

Class for forward modeling of Seismic Refraction Tomography (SRT) data.

classmethod create_synthetic_data(sensor_x: ndarray, surface_points: ndarray | None = None, mesh: pygimli.Mesh | None = None, velocity_model: ndarray | None = None, slowness: bool = False, shot_distance: float = 5, noise_level: float = 0.05, noise_abs: float = 1e-05, save_path: str | None = None, show_data: bool = False, verbose: bool = False, seed: int | None = None) → Tuple[pygimli.DataContainer, pygimli.Mesh]

Create synthetic seismic data using forward modeling.

This method simulates a seismic survey by placing geophones along a surface, creating a measurement scheme, and performing forward modeling to generate synthetic travel time data.

Parameters:

• sensor_x – X-coordinates of geophones

• surface_points – Surface coordinates for placing geophones [[x,y],…] If None, geophones will be placed on flat surface

• mesh – Mesh for forward modeling

• velocity_model – Velocity model values

• slowness – Whether velocity_model is slowness (1/v)

• shot_distance – Distance between shots

• noise_level – Level of relative noise to add

• noise_abs – Level of absolute noise to add

• save_path – Path to save synthetic data (if None, does not save)

• show_data – Whether to display data after creation

• verbose – Whether to show verbose output

• seed – Random seed for noise generation

Returns:

Tuple of (synthetic seismic data container, simulation mesh)

static draw_first_picks(ax, data, tt=None, plotva=False, **kwargs)

Plot first arrivals as lines.

Parameters:

• ax (matplotlib.axes) – axis to draw the lines in

• data (:gimliapi:`GIMLI::DataContainer`) – data containing shots (“s”), geophones (“g”) and traveltimes (“t”)

• tt (array, optional) – traveltimes to use instead of data(“t”)

• plotva (bool, optional) – plot apparent velocity instead of traveltimes

Returns:

ax – the modified axis

Return type:

matplotlib.axes

forward(velocity_model: ndarray, slowness: bool = True) → ndarray

Compute forward response for a given velocity model.

Parameters:

• velocity_model – Velocity model values (or slowness if slowness=True)

• slowness – Whether velocity_model is slowness (1/v)

Returns:

Forward response (travel times)

set_mesh(mesh: pygimli.Mesh) → None

Set mesh for forward modeling.

Parameters:

mesh – PyGIMLI mesh

set_scheme(scheme: pygimli.DataContainer) → None

Set seismic data scheme for forward modeling.

Parameters:

scheme – Seismic data scheme

Module contents

Forward modeling utilities for geophysical simulations.

class forward.ERTForwardModeling(mesh: pygimli.Mesh, data: pygimli.DataContainer | None = None)

Bases: object

Class for forward modeling of Electrical Resistivity Tomography (ERT) data.

create_synthetic_data(xpos: ndarray, ypos: ndarray | None = None, mesh: pygimli.Mesh | None = None, res_models: ndarray | None = None, schemeName: str = 'wa', noise_level: float = 0.05, absolute_error: float = 0.0, relative_error: float = 0.05, save_path: str | None = None, show_data: bool = False, seed: int | None = None, xbound: float = 100, ybound: float = 100) → Tuple[pygimli.DataContainer, pygimli.Mesh]

Create synthetic ERT data using forward modeling.

This method simulates an ERT survey by placing electrodes, creating a measurement scheme, performing forward modeling to generate synthetic data, and adding noise.

Parameters:

• xpos – X-coordinates of electrodes

• ypos – Y-coordinates of electrodes (if None, uses flat surface)

• mesh – Mesh for forward modeling

• res_models – Resistivity model values

• schemeName – Name of measurement scheme (‘wa’, ‘dd’, etc.)

• noise_level – Level of Gaussian noise to add

• absolute_error – Absolute error for data estimation

• relative_error – Relative error for data estimation

• save_path – Path to save synthetic data (if None, does not save)

• show_data – Whether to display data after creation

• seed – Random seed for noise generation

• xbound – X boundary extension for mesh

• ybound – Y boundary extension for mesh

Returns:

Tuple of (synthetic ERT data container, simulation mesh)

forward(resistivity_model: ndarray, log_transform: bool = True) → ndarray

Compute forward response for a given resistivity model.

Parameters:

• resistivity_model – Resistivity model values

• log_transform – Whether resistivity_model is log-transformed

Returns:

Forward response (apparent resistivity)

forward_and_jacobian(resistivity_model: ndarray, log_transform: bool = True) → Tuple[ndarray, ndarray]

Compute forward response and Jacobian matrix.

Parameters:

• resistivity_model – Resistivity model values

• log_transform – Whether resistivity_model is log-transformed

Returns:

Tuple of (forward response, Jacobian matrix)

get_coverage(resistivity_model: ndarray, log_transform: bool = True) → ndarray

Compute coverage (resolution) for a given resistivity model.

Parameters:

• resistivity_model – Resistivity model values

• log_transform – Whether resistivity_model is log-transformed

Returns:

Coverage values for each cell

set_data(data: pygimli.DataContainer) → None

Set ERT data for forward modeling.

Parameters:

data – ERT data container

set_mesh(mesh: pygimli.Mesh) → None

Set mesh for forward modeling.

Parameters:

mesh – PyGIMLI mesh

class forward.SeismicForwardModeling(mesh: pygimli.Mesh, scheme: pygimli.DataContainer | None = None)

Bases: object

Class for forward modeling of Seismic Refraction Tomography (SRT) data.

classmethod create_synthetic_data(sensor_x: ndarray, surface_points: ndarray | None = None, mesh: pygimli.Mesh | None = None, velocity_model: ndarray | None = None, slowness: bool = False, shot_distance: float = 5, noise_level: float = 0.05, noise_abs: float = 1e-05, save_path: str | None = None, show_data: bool = False, verbose: bool = False, seed: int | None = None) → Tuple[pygimli.DataContainer, pygimli.Mesh]

Create synthetic seismic data using forward modeling.

This method simulates a seismic survey by placing geophones along a surface, creating a measurement scheme, and performing forward modeling to generate synthetic travel time data.

Parameters:

• sensor_x – X-coordinates of geophones

• surface_points – Surface coordinates for placing geophones [[x,y],…] If None, geophones will be placed on flat surface

• mesh – Mesh for forward modeling

• velocity_model – Velocity model values

• slowness – Whether velocity_model is slowness (1/v)

• shot_distance – Distance between shots

• noise_level – Level of relative noise to add

• noise_abs – Level of absolute noise to add

• save_path – Path to save synthetic data (if None, does not save)

• show_data – Whether to display data after creation

• verbose – Whether to show verbose output

• seed – Random seed for noise generation

Returns:

Tuple of (synthetic seismic data container, simulation mesh)

static draw_first_picks(ax, data, tt=None, plotva=False, **kwargs)

Plot first arrivals as lines.

Parameters:

• ax (matplotlib.axes) – axis to draw the lines in

• data (:gimliapi:`GIMLI::DataContainer`) – data containing shots (“s”), geophones (“g”) and traveltimes (“t”)

• tt (array, optional) – traveltimes to use instead of data(“t”)

• plotva (bool, optional) – plot apparent velocity instead of traveltimes

Returns:

ax – the modified axis

Return type:

matplotlib.axes

forward(velocity_model: ndarray, slowness: bool = True) → ndarray

Compute forward response for a given velocity model.

Parameters:

• velocity_model – Velocity model values (or slowness if slowness=True)

• slowness – Whether velocity_model is slowness (1/v)

Returns:

Forward response (travel times)

set_mesh(mesh: pygimli.Mesh) → None

Set mesh for forward modeling.

Parameters:

mesh – PyGIMLI mesh

set_scheme(scheme: pygimli.DataContainer) → None

Set seismic data scheme for forward modeling.

Parameters:

scheme – Seismic data scheme

forward.ertforandjac(fob, rhomodel, xr)

Forward model and Jacobian for ERT.

Parameters:

• fob (pygimli.ERTModelling) – ERT forward operator.

• rhomodel (pg.RVector) – Resistivity model.

• xr (np.ndarray) – Log-transformed model parameter.

Returns:

Log-transformed forward response. J (np.ndarray): Jacobian matrix.

Return type:

dr (np.ndarray)

forward.ertforandjac2(fob, xr, mesh)

Alternative ERT forward model and Jacobian using log-resistivity values.

Parameters:

• fob (pygimli.ERTModelling) – ERT forward operator.

• xr (np.ndarray) – Log-transformed model parameter.

• mesh (pg.Mesh) – Mesh for the forward model.

Returns:

Log-transformed forward response. J (np.ndarray): Jacobian matrix.

Return type:

dr (np.ndarray)

forward.ertforward(fob, mesh, rhomodel, xr)

Forward model for ERT.

Parameters:

• fob (pygimli.ERTModelling) – ERT forward operator.

• mesh (pg.Mesh) – Mesh for the forward model.

• rhomodel (pg.RVector) – Resistivity model vector.

• xr (np.ndarray) – Log-transformed model parameter (resistivity).

Returns:

Log-transformed forward response. rhomodel (pg.RVector): Updated resistivity model.

Return type:

dr (np.ndarray)

forward.ertforward2(fob, xr, mesh)

Simplified ERT forward model.

Parameters:

• fob (pygimli.ERTModelling) – ERT forward operator.

• xr (np.ndarray) – Log-transformed model parameter.

• mesh (pg.Mesh) – Mesh for the forward model.

Returns:

Log-transformed forward response.

Return type:

dr (np.ndarray)