"""
A simulation is the computation (modelling) of electromagnetic responses of a
resistivity (conductivity) model for a given survey.
In its heart, `emg3d` is a multigrid solver for 3D electromagnetic diffusion
with tri-axial electrical anisotropy. However, it contains most functionalities
to also act as a modeller. The simulation module combines all these things
by combining surveys with computational meshes and fields and providing
high-level, specialised modelling routines.
"""
# Copyright 2018-2020 The emg3d Developers.
#
# This file is part of emg3d.
#
# Licensed under the Apache License, Version 2.0 (the "License"); you may not
# use this file except in compliance with the License. You may obtain a copy
# of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
# WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
# License for the specific language governing permissions and limitations under
# the License.
import itertools
from copy import deepcopy
import numpy as np
try:
from tqdm.contrib.concurrent import process_map
except ImportError:
# If you have tqdm installed, but don't want to use it, simply do
# `emg3d.simulation.process_map = emg3d.utils._process_map`.
from emg3d.utils import _process_map as process_map
from emg3d import fields, solver, surveys, models, meshes, optimize
__all__ = ['Simulation']
[docs]class Simulation:
"""Create a simulation for a given survey on a given model.
The computational grid(s) can be either the same as the provided model
grid, or automatic gridding can be used.
.. note::
The Simulation-class has currently a few limitations:
- `gridding` must be `'same'`;
- `survey.fixed`: must be `False`;
- sources and receivers must be electric;
- Anything related to `optimization` is considered experimental/alpha,
and might change in the future.
Parameters
----------
survey : :class:`emg3d.surveys.Survey`
The survey layout, containing sources, receivers, frequencies, and
optionally the measured data.
The survey-data will be modified in place. Provide survey.copy() if you
want to avoid this.
grid : :class:`meshes.TensorMesh`
The grid. See :class:`meshes.TensorMesh`.
model : :class:`emg3d.models.Model`
The model. See :class:`emg3d.models.Model`.
max_workers : int
The maximum number of processes that can be used to execute the
given calls. Default is 4.
gridding : str, TensorMesh, or dict
Method how the computational grids are computed. The default is
currently 'same', the only supported string-method so far (automatic
gridding will be implemented in the future).
- 'same': Same grid as for the input model.
- TensorMesh: The provided TensorMesh is used for all sources and
frequencies.
- dict: The dict must have the form `dict[source][frequency]`,
containing a TensorMesh for each source-frequency pair.
solver_opts : dict, optional
Passed through to :func:`emg3d.solver.solve`. The dict can contain any
parameter that is accepted by the :func:`emg3d.solver.solve` except for
`grid`, `model`, `sfield`, and `efield`.
If not provided the following defaults are used:
- `sslsolver = True`;
- `semicoarsening = True`;
- `linerelaxation = True`;
- `verb = 0` (yet warnings are capture and shown).
Note that these defaults are different from the defaults in
:func:`emg3d.solver.solve`. The defaults chosen here will be slower in
many cases, but they are the most robust combination at which you can
throw most things.
data_weight_opts : dict, optional
Applied in :func:`emg3d.optimize.data_weighting` (defaults in
<brackets>):
- `gamma_d` : float <0.5>; Offset weighting exponent.
- `beta_d` : float <1.0>; Data weighting exponent.
- `beta_f` : float <0.25>; Frequency weighting exponent.
- `noise_floor` : float <1e-15>; Data with amplitudes below the noise
floor are switched off.
- `min_off`: float <1000>; Receiver closer to the source than
`min_offest` are switched off.
- `reference`: str <'reference'>; Name of the data to use for
normalization. By default the data from the reference model; if not
found, the observed data are used.
verb : int; optional
Level of verbosity. Default is 0.
- -1: Error.
- 0: Warning.
- 1: Info.
- 2: Debug.
"""
def __init__(self, name, survey, grid, model, max_workers=4,
gridding='same', **kwargs):
"""Initiate a new Simulation instance."""
# Store inputs.
self.name = name
self.survey = survey
self.grid = grid
self.model = model
self.max_workers = max_workers
self.verb = kwargs.pop('verb', 0)
# Get gridding options, set to defaults if not provided.
self._gridding_descr = {
'same': 'Same grid as for model',
'single': 'A single grid for all sources and frequencies',
'frequency': 'Frequency-dependent grids',
'source': 'Source-dependent grids',
'both': 'Frequency- and source-dependent grids',
}
# gridding_opts will be used for the automatic gridding.
self.gridding_opts = kwargs.pop('gridding_opts', {})
self._initiate_model_grid(gridding)
# Get kwargs.
self.solver_opts = {
'sslsolver': True, # Default in solve is False.
'semicoarsening': True, # "
'linerelaxation': True, # "
'verb': 0,
**kwargs.pop('solver_opts', {}), # Overwrites defaults.
}
self.data_weight_opts = kwargs.pop('data_weight_opts', {})
# Ensure no kwargs left (currently kwargs is not used).
if kwargs:
raise TypeError(f"Unexpected **kwargs: {list(kwargs.keys())}")
if self.survey.fixed:
raise NotImplementedError(
"Simulation currently only implemented for "
"`survey.fixed=False`.")
# Magnetic sources are not yet implemented in simulation.
if sum([not s.electric for s in survey.sources.values()]) > 0:
raise NotImplementedError(
"Simulation not yet implemented for magnetic sources.")
# Magnetic receivers are not yet implemented in simulation.
if sum([not r.electric for r in survey.receivers.values()]) > 0:
raise NotImplementedError(
"Simulation not yet implemented for magnetic receivers.")
# Initiate dictionaries and other values with None's.
self._dict_sfield = self._dict_initiate
self._dict_efield = self._dict_initiate
self._dict_hfield = self._dict_initiate
self._dict_efield_info = self._dict_initiate
self._gradient = None
self._misfit = None
# Initiate synthetic data with NaN's.
self.survey._data['synthetic'] = self.survey.data.observed*np.nan
# `tqdm`-options; undocumented for the moment.
# This is likely to change with regards to verbosity and logging.
self._tqdm_opts = {
'bar_format': '{desc}: {bar}{n_fmt}/{total_fmt} [{elapsed}]',
}
def __repr__(self):
return (f"*{self.__class__.__name__}* «{self.name}» "
f"of {self.survey.__class__.__name__} «{self.survey.name}»\n\n"
f"- {self.survey.__class__.__name__}: "
f"{self.survey.shape[0]} sources; "
f"{self.survey.shape[1]} receivers; "
f"{self.survey.shape[2]} frequencies\n"
f"- {self.model.__repr__()}\n"
f"- Gridding: {self._gridding_descr[self.gridding]}")
def _repr_html_(self):
return (f"<h3>{self.__class__.__name__} «{self.name}»</h3>"
f"of {self.survey.__class__.__name__} «{self.survey.name}»<ul>"
f"<li>{self.survey.__class__.__name__}: "
f"{self.survey.shape[0]} sources; "
f"{self.survey.shape[1]} receivers; "
f"{self.survey.shape[2]} frequencies</li>"
f"<li>{self.model.__repr__()}</li>"
f"<li>Gridding: "
f"{self._gridding_descr[self.gridding]}</li>"
f"</ul>")
[docs] def copy(self, what='computed'):
"""Return a copy of the Simulation.
See `to_file` for more information regarding `what`.
"""
return self.from_dict(self.to_dict(what, True))
[docs] def to_dict(self, what='computed', copy=False):
"""Store the necessary information of the Simulation in a dict.
See `to_file` for more information regarding `what`.
"""
if what not in ['computed', 'results', 'all', 'plain']:
raise TypeError(f"Unrecognized `what`: {what}")
# If to_dict is called from to_file, it has a _what_to_file attribute.
if hasattr(self, '_what_to_file'):
what = self._what_to_file
delattr(self, '_what_to_file')
# Initiate dict.
out = {'name': self.name, '__class__': self.__class__.__name__}
# Add initiation parameters.
out['survey'] = self.survey.to_dict()
out['grid'] = self.grid.to_dict()
out['model'] = self.model.to_dict()
out['max_workers'] = self.max_workers
out['gridding'] = self.gridding
out['solver_opts'] = self.solver_opts
# Get required properties.
store = []
if what == 'all':
store += ['_dict_grid', '_dict_model', '_dict_sfield',
'_dict_hfield']
if what in ['computed', 'all']:
store += ['_dict_efield', '_dict_efield_info']
# store dicts.
for name in store:
out[name] = getattr(self, name)
# store data.
out['data'] = {}
if what in ['computed', 'results', 'all']:
for name in list(self.data.data_vars):
# These two are stored in the Survey instance.
if name not in ['observed', 'reference']:
out['data'][name] = self.data.get(name)
out['gradient'] = self._gradient
out['misfit'] = self._misfit
if copy:
return deepcopy(out)
else:
return out
[docs] @classmethod
def from_dict(cls, inp):
"""Convert dictionary into :class:`Simulation` instance.
Parameters
----------
inp : dict
Dictionary as obtained from :func:`Simulation.to_dict`.
Returns
-------
obj : :class:`Simulation` instance
"""
from emg3d import io
try:
# Initiate class.
out = cls(
name=inp['name'],
survey=surveys.Survey.from_dict(inp['survey']),
grid=meshes.TensorMesh.from_dict(inp['grid']),
model=models.Model.from_dict(inp['model']),
max_workers=inp['max_workers'],
gridding=inp['gridding'],
solver_opts=inp['solver_opts'],
)
# Add existing derived/computed properties.
data = ['_dict_grid', '_dict_model', '_dict_sfield',
'_dict_hfield', '_dict_efield', '_dict_efield_info']
for name in data:
if name in inp.keys():
values = inp.get(name)
# Storing to_file makes strings out of the freq-keys.
# Undo this.
new_values = {}
for src, val in values.items():
new_values[src] = {}
for freq, v in val.items():
new_values[src][float(freq)] = val.get(freq)
# De-serialize Model, Field, and TensorMesh instances.
io._dict_deserialize(new_values)
setattr(out, name, new_values)
data = ['gradient', 'misfit']
for name in data:
if name in inp.keys():
setattr(out, '_'+name, inp.get(name))
# Add stored data (synthetic, residual, etc).
for name in inp['data'].keys():
out.data[name] = out.data.observed*inp['data'][name]
return out
except KeyError as e:
raise KeyError(f"Variable {e} missing in `inp`.") from e
[docs] def to_file(self, fname, what='computed', name='simulation', **kwargs):
"""Store Simulation to a file.
Parameters
----------
fname : str
File name inclusive ending, which defines the used data format.
Implemented are currently:
- `.h5` (default): Uses `h5py` to store inputs to a hierarchical,
compressed binary hdf5 file. Recommended file format, but
requires the module `h5py`. Default format if ending is not
provided or not recognized.
- `.npz`: Uses `numpy` to store inputs to a flat, compressed binary
file. Default format if `h5py` is not installed.
- `.json`: Uses `json` to store inputs to a hierarchical, plain
text file.
what : str
What to store. Currently implemented:
- 'computed' (default):
Stores all computed properties: electric fields and responses at
receiver locations.
- 'results':
Stores only the response at receiver locations.
- 'all':
Stores everything.
- 'plain':
Only stores the plain Simulation (as initiated).
name : str
Name under which the survey is stored within the file.
kwargs : Keyword arguments, optional
Passed through to :func:`io.save`.
"""
from emg3d import io
# Add what to self, will be removed in to_dict.
self._what_to_file = what
kwargs[name] = self # Add simulation to dict.
kwargs['collect_classes'] = False # Ensure classes are not collected.
# If verb is not defined, use verbosity of simulation.
if 'verb' not in kwargs:
kwargs['verb'] = self.verb
io.save(fname, **kwargs)
[docs] @classmethod
def from_file(cls, fname, name='simulation', **kwargs):
"""Load Simulation from a file.
Parameters
----------
fname : str
File name including extension. Used backend depends on the file
extensions:
- '.npz': numpy-binary
- '.h5': h5py-binary (needs `h5py`)
- '.json': json
name : str
Name under which the simulation is stored within the file.
kwargs : Keyword arguments, optional
Passed through to :func:`io.load`.
Returns
-------
simulation : :class:`Simulation`
The simulation that was stored in the file.
"""
from emg3d import io
return io.load(fname, **kwargs)[name]
# GET FUNCTIONS
[docs] def get_grid(self, source, frequency):
"""Return computational grid of the given source and frequency."""
freq = float(frequency)
# Get grid if it is not stored yet.
if self._dict_grid[source][freq] is None:
# Act depending on gridding:
if self.gridding in ['same', 'single']:
# Store link to grid.
self._dict_grid[source][freq] = self._grid_comp
else: # self.gridding == 'both'
raise TypeError(
"Provided grid-dict misses the following "
"source-frequency pair: {source}, {freq} Hz.")
# Return grid.
return self._dict_grid[source][freq]
[docs] def get_model(self, source, frequency):
"""Return model on the grid of the given source and frequency."""
freq = float(frequency)
# Get model if it is not stored yet.
if self._dict_model[source][freq] is None:
# Act depending on gridding:
if self.gridding in ['same', 'single']:
# Store link to model.
self._dict_model[source][freq] = self._model_comp
elif self.gridding == 'both': # Src- & freq-dependent grids.
# Get model and store it.
model = self._model_comp.interpolate2grid(
self._grid_comp, self.get_grid(source, freq))
self._dict_model[source][freq] = model
# Return model.
return self._dict_model[source][freq]
[docs] def get_sfield(self, source, frequency):
"""Return source field for given source and frequency."""
freq = float(frequency)
# Get source field if it is not stored yet.
if self._dict_sfield[source][freq] is None:
# Get source and source strength.
src = self.survey.sources[source]
if hasattr(src, 'strength'):
strength = src.strength
else:
strength = 0
sfield = fields.get_source_field(
grid=self.get_grid(source, frequency),
src=src.coordinates,
freq=frequency,
strength=strength)
self._dict_sfield[source][freq] = sfield
# Return source field.
return self._dict_sfield[source][freq]
[docs] def get_efield(self, source, frequency, **kwargs):
"""Return electric field for given source and frequency."""
freq = float(frequency)
# Get call_from_compute and ensure no kwargs are left.
call_from_compute = kwargs.pop('call_from_compute', False)
if kwargs:
raise TypeError(f"Unexpected **kwargs: {list(kwargs.keys())}")
# Compute electric field if it is not stored yet.
if self._dict_efield[source][freq] is None:
# Input parameters.
solver_input = {
**self.solver_opts,
'grid': self.get_grid(source, freq),
'model': self.get_model(source, freq),
'sfield': self.get_sfield(source, freq),
'return_info': True,
}
# Compute electric field.
efield, info = solver.solve(**solver_input)
# Store electric field and info.
self._dict_efield[source][freq] = efield
self._dict_efield_info[source][freq] = info
# Clean corresponding hfield, so it will be recomputed.
del self._dict_hfield[source][freq]
self._dict_hfield[source][freq] = None
# Get receiver coordinates.
rec_coords = self.survey.rec_coords
# For fixed surveys:
# rec_coords = self.survey.rec_coords[source]
# Extract data at receivers.
resp = fields.get_receiver_response(
grid=self._dict_grid[source][freq],
field=self._dict_efield[source][freq],
rec=rec_coords
)
# Store the receiver response.
self.data.synthetic.loc[source, :, freq] = resp
# Return electric field.
if call_from_compute:
return (self._dict_efield[source][freq],
self._dict_efield_info[source][freq],
self.data.synthetic.loc[source, :, freq].data)
else:
return self._dict_efield[source][freq]
[docs] def get_hfield(self, source, frequency, **kwargs):
"""Return magnetic field for given source and frequency."""
freq = float(frequency)
# If magnetic field not computed yet compute it.
if self._dict_hfield[source][freq] is None:
self._dict_hfield[source][freq] = fields.get_h_field(
self.get_grid(source, freq),
self.get_model(source, freq),
self.get_efield(source, freq, **kwargs))
# Return magnetic field.
return self._dict_hfield[source][freq]
[docs] def get_efield_info(self, source, frequency):
"""Return the solver information of the corresponding computation."""
return self._dict_efield_info[source][float(frequency)]
# ASYNCHRONOUS COMPUTATION
def _get_efield(self, inp):
"""Wrapper of `get_efield` for `concurrent.futures`."""
return self.get_efield(*inp, call_from_compute=True)
[docs] def compute(self, observed=False, reference=False):
"""Compute efields asynchronously for all sources and frequencies.
Parameters
----------
observed : bool
If True, it stores the current result also as observed model.
This is usually done for pure forward modelling (not inversion).
It will as such be stored within the survey.
reference : bool
If True, it stores the current result also as reference model,
which is used by the data weighting functions. This is usually
done for the initial model in an inversion.
"""
srcfreq = self._srcfreq.copy()
# We remove the ones that were already computed.
remove = []
for src, freq in srcfreq:
if self._dict_efield[src][freq] is not None:
remove += [(src, freq)]
for src, freq in remove:
srcfreq.remove((src, freq))
# Ensure grids, models, and source fields are computed.
#
# => This could be done within the field computation. But then it might
# have to be done multiple times even if 'single' or 'same' grid.
# Something to keep in mind.
# For `gridding='same'` it does not really matter.
for src, freq in srcfreq:
_ = self.get_grid(src, freq)
_ = self.get_model(src, freq)
_ = self.get_sfield(src, freq)
# Initiate futures-dict to store output.
out = process_map(
self._get_efield,
srcfreq,
max_workers=self.max_workers,
**{'desc': 'Compute efields', **self._tqdm_opts},
)
# Clean hfields, so they will be recomputed.
del self._dict_hfield
self._dict_hfield = self._dict_initiate
# Loop over src-freq combinations to extract and store.
warned = False # Flag for warnings.
for i, (src, freq) in enumerate(srcfreq):
# Store efield.
self._dict_efield[src][freq] = out[i][0]
# Store solver info.
info = out[i][1]
self._dict_efield_info[src][freq] = info
if info['exit'] != 0 and self.verb >= 0:
if not warned:
print("Solver warnings:")
warned = True
print(f"- Src {src}; {freq} Hz : {info['exit_message']}")
# Store responses at receivers.
self.data['synthetic'].loc[src, :, freq] = out[i][2]
# If it shall be used as observed or as a reference save a copy.
if observed:
self.data['observed'] = self.data['synthetic'].copy()
if reference:
self.data['reference'] = self.data['synthetic'].copy()
# GRIDDING
def _initiate_model_grid(self, gridding):
"""Initiate the computational grids and models."""
# Initiate grid- and model-dicts.
self._dict_grid = self._dict_initiate
self._dict_model = self._dict_initiate
if isinstance(gridding, str):
if gridding not in ['single', 'same']:
raise TypeError(f"Unknown `gridding`-option: '{gridding}'.")
self._grid_comp = self.grid
self._model_comp = self.model
self.gridding = gridding
elif isinstance(gridding, meshes.TensorMesh):
self._grid_comp = gridding
self._model_comp = self.model.interpolate2grid(self.grid, gridding)
self.gridding = 'single'
elif isinstance(gridding, dict):
for src, freq in self._srcfreq:
self._dict_grid[src][freq] = gridding.get(
src, {}).get(freq, None)
self._grid_comp = self.grid
self._model_comp = self.model
self.gridding = 'both'
# DATA
@property
def data(self):
"""Shortcut to survey.data."""
return self.survey.data
# OPTIMIZATION
@property
def gradient(self):
"""Return the gradient of the misfit function.
See :func:`emg3d.optimize.gradient`.
"""
# Compute it if not stored already.
if self._gradient is None:
self._gradient = optimize.gradient(self)
return self._gradient
@property
def misfit(self):
"""Return the misfit function.
See :func:`emg3d.optimize.misfit`.
"""
# Compute it if not stored already.
if self._misfit is None:
self._misfit = optimize.misfit(self)
return self._misfit
# UTILS
[docs] def clean(self, what='computed'):
"""Clean part of the data base.
Parameters
----------
what : str
What to clean. Currently implemented:
- 'computed' (default):
Removes all computed properties: electric and magnetic fields and
responses at receiver locations.
- 'keepresults':
Removes everything except for the responses at receiver
locations.
- 'all':
Removes everything (leaves it plain as initiated).
"""
if what not in ['computed', 'keepresults', 'all']:
raise TypeError(f"Unrecognized `what`: {what}")
clean = []
if what in ['keepresults', 'all']:
clean += ['_dict_grid', '_dict_model', '_dict_sfield']
if what in ['computed', 'keepresults', 'all']:
clean += ['_dict_efield', '_dict_efield_info', '_dict_hfield']
# Clean dicts.
for name in clean:
delattr(self, name)
setattr(self, name, self._dict_initiate)
# Clean data.
if what in ['computed', 'all']:
for name in list(self.data.data_vars):
if name not in ['observed', 'reference']:
del self.data[name]
self.data['synthetic'] = self.data.observed*np.nan
for name in ['_gradient', '_misfit']:
delattr(self, name)
setattr(self, name, None)
@property
def _dict_initiate(self):
"""Returns a dict of the structure `dict[source][freq]=None`."""
return {src: {freq: None for freq in self.survey.frequencies}
for src in self.survey.sources.keys()}
@property
def _srcfreq(self):
"""Return list of all source-frequency pairs."""
if getattr(self, '__srcfreq', None) is None:
self.__srcfreq = list(
itertools.product(self.survey.sources.keys(),
self.survey.frequencies))
return self.__srcfreq
# BACKWARDS PROPAGATING FIELD
# This stuff would probably be better at home in `optimize`.
def _get_bfields(self, inp):
"""Return back-propagated electric field for given inp (src, freq)."""
# Input parameters.
solver_input = {
**self.solver_opts,
'grid': self.get_grid(*inp),
'model': self.get_model(*inp),
'sfield': self._get_rfield(*inp), # Residual field.
'return_info': True,
}
# Compute and return back-propagated electric field.
return solver.solve(**solver_input)
def _bcompute(self):
"""Compute bfields asynchronously for all sources and frequencies."""
# Initiate futures-dict to store output.
out = process_map(
self._get_bfields,
self._srcfreq,
max_workers=self.max_workers,
**{'desc': 'Back-propagate ', **self._tqdm_opts},
)
# Store back-propagated electric field and info.
if not hasattr(self, '_dict_bfield'):
self._dict_bfield = self._dict_initiate
self._dict_bfield_info = self._dict_initiate
# Loop over src-freq combinations to extract and store.
warned = False # Flag for warnings.
for i, (src, freq) in enumerate(self._srcfreq):
# Store bfield.
self._dict_bfield[src][freq] = out[i][0]
# Store solver info.
info = out[i][1]
self._dict_bfield_info[src][freq] = info
if info['exit'] != 0 and self.verb >= 0:
if not warned:
print("Solver warnings:")
warned = True
print(f"- Src {src}; {freq} Hz : {info['exit_message']}")
def _get_rfield(self, source, frequency):
"""Return residual source field for given source and frequency."""
freq = float(frequency)
grid = self.get_grid(source, frequency)
# Initiate empty field
ResidualField = fields.SourceField(grid, freq=frequency)
# Loop over receivers, input as source.
for name, rec in self.survey.receivers.items():
# Strength: in get_source_field the strength is multiplied with
# iwmu; so we undo this here.
strength = self.data.wresidual.loc[source, name, freq].data.conj()
strength /= ResidualField.smu0
# If strength is zero (very unlikely), get_source_field would
# return a normalized field for a unit source. However, in this
# case we do not want that.
if strength != 0:
ResidualField += fields.get_source_field(
grid=grid,
src=rec.coordinates,
freq=frequency,
strength=strength,
)
return ResidualField