Source code for emg3d.simulations

A simulation is the computation (modelling) of the electromagnetic responses
due to a given model and survey.

The simulation module combines the different pieces of ``emg3d`` providing
a high-level, specialised modelling tool for the end user.
# Copyright 2018-2022 The emsig community.
# 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
# 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 os
import warnings
import itertools
from pathlib import Path
from copy import deepcopy

import numpy as np

from emg3d import fields, io, maps, meshes, models, solver, surveys, utils

__all__ = ['Simulation', ]

[docs]@utils._known_class class Simulation: """Create a simulation for a given survey on a given model. A simulation can be used to compute responses for an entire survey, hence for an arbitrary amount of sources, receivers, and frequencies. The responses are computed in parallel over sources and frequencies. It can also be used to compute the misfit with the data and to compute the gradient of the misfit function. The computational grid(s) can either be provided, or automatic gridding can be used; see the description of the parameters ``gridding`` and ``gridding_opts`` for more details. .. note:: The automatic gridding does its best to generate meshes that are suitable for the provided model and survey. However, CSEM spans a wide range of acquisition layouts, and both frequencies and conductivities or resistivities span many orders of magnitude. This makes it hard to have a function that fits all purposes. Check the meshes with your expert knowledge. Also, the automatic gridding is conservative in its estimate, trying to be on the save side (correct results over speed). This means, however, that often smaller grids could be used by providing the appropriate options in ``gridding_opts`` or directly providing your own computational grids. .. note:: The package ``xarray`` has to be installed in order to use ``Simulation``: ``pip install xarray`` or ``conda install -c conda-forge xarray``. Parameters ---------- survey : Survey The survey; a :class:`emg3d.surveys.Survey` instance. The survey contains sources, receivers, frequencies, and optionally data. The survey-data will be modified in place. Provide ``survey.copy()`` if you want to avoid this. model : Model The model; a :class:`emg3d.models.Model` instance. max_workers : int, default: 4 The maximum number of processes that can be used to execute the given calls. gridding : str, default: 'single' Method to create the computational grids. The different methods are: - ``'same'``: Same grid as for the input model. - ``'single'``: A single grid for all sources and frequencies. - ``'frequency'``: Frequency-dependent grids. - ``'source'``: Source-dependent grids. - ``'both'``: Frequency- and source-dependent grids. - ``'input'``: Same as ``'single'``, but the grid has to be provided in ``gridding_opts`` instead of being automatically created. - ``'dict'``: Same as ``'both'``, but the grids have to be provided in ``gridding_opts`` in the form of ``dict[source][frequency]`` instead of being automatically created. See the parameter ``gridding_opts`` for more details. If ``gridding`` is ``'same'`` or ``'input'``, the input grid is checked if it is a sensible grid for emg3d; if not, it throws a warning. In the other cases the grids are created by emg3d itself, they will be fine. (If ``'dict'`` we assume the user knows how to provide good grids.) gridding_opts : {dict, TensorMesh}, default: {} Input format depends on ``gridding``: - ``'same'``: Nothing, ``gridding_opts`` is not permitted. - ``'single'``, ``'frequency'``, ``'source'``, ``'both'``: Described below. - ``'input'``: A :class:`emg3d.meshes.TensorMesh`. - ``'dict'``: Dictionary of the format ``dict[source][frequency]`` containing a :class:`emg3d.meshes.TensorMesh` for each source-frequency pair. The dict in the case of ``'single'``, ``'frequency'``, ``'source'``, ``'both``' is passed to :func:`emg3d.meshes.construct_mesh`; consult the corresponding documentation for more information. Parameters that are not provided are estimated from the provided model, grid, and survey using :func:`emg3d.meshes.estimate_gridding_opts`, which documentation contains more information too. There are two notably differences to the parameters described in :func:`emg3d.meshes.construct_mesh`: - ``vector``: besides the normal possibility it can also be a string containing one or several of ``'x'``, ``'y'``, and ``'z'``. In these cases the corresponding dimension of the input mesh is provided as vector. See :func:`emg3d.meshes.estimate_gridding_opts`. - ``expand``: in the format of ``[property_sea, property_air]``; if provided, the input model is expanded up to the seasurface with sea water, and an air layer is added. The actual height of the seasurface can be defined with the key ``seasurface``. See :func:`emg3d.models.expand_grid_model`. NOTE: ``expand`` is deprecated in v1.7.0, and will be removed in v1.9.0. A property-complete model has to be provided. solver_opts : dict, default: {'verb': 1'} Passed through to :func:`emg3d.solver.solve`. The dict can contain any parameter that is accepted by the :func:`emg3d.solver.solve` except for ``model``, ``sfield``, ``efield``, ``return_info``, and ``log``. Default verbosity is ``verb=2``. verb : int, default: 0 Level of verbosity. Possible options: - -1: Errors. - 0: Warnings. - 1: Info. name : str, default: None Name of the simulation. info : str, default: None Simulation info or any other info (e.g., what was the purpose of this simulation). receiver_interpolation : str, default: 'cubic': Interpolation method to obtain the response at receiver location; 'cubic' or 'linear'. Cubic is more precise. However, if you are interested in the gradient, you need to choose 'linear' at the moment, as there are only linearly interpolated source functions. To be the proper adjoint for the gradient the receiver has to be interpolated linearly too. file_dir : str, default: None Absolute or relative path, where temporary files should be stored. By default, everything is done in memory. However, for large models with many sources and frequencies this can become memory consuming. Providing a ``file_dir`` can help with this. Fields and models are then stored to disk, and each process accesses the files it needs. There is only a gain if there are more source-frequency pairs than concurrent running processes. Note that the directory is created if it does not exist. However, the parent directory must exist. Also note that the files are stored as .h5-files, and you need to have ``h5py`` installed to use this feature. tqdm_opts : {bool, dict}, default: True Boolean if a progress bar should be shown (only if ``tqdm`` is installed). If a dict is provided it will be forwarded to ``tqdm``. """ # Gridding descriptions (for repr's). _gridding_descr = { 'same': 'Same grid as for model', 'single': 'Single grid for all sources and frequencies', 'frequency': 'Frequency-dependent grids', 'source': 'Source-dependent grids', 'both': 'Frequency- and source-dependent grids', 'input': 'Provided grid, same for all sources/frequencies', 'dict': 'Provided grids, frequency-/source-dependent', } def __init__(self, survey, model, max_workers=4, gridding='single', **kwargs): """Initiate a new Simulation instance.""" # Store some inputs as is, optional ones with defaults. self.survey = survey self.max_workers = max_workers self.gridding = gridding self.verb = kwargs.pop('verb', 0) = kwargs.pop('name', None) = kwargs.pop('info', None) self.receiver_interpolation = kwargs.pop( 'receiver_interpolation', 'cubic') # Assemble solver_opts. self.solver_opts = { 'verb': 1, # Default verbosity, can be overwritten. 'log': -1, # Default only log, can be overwritten. **kwargs.pop('solver_opts', {}), # User setting. 'return_info': True, # return_info=True is forced. } # Initiate dictionaries and other values with None's. self._dict_grid = self._dict_initiate self._dict_efield = self._dict_initiate self._dict_efield_info = self._dict_initiate self._gradient = None self._misfit = None # Initiate file_dir self.file_dir = kwargs.pop('file_dir', None) if self.file_dir: self.file_dir = os.path.abspath(self.file_dir) # Create directory if it doesn't exist yet. Path(self.file_dir).mkdir(exist_ok=True) # Get model taking gridding_opts into account. # Sets self.model and self.gridding_opts. self._set_model(model, kwargs) # Initiate synthetic data with NaN's if they don't exist. if 'synthetic' not in self.survey._data['synthetic'] = data=np.full(self.survey.shape, np.nan+1j*np.nan)) # `tqdm`-options. tqdm_opts = kwargs.pop('tqdm_opts', {}) if isinstance(tqdm_opts, bool): tqdm_opts = {'disable': not tqdm_opts} self._tqdm_opts = { **{'bar_format': '{desc} {bar} {n_fmt}/{total_fmt} [{elapsed}]'}, **tqdm_opts, } # Ensure no kwargs left. if kwargs: raise TypeError(f"Unexpected **kwargs: {list(kwargs.keys())}.") # Check the grid if one was explicitly provided. if gridding == 'same': meshes.check_mesh(self.model.grid) elif gridding == 'input': meshes.check_mesh(self._grid_single) def __repr__(self): """Simple representation.""" name = f" «{}»" if else "" info = f"{}\n" if else "" survey = f" «{}»" if else "" return (f":: {self.__class__.__name__}{name} ::\n{info}\n" f"- {self.survey.__class__.__name__}{survey}: " 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]}; " f"{self._info_grids}") def _repr_html_(self): """HTML representation.""" name = f" «{}»" if else "" info = f"{}<br>" if else "" survey = f" «{}»" if else "" return (f"<h3>{self.__class__.__name__}{name}</h3>{info}" f"<ul>" f" <li>{self.survey.__class__.__name__}{survey}:" 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: {self._gridding_descr[self.gridding]}; " f" {self._info_grids}</li>" f"</ul>")
[docs] def clean(self, what='computed'): """Clean part of the data base. Parameters ---------- what : str, default: 'computed' What to clean. Possibilities: - ``'computed'``: 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 grid/model-dicts. if what in ['keepresults', 'all']: # These exist always and have to be initiated. for name in ['_dict_grid', ]: delattr(self, name) setattr(self, name, self._dict_initiate) # Clean field-dicts. if what in ['computed', 'keepresults', 'all']: # These exist always and have to be initiated. for name in ['_dict_efield', '_dict_efield_info']: delattr(self, name) setattr(self, name, self._dict_initiate) # These only exist with gradient; don't initiate them. for name in ['_dict_bfield', '_dict_bfield_info']: if hasattr(self, name): delattr(self, name) # Remove files if they exist. if self.file_dir: for p in Path(self.file_dir).glob('[ebg]field_*.h5'): p.unlink() # Clean data. if what in ['computed', 'all']: for key in ['residual', 'weight']: if key in del[key]['synthetic'] = data=np.full(self.survey.shape, np.nan+1j*np.nan)) for name in ['_gradient', '_misfit']: delattr(self, name) setattr(self, name, None)
[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 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') if what not in ['computed', 'results', 'all', 'plain']: raise TypeError(f"Unrecognized `what`: {what}.") # Initiate dict with input parameters. out = { '__class__': self.__class__.__name__, 'survey': self.survey.to_dict(), 'model': self.model.to_dict(), 'max_workers': self.max_workers, 'gridding': self.gridding, 'gridding_opts': self.gridding_opts, 'solver_opts': self.solver_opts, 'verb': self.verb, 'name':, 'info':, 'tqdm_opts': self._tqdm_opts, 'receiver_interpolation': self.receiver_interpolation, 'file_dir': self.file_dir, '_input_sc2': self._input_sc2, } # Clean unwanted data if plain. if what == 'plain': for key in ['synthetic', 'residual', 'weights']: if key in out['survey']['data'].keys(): del out['survey']['data'][key] # Store wanted dicts. if what in ['computed', 'all']: for name in ['_dict_grid', '_dict_efield', '_dict_efield_info', '_dict_bfield', '_dict_bfield_info']: if hasattr(self, name): out[name] = getattr(self, name) # Store gradient and misfit. if what in ['computed', 'results', 'all']: out['gradient'] = self._gradient out['misfit'] = self._misfit if copy: return deepcopy(out) else: return out
[docs] @classmethod def from_dict(cls, inp): """Convert dict into :class:`emg3d.simulations.Simulation` instance. Parameters ---------- inp : dict Dictionary as obtained from :func:`emg3d.simulations.Simulation.to_dict`. Returns ------- simulation : Simulation A :class:`emg3d.simulations.Simulation` instance. """ inp = {k: v for k, v in inp.items() if k != '__class__'} # Get all class-inputs. inp_names = ['survey', 'model', 'max_workers', 'gridding', 'solver_opts', 'verb', 'name', 'info'] cls_inp = {k: inp.pop(k) for k in inp_names} cls_inp['gridding_opts'] = inp.pop('gridding_opts', {}) cls_inp['survey'] = surveys.Survey.from_dict(cls_inp['survey']) cls_inp['model'] = models.Model.from_dict(cls_inp['model']) input_sc2 = inp.pop('_input_sc2', False) if input_sc2: cls_inp['_input_sc2'] = input_sc2 cls_inp['receiver_interpolation'] = inp.pop( 'receiver_interpolation', 'cubic') cls_inp['file_dir'] = inp.pop('file_dir', None) cls_inp['tqdm_opts'] = inp.pop('tqdm_opts', {}) # Instantiate the class. out = cls(**cls_inp) # Add existing derived/computed properties. data = ['_dict_grid', '_dict_efield', '_dict_efield_info', '_dict_bfield', '_dict_bfield_info'] for name in data: if name in inp.keys(): values = inp.pop(name) # De-serialize Model, Field, and TensorMesh instances. io._dict_deserialize(values) setattr(out, name, values) # Add gradient and misfit. data = ['gradient', 'misfit'] for name in data: if name in inp.keys(): setattr(out, '_'+name, inp.pop(name)) return out
[docs] def to_file(self, fname, what='computed', name='simulation', **kwargs): """Store Simulation to a file. Parameters ---------- fname : str Absolute or relative file name including ending, which defines the used data format. See :func:`` for the options. what : str, default: 'computed' What to store. Possibilities: - ``'computed'``, ``'all'``: Stores all computed properties: electric fields and responses at receiver locations. - '``results'``: Stores only the response at receiver locations. - ``'plain'``: Only stores the plain Simulation (as initiated). Note that if ``file_dir`` is set, those files will remain there. name : str, default: 'simulation' Name with which the simulation is stored in the file. kwargs : Keyword arguments, optional Passed through to :func:``. """ # Add what to self, will be removed in to_dict. self._what_to_file = what # Add simulation to dict. kwargs[name] = self # If verb is not defined, use verbosity of simulation. kwargs['verb'] = kwargs.get('verb', self.verb) return, **kwargs)
[docs] @classmethod def from_file(cls, fname, name='simulation', **kwargs): """Load Simulation from a file. Parameters ---------- fname : str Absolute or relative file name including extension. name : str, default: 'simulation' Name under which the simulation is stored within the file. kwargs : Keyword arguments, optional Passed through to :func:`io.load`. Returns ------- simulation : Simulation A :class:`emg3d.simulations.Simulation` instance. info : str, returned if verb<0 Info-string. """ out = io.load(fname, **kwargs) if 'verb' in kwargs and kwargs['verb'] < 0: return out[0][name], out[1] else: return out[name]
# GET FUNCTIONS @property def data(self): """Shortcut to""" return
[docs] def get_grid(self, source, frequency): """Return computational grid of the given source and frequency.""" freq = self._freq_inp2key(frequency) # Return grid if it exists already. if self._dict_grid[source][freq] is not None: return self._dict_grid[source][freq] # Same grid as for provided model. if self.gridding == 'same': # Store link to grid. self._dict_grid[source][freq] = self.model.grid # Frequency-dependent grids. elif self.gridding == 'frequency': # Initiate dict. if not hasattr(self, '_grid_frequency'): self._grid_frequency = {} # Get grid for this frequency if not yet computed. if freq not in self._grid_frequency.keys(): # Get grid and store it. inp = {**self.gridding_opts, 'frequency': self.survey.frequencies[freq]} self._grid_frequency[freq] = meshes.construct_mesh(**inp) # Store link to grid. self._dict_grid[source][freq] = self._grid_frequency[freq] # Source-dependent grids. elif self.gridding == 'source': # Initiate dict. if not hasattr(self, '_grid_source'): self._grid_source = {} # Get grid for this source if not yet computed. if source not in self._grid_source.keys(): # Get grid and store it. center = self.survey.sources[source].center inp = {**self.gridding_opts, 'center': center} self._grid_source[source] = meshes.construct_mesh(**inp) # Store link to grid. self._dict_grid[source][freq] = self._grid_source[source] # Source- and frequency-dependent grids. elif self.gridding == 'both': # Get grid and store it. center = self.survey.sources[source].center inp = {**self.gridding_opts, 'frequency': self.survey.frequencies[freq], 'center': center} self._dict_grid[source][freq] = meshes.construct_mesh(**inp) # Use a single grid for all sources and receivers. # Default case; catches 'single' but also anything else. else: # Get grid if not yet computed. if not hasattr(self, '_grid_single'): # Get grid and store it. self._grid_single = meshes.construct_mesh(**self.gridding_opts) # Store link to grid. self._dict_grid[source][freq] = self._grid_single # Use recursion to return grid. return self.get_grid(source, frequency)
[docs] def get_model(self, source, frequency): """Return model on the grid of the given source and frequency.""" grid = self.get_grid(source, self._freq_inp2key(frequency)) return self.model.interpolate_to_grid(grid)
[docs] def get_efield(self, source, frequency): """Return electric field for given source and frequency.""" freq = self._freq_inp2key(frequency) # If it doesn't exist yet, compute it. if self._dict_get('efield', source, freq) is None: self.compute(source=source, frequency=freq) return self._dict_get('efield', source, freq)
[docs] def get_hfield(self, source, frequency): """Return magnetic field for given source and frequency.""" freq = self._freq_inp2key(frequency) # If electric field not computed yet compute it. if self._dict_get('efield', source, freq) is None: self.compute(source=source, frequency=freq) # Return magnetic field. return fields.get_magnetic_field( self.get_model(source, freq), self._dict_get('efield', source, freq), )
[docs] def get_efield_info(self, source, frequency): """Return the solver information of the corresponding computation.""" freq = self._freq_inp2key(frequency) return self._dict_get('efield_info', source, freq)
def _dict_get(self, which, source, frequency): """Return source-frequency pair from dictionary `which`. Thin wrapper for ``self._dict_{which}[{source}][{frequency}]``, that works as well for file-based computations. """ value = getattr(self, f"_dict_{which}")[source][frequency] return self._load(value, ['efield', 'info']['info' in which]) def _load(self, value, what): """Returns `value` (memory) or loads `value[what]` (files).""" if self.file_dir and value is not None: return io.load(value, verb=0)[what] else: return value def _data_or_file(self, what, source, frequency, data): """Return data or file-name for given what, source, and frequency.""" if self.file_dir: fname = os.path.join( self.file_dir, f"{what}_{source}_{frequency}.h5"), data=data, verb=0) return fname else: return data def _get_responses(self, source, frequency, efield=None): """Return electric and magnetic fields at receiver locations.""" # Get receiver types and their coordinates. erec, mrec = self.survey._irec_types erec_coord, mrec_coord = self.survey._rec_types_coord(source) # Initiate output. resp = np.zeros_like([source, :, frequency]) # efield of this source/frequency if not provided. if efield is None: efield = self._dict_get('efield', source, frequency) if erec.size: # Store electric receivers. resp[erec] = efield.get_receiver( receiver=erec_coord, method=self.receiver_interpolation, ) if mrec.size: # Compute magnetic field. hfield = fields.get_magnetic_field( self.get_model(source, frequency), efield, ) # Store electric receivers. resp[mrec] = hfield.get_receiver( receiver=mrec_coord, method=self.receiver_interpolation, ) return resp # ASYNCHRONOUS COMPUTATION
[docs] def compute(self, observed=False, **kwargs): """Compute efields asynchronously for all sources and frequencies. Parameters ---------- observed : bool, default: False If True, it stores the current `synthetic` responses also as `observed` responses. add_noise : bool, default: True Boolean if to add noise to observed data (if ``observed=True``). All remaining ``kwargs`` are forwarded to :meth:`emg3d.surveys.Survey.add_noise`. """ # Undocumented (internal): # If the call is from `get_efield`, it will have source/frequency. # This use is only internal. End users should use `get_efield()`. srcfreq = [ (kwargs.pop('source', None), kwargs.pop('frequency', None)), ] if not srcfreq[0][0]: # "Normal" case: all source-frequency pairs. srcfreq = self._srcfreq # Create iterable from src/freq-list for parallel computation. def collect_efield_inputs(inp): """Collect inputs.""" source, freq = inp data = { 'model': self.model, 'grid': self.get_grid(source, freq), 'source': self.survey.sources[source], 'frequency': self.survey.frequencies[freq], # efield is None if not comp. yet; else it is the solution. 'efield': self._dict_get('efield', source, freq), 'solver_opts': self.solver_opts, } return self._data_or_file('efield', source, freq, data) # Compute fields in parallel. out = self._compute(collect_efield_inputs, 'Compute efields', srcfreq) # Loop over src-freq combinations to extract and store. for i, (src, freq) in enumerate(srcfreq): # Store efield and solver info. self._dict_efield[src][freq] = out[i][0] self._dict_efield_info[src][freq] = out[i][1] # Store responses at receiver locations. resp = self._get_responses(src, freq)['synthetic'].loc[src, :, freq] = resp # Print solver info. self.print_solver_info('efield', verb=self.verb) # If it shall be used as observed data save a copy. if observed: # Copy synthetic to observed.['observed'] =['synthetic'].copy() # Add noise. if kwargs.pop('add_noise', True): self.survey.add_noise(**kwargs)
def _compute(self, fn, description, srcfreq=None): """Use utils._process_map to call solver._solve asynchronously.""" return utils._process_map( solver._solve, list(map(fn, self._srcfreq if srcfreq is None else srcfreq)), max_workers=self.max_workers, **{'desc': description, **self._tqdm_opts}, ) # OPTIMIZATION @property def gradient(self): r"""Compute the discrete gradient using the adjoint-state method. The discrete adjoint-state gradient for a single source at a single frequency is given by Equation (10) in [PlMu08]_, .. math:: \nabla_p \phi(\textbf{p}) = -&\sum_{k,l,m}\mathbf{\bar{\lambda}}_{x; k+\frac{1}{2}, l, m} \frac{\partial S_{k+\frac{1}{2}, l, m}}{\partial \textbf{p}} \textbf{E}_{x; k+\frac{1}{2}, l, m}\\ -&\sum_{k,l,m}\mathbf{\bar{\lambda}}_{y; k, l+\frac{1}{2}, m} \frac{\partial S_{k, l+\frac{1}{2}, m}}{\partial \textbf{p}} \textbf{E}_{y; k, l+\frac{1}{2}, m}\\ -&\sum_{k,l,m}\mathbf{\bar{\lambda}}_{z; k, l, m+\frac{1}{2}} \frac{\partial S_{k, l, m+\frac{1}{2}}}{\partial \textbf{p}} \textbf{E}_{z; k, l, m+\frac{1}{2}}\, , where :math:`\textbf{E}` is the electric (forward) field and :math:`\mathbf{\lambda}` is the back-propagated residual field (from electric and magnetic receivers); :math:`\bar{~}` denotes conjugate. The :math:`\partial S`-part takes care of the volume-averaged model parameters. .. warning:: To obtain the proper adjoint-state gradient you have to choose linear interpolation for the receiver responses: ``emg3d.Simulation(..., receiver_interpolation='linear')``. The reason is that the point-source is the adjoint of a tri-linear interpolation, so the residual should come from a linear interpolation. .. note:: The currently implemented gradient does only work for models without relative electric permittivity nor relative magnetic permeability. Returns ------- grad : ndarray Adjoint-state gradient. Shape depends on the anisotropy type: - isotropic: (nx, ny, nz) - HTI/VTI: (2, nx, ny, nz) - triaxial: (3, nx, ny, nz) """ if self._gradient is None: # Warn that cubic is not good for adjoint-state gradient. if self.receiver_interpolation == 'cubic': msg = ( "emg3d: Receiver responses were obtained with cubic " "interpolation. This will not yield the exact gradient. " "Change `receiver_interpolation='linear'` in the call to " "Simulation()." ) warnings.warn(msg, UserWarning) # Check limitation: No epsilon_r, mu_r. var = (self.model.epsilon_r, self.model.mu_r) for v, n in zip(var, ('el. permittivity', 'magn. permeability')): if v is not None and not np.allclose(v, 1.0): raise NotImplementedError( f"Gradient not implemented for {n}." ) # Ensure misfit has been computed # (and therefore the electric fields). _ = self.misfit # Compute back-propagating electric fields. self._bcompute() # Inversion grid and its shape. igrid = self.model.grid ishape = igrid.shape_cells # Pre-allocate the gradient on the mesh. gradient = np.zeros((3, *ishape), order='F') # Loop over source-frequency pairs. for src, freq in self._srcfreq: efield = self._dict_get('efield', src, freq) bfield = self._dict_get('bfield', src, freq) # Multiply forward field with backward field; take real part. gfield = fields.Field( grid=efield.grid, data=np.real(bfield.field * efield.smu0 * efield.field), ) # Pre-allocate the gradient for the computational grid. shape = gfield.grid.shape_cells grad = np.zeros((3, *shape), order='F') # Map the field to cell centers times volume. cell_volumes = gfield.grid.cell_volumes maps.interp_edges_to_vol_averages( ex=gfield.fx, ey=gfield.fy, ez=gfield.fz, volumes=cell_volumes.reshape(shape, order='F'), ox=grad[0, ...], oy=grad[1, ...], oz=grad[2, ...]) # Bring gradient back from computation grid to inversion grid # and add it to the total gradient. if igrid != gfield.grid: # Requires discretize; for this reason wrapped in own fct. maps._interp_volume_average_adj( oval=gradient, ogrid=igrid, nval=grad, ngrid=gfield.grid, ) else: gradient += grad # Apply derivative-chain of property-map (only relevant if # `mapping` is something else than conductivity) and collect. indices = [0, ] if in ['HTI', 'triaxial']: gradient[1, ...], self.model.property_y) indices.append(1) else: gradient[0, ...] += gradient[1, ...] if in ['VTI', 'triaxial']: gradient[2, ...], self.model.property_z) indices.append(2) else: gradient[0, ...] += gradient[2, ...] gradient[0, ...], self.model.property_x) # Select required directions, excluded "expanded" layers & squeeze. self._gradient = gradient[indices, ..., :self._input_sc2].squeeze() return self._gradient @property def misfit(self): r"""Misfit or cost function. The data misfit or weighted least-squares functional using an :math:`l_2` norm is given by .. math:: :label: misfit \phi = \frac{1}{2} \sum_s\sum_r\sum_f \left\lVert W_{s,r,f} \left( \textbf{d}_{s,r,f}^\text{pred} -\textbf{d}_{s,r,f}^\text{obs} \right) \right\rVert^2 \, , where :math:`s, r, f` stand for source, receiver, and frequency, respectively; :math:`\textbf{d}^\text{obs}` are the observed electric and magnetic data, and :math:`\textbf{d}^\text{pred}` are the synthetic electric and magnetic data. As of now the misfit does not include any regularization term. The data weight of observation :math:`d_i` is given by :math:`W_i = \varsigma^{-1}_i`, where :math:`\varsigma_i` is the standard deviation of the observation, see :attr:`emg3d.surveys.Survey.standard_deviation`. .. note:: You can easily implement your own misfit function (to include, e.g., a regularization term) by monkey patching this misfit function with your own:: @property # misfit is a property def my_misfit_function(self): '''Returns the misfit as a float.''' if self._misfit is None: self.compute() # Ensures fields are computed. # Computing your misfit... self._misfit = your misfit return self._misfit # Monkey patch simulation.misfit: emg3d.simulation.Simulation.misfit = my_misfit_function # And now all the regular stuff, initiate a Simulation etc simulation = emg3d.Simulation(survey, grid, model) simulation.misfit # => will return your misfit # (will also be used for the adjoint-state gradient). Returns ------- misfit : float Value of the misfit function. """ if self._misfit is None: # Ensure efields are computed self.compute() # Check if weights are stored already. (weights are currently # simply 1/std^2; but might change in the future). if 'weights' not in # Get standard deviation, raise warning if not set. std = self.survey.standard_deviation if std is None: raise ValueError( "Either `noise_floor` or `relative_error` or both " "must be provided (>0) to compute the " "`standard_deviation`. It can also be set directly " "(same shape as data). The standard deviation is " "required to compute the misfit." ) # Store weights['weights'] = std**-2 # Calculate and store residual. residual = -['residual'] = residual # Get weights, calculate misfit. weights =['weights'] self._misfit = np.sum(weights*(residual.conj()*residual)).real/2 return self._misfit def _bcompute(self): """Compute bfields asynchronously for all sources and frequencies.""" # Initiate back-propagated electric field and info dicts. if not hasattr(self, '_dict_bfield'): self._dict_bfield = self._dict_initiate self._dict_bfield_info = self._dict_initiate # Create iterable from src/freq-list for parallel computation. def collect_bfield_inputs(inp): """Collect inputs.""" source, freq = inp data = { 'model': self.model, 'sfield': self._get_rfield(source, freq), # bfield is None unless it was explicitly set. 'efield': self._dict_get('bfield', source, freq), 'solver_opts': self.solver_opts } return self._data_or_file('bfield', source, freq, data) # Compute fields in parallel. out = self._compute(collect_bfield_inputs, 'Back-propagate') # Loop over src-freq combinations to extract and store. for i, (src, freq) in enumerate(self._srcfreq): # Store bfield and solver info. self._dict_bfield[src][freq] = out[i][0] self._dict_bfield_info[src][freq] = out[i][1] # Print solver info. self.print_solver_info('bfield', verb=self.verb) def _get_rfield(self, source, frequency): """Return residual source field for given source and frequency.""" freq = self.survey.frequencies[frequency] # Get values for this source and frequency. grid = self.get_grid(source, frequency) residual =[source, :, frequency].data weight =[source, :, frequency].data # Initiate empty residual source field. rfield = fields.Field(grid, frequency=freq) # Residual source strength: Weighted residual, normalized by -smu0. strength = np.conj(residual * weight / -rfield.smu0) # Loop over receivers, input as source. for i, rec in enumerate(self.survey.receivers.values()): # Skip if no data. if np.isnan(residual[i]): continue # Get absolute coordinates as fct of source. # (Only relevant in case of "relative" receivers.) coords = rec.coordinates_abs(self.survey.sources[source]) # Create adjoint source. src = rec._adjoint_source(coords, strength=strength[i]) # Get and add this source field. rfield.field += src.get_field(grid=grid, frequency=freq).field return rfield
[docs] @utils._requires('discretize') def jvec(self, vector): r"""Compute the sensitivity times a vector. .. math:: :label: jvec J v = P A^{-1} G v \ , where :math:`v` has size of the model. Parameters ---------- vector : ndarray Vector applied to J. Shape depends on the anisotropy type: - isotropic: (nx, ny, nz) or (1, nx, ny, nz) - HTI/VTI: (2, nx, ny, nz) - triaxial: (3, nx, ny, nz) Returns ------- jvec : ndarray Shape of the data. """ # Missing for jvec/jtvec # - Refactor `compute/gradient/_bcompute/_get_rfield/jvec/jtvec`. # - Document properly jvec and jtvec. # - Would gradient (?, nx, ny, nz) be better a Model-like instance? # Ensure misfit has been computed (and therefore the electric fields). _ = self.misfit # Apply derivative-chain of property-map (copy to not overwrite). if vector.ndim == 3: vector = vector[None, ...].copy() else: vector = vector.copy()[0, ...], self.model.property_x) if in ['HTI', 'triaxial']: vector[1, ...], self.model.property_y) if in ['VTI', 'triaxial']: n = 1 if == 'VTI' else 2 vector[n, ...], self.model.property_z) # Interpolation options. iopts = {'method': 'volume', 'extrapolate': True, 'log': False, 'grid': self.model.grid} # Create iterable from src/freq-list for parallel computation. def collect_gfield_inputs(inp, vector=vector): """Collect inputs.""" source, freq = inp # Forward electric field efield = self._dict_get('efield', source, freq) # Interpolate to computational grid. cvector = [ maps.interpolate(values=v, xi=efield.grid, **iopts).ravel('F') for v in vector[:, ...] ] if == 'isotropic': ncase = 1 cvector = cvector[0] else: ncase = 3 if == 'HTI': cvector = np.r_[cvector[0], cvector[1], cvector[0]] elif == 'VTI': cvector = np.r_[cvector[0], cvector[0], cvector[1]] else: cvector = np.r_[cvector].ravel() # Compute gvec = G * vector (using discretize). gvec = efield.grid.get_edge_inner_product_deriv( np.ones(efield.grid.n_cells*ncase) )(efield.field) * cvector # Create source field. gfield = fields.Field( grid=efield.grid, data=-efield.smu0*gvec, # -iwu: To get complete source field. frequency=efield.frequency ) data = { 'model': self.model, 'sfield': gfield, 'efield': None, 'solver_opts': self.solver_opts, } return self._data_or_file('gfield', source, freq, data) # Compute fields (A^-1 * G * vector) in parallel. out = self._compute(collect_gfield_inputs, 'Compute jvec') # Initiate jvec data with NaN's if it doesn't exist. if 'jvec' not in['jvec'] = data=np.full(self.survey.shape, np.nan+1j*np.nan)) # Loop over src-freq combinations to extract and store. for i, (src, freq) in enumerate(self._srcfreq): gfield = self._load(out[i][0], 'efield') resp = self._get_responses(src, freq, gfield)['jvec'].loc[src, :, freq] = resp return['jvec'].data
[docs] def jtvec(self, vector): r"""Compute the sensitivity transpose times a vector. If ``vector=residual*weights``, ``jtvec`` corresponds to the ``gradient``. .. math:: :label: jtvec J^H v = G^H A^{-H} P^H v \ , where :math:`v` has the shape of the data. Parameters ---------- vector : ndarray, DataArray An array with the shape of the data, or directly a DataArray as stored in the :class:`emg3d.surveys.Survey`. Returns ------- jtvec : ndarray Adjoint-state gradient for the provided vector. Shape depends on the anisotropy type: - isotropic: (nx, ny, nz) - HTI/VTI: (2, nx, ny, nz) - triaxial: (3, nx, ny, nz) """ # Replace residual by provided vector # (division by weight is undone in gradient).[...] = vector/ # Reset gradient, so it will be computed. self._gradient = None for name in ['_dict_bfield', '_dict_bfield_info']: if hasattr(self, name): delattr(self, name) # Return gradient from weighted residual `vector`. return self.gradient
# UTILS @property def _dict_initiate(self): """Return 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.keys() ) ) return self.__srcfreq def _freq_inp2key(self, frequency): """Return key of frequency entry given its key or its value. """ if not isinstance(frequency, str): if not hasattr(self, '__freq_inp2key'): self.__freq_inp2key = { float(v): k for k, v in self.survey.frequencies.items() } frequency = self.__freq_inp2key[frequency] return frequency @property def _info_grids(self): """Return a string with "min {- max}" grid size.""" # Single grid for all sources and receivers. if self.gridding in ['same', 'single', 'input']: grid = self.get_grid(*self._srcfreq[0]) min_nc = grid.n_cells min_vc = grid.shape_cells has_minmax = False # Source- and/or frequency-dependent grids. else: min_nc = 1e100 max_nc = 0 # Loop over all grids and get smallest/biggest values. for src, freq in self._srcfreq: grid = self.get_grid(src, freq) if grid.n_cells > max_nc: max_nc = grid.n_cells max_vc = grid.shape_cells if grid.n_cells < min_nc: min_nc = grid.n_cells min_vc = grid.shape_cells has_minmax = min_nc != max_nc # Assemble info. info = f"{min_vc[0]} x {min_vc[1]} x {min_vc[2]} ({min_nc:,})" if has_minmax: info += f" - {max_vc[0]} x {max_vc[1]} x {max_vc[2]} ({max_nc:,})" return info
[docs] def print_grid_info(self, verb=1, return_info=False): """Print info for all generated grids.""" def get_grid_info(src, freq): """Return grid info for given source and frequency.""" grid = self.get_grid(src, freq) out = '' if verb != 0 and hasattr(grid, 'construct_mesh_info'): out += grid.construct_mesh_info out += grid.__repr__() return out # Act depending on gridding: out = "" # Frequency-dependent. if self.gridding == 'frequency': for freq in self.survey.frequencies.values(): out += f"= Source: all; Frequency: {freq} Hz =\n" out += get_grid_info(self._srcfreq[0][0], freq) # Source-dependent. elif self.gridding == 'source': for src in self.survey.sources.keys(): out += f"= Source: {src}; Frequency: all =\n" out += get_grid_info(src, self._srcfreq[0][1]) # Source- and frequency-dependent. elif self.gridding == 'both': for src, freq in self._srcfreq: out += f"= Source: {src}; Frequency: " out += f"{self.survey.frequencies[freq]} Hz =\n" out += get_grid_info(src, freq) # Single grid. else: out += "= Source: all; Frequency: all =\n" out += get_grid_info(self._srcfreq[0][0], self._srcfreq[0][1]) if return_info: return out elif out: print(out)
[docs] def print_solver_info(self, field='efield', verb=1, return_info=False): """Print solver info.""" # If not verbose, return. if verb < 0: return # Get info dict. out = "" # Loop over sources and frequencies. for src, freq in self._srcfreq: cinfo = self._dict_get(f"{field}_info", src, freq) # Print if verbose or not converged. if cinfo is not None and (verb > 0 or cinfo['exit'] != 0): # Initial message. if not out: out += "\n" if verb > 0: out += f" - SOLVER INFO <{field}> -\n\n" # Source and frequency info. out += f"= Source {src}; Frequency " out += f"{self.survey.frequencies[freq]} Hz =" # Print log depending on solver and simulation verbosities. if verb == 0 or self.solver_opts['verb'] != 1: out += f" {cinfo['exit_message']}\n" if verb == 1 and self.solver_opts['verb'] == 1: out += f" {cinfo['log'][12:]}" if verb == 1 and self.solver_opts['verb'] > 1: out += f"\n{cinfo['log']}\n" if return_info: return out elif out: print(out)
def _set_model(self, model, kwargs): """Set self.model and self.gridding_opts.""" # Store original input_sc2. Undocumented. # This should eventually be replaced by an `active_cells` mask. self._input_sc2 = kwargs.pop('_input_sc2', model.shape[2]) # Get gridding_opts from kwargs. gridding_opts = kwargs.pop('gridding_opts', {}) # If 'dict', entire dict should be provided. if self.gridding == 'dict': self._dict_grid = gridding_opts # If 'input', TensorMesh should be provided elif self.gridding == 'input': self._grid_single = gridding_opts # If 'same', there shouldn't be any options. elif self.gridding == 'same': if gridding_opts: msg = "`gridding_opts` is not permitted if `gridding='same'`." raise TypeError(msg) # If 'source', 'frequency', 'both', 'single' => automatic gridding. else: g_opts = gridding_opts.copy() # Expand model by water and air if required. expand = g_opts.pop('expand', None) if expand is not None: msg = ("emg3d: `expand` is deprecated and will be removed in " "v1.9.0. A property-complete model has to be provided.") warnings.warn(msg, FutureWarning) try: interface = g_opts['seasurface'] except KeyError as e: msg = ("`g_opts['seasurface']` is required if " "`g_opts['expand']` is provided.") raise KeyError(msg) from e model = models.expand_grid_model(model, expand, interface) # Get automatic gridding input. # Estimate the parameters from survey and model if not provided. gridding_opts = meshes.estimate_gridding_opts( g_opts, model, self.survey, self._input_sc2) self.gridding_opts = gridding_opts self.model = model