Grid Classes

plateflex defines the following Grid classes:

Grid
TopoGrid
GravGrid
BougGrid
FairGrid
RhocGrid
ZcGrid

These classes can be initialized with a grid of the corresponding data type, and contain methods for the following functionality:

Extracting contours at some level of the grid
Performing a wavelet transform using a Morlet wavelet
Obtaining the wavelet scalogram from the wavelet transform
Plotting the input grids, wavelet transform components, and scalograms

Grid

class plateflex.classes.Grid(grid, dx, dy)

An object containing a 2D array of data and Cartesian coordinates specifying the bounding box of the array. Contains methods to calculate the wavelet transform, wavelet scalogram and to plot those quantities at a specified wavenumber index.

Parameters:

grid (ndarray) – 2D array of of topography/gravity data
dx (float) – Grid spacing in the x-direction (km)
dy (float) – Grid spacing in the y-direction (km)

Grid must be projected in km.

Default Attributes

datandarray: 2D array of topography/gravity data (shape (nx,ny))
dxfloat: Grid spacing in the x-direction in km
dyfloat: Grid spacing in the y-direction in km
nxint: Number of grid cells in the x-direction
nyint: Number of grid cells in the y-direction
unitsstr: Units of data set
sg_unitsstr: Units of power-spectral density of data set
logsg_unitsstr: Units of power-spectral density of data set in log
titlestr: Descriptor for data set - used in title of plots
ns int: Number of wavenumber samples
knp.ndarray: 1D array of wavenumbers

>>> import numpy as np
>>> from plateflex import Grid
>>> # Create zero-valued square grid
>>> nn = 200; dd = 10.
>>> xmin = ymin = 0.
>>> xmax = ymax = (nn-1)*dd
>>> data = np.zeros((nn, nn))
>>> grid = Grid(data, dx, dy)
>>> grid
<plateflex.grids.Grid object at 0x10613fe10>

make_contours(level=0.0)

This function returns the contours as a List of coordinate positions at one given level - run this more than once with different levels if desired

Parameters:: level (float) – Level (z value) of grid to contour
Returns:: contours: List of contours with coordinate positions

wlet_transform()

This method uses the module cpwt to calculate the wavelet transform of the grid. By default the method mirrors the grid edges, tapers them (10 points on each edge) and pads the array with zeros to the next power of 2. The wavelet transform is stored as an attribute of the object.

Additional Attributes

wl_transndarray: Wavelet transform of the grid (shape (nx,ny,na,ns))

Example

>>> import numpy as np
>>> from plateflex import Grid
>>> # Create zero-valued square array
>>> nn = 200; dd = 10.
>>> xmin = ymin = 0.
>>> xmax = ymax = (nn-1)*dd
>>> data = np.zeros((nn, nn))
>>> grid = Grid(data, dx, dy)
>>> grid.wlet_transform()
 #loops = 13:  1  2  3  4  5  6  7  8  9 10 11 12 13
>>> grid.wl_trans.shape
(100, 100, 11, 13)

wlet_scalogram()

This method uses the module cpwt to calculate the wavelet scalogram of the grid.

Note

If no wl_trans attribute is found, the method automatically calculates the wavelet transform first.

The wavelet scalogram is stored as an attribute of the object.

Additional Attributes

wl_sgndarray: Wavelet scalogram of the grid (shape (nx,ny,na,ns))

Examples

>>> import numpy as np
>>> from plateflex import Grid

>>> # Create random-valued square grid
>>> nn = 200; dd = 10.
>>> xmin = ymin = 0.
>>> xmax = ymax = (nn-1)*dd
>>> # set random seed
>>> np.random.seed(0)
>>> data = np.random.randn(nn, nn)
>>> grid1 = Grid(data, dx, dy)
>>> grid1.wlet_scalogram()
 #loops = 17:  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17
>>> grid1.wl_sg.shape
(200, 200, 17)

>>> # Perform wavelet transform first
>>> grid2 = Grid(data, dx, dy)
>>> grid2.wlet_transform()
 #loops = 17:  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17
>>> grid2.wlet_scalogram()
>>> np.allclose(grid1.wl_sg, grid2.wl_sg)
True

plot_transform(kindex=None, aindex=None, log=False, mask=None, save=None, clabel=None, contours=None, **kwargs)

This method plots the real and imaginary components of the wavelet transform of a Grid object at wavenumber and angle indices (int). Raises Exception for the cases where:

no wavenumber OR angle index is specified (kindex and aindex)
wavenumber index is lower than 0 or larger than self.ns
angle index is lower than 0 or larger than 11 (hardcoded)

Note

If no wl_trans attribute is found, the method automatically calculates the wavelet transform first.

plot_scalogram(kindex=None, log=True, mask=None, title='Wavelet scalogram', save=None, clabel=None, contours=None, **kwargs)

This method plots the wavelet scalogram of a Grid object at a wavenumber index (int). Raises Exception for the cases where:

no wavenumber index is specified (kindex)
wavenumber index is lower than 0 or larger than self.ns - 1

Note

If no wl_sg attribute is found, the method automatically calculates the wavelet scalogram (and maybe also the wavelet transform) first.

TopoGrid

class plateflex.classes.TopoGrid(grid, dx, dy)

Basic grid class of plateflex for Topography data that inherits from Grid

Additional Attributes

unitsstr: Units of Topography (’\(m\)’)
sg_unitsstr: Units of wavelet PSD (scalogram) (’\(m^2/|k|\)’)
logsg_unitsstr: Units of log of wavelet PSD (log(scalogram)) (’\(log(m^2/|k|)\)’)
title: str: Descriptor for Topography data

>>> import numpy as np
>>> from plateflex import Grid, TopoGrid
>>> nn = 200; dd = 10.
>>> topogrid = TopoGrid(np.random.randn(nn, nn), dd, dd)
>>> isinstance(topogrid, Grid)
True

Note

Automatically converts grid values to ‘meters’ if standard deviation is lower than 20

GravGrid

class plateflex.classes.GravGrid(grid, dx, dy)

Basic grid class of plateflex for gravity data that inherits from Grid

Additional Attributes

unitsstr: Units of Gravity anomaly (’\(mGal\)’)
sg_unitsstr: Units of wavelet PSD (scalogram) (’\(mGal^2/|k|\)’)
logsg_unitsstr: Units of log of wavelet PSD (log(scalogram)) (’\(log(mGal^2/|k|)\)’)
title: str: Descriptor for Gravity data

>>> import numpy as np
>>> from plateflex import Grid, GravGrid
>>> nn = 200; dd = 10.
>>> gravgrid = GravGrid(np.random.randn(nn, nn), dd, dd)
>>> isinstance(gravgrid, Grid)
True

BougGrid

class plateflex.classes.BougGrid(grid, dx, dy)

Basic grid class of plateflex for Bouguer gravity data that inherits from GravGrid

Additional Attributes

title: str: Descriptor for Bouguer gravity data

>>> import numpy as np
>>> from plateflex import Grid, BougGrid, GravGrid
>>> nn = 200; dd = 10.
>>> bouggrid = BougGrid(np.random.randn(nn, nn), dd, dd)
>>> isinstance(bouggrid, GravGrid)
True
>>> isinstance(bouggrid, Grid)
True

FairGrid

class plateflex.classes.FairGrid(grid, dx, dy)

Basic grid class of plateflex for Free-air gravity data that inherits from GravGrid

Additional Attributes

title: str: Descriptor for Free-air gravity data

>>> import numpy as np
>>> from plateflex import Grid, FairGrid, GravGrid
>>> nn = 200; dd = 10.
>>> fairgrid = FaiorGrid(np.random.randn(nn, nn), dd, dd)
>>> isinstance(fairgrid, GravGrid)
True
>>> isinstance(fairgrid, Grid)
True

RhocGrid

class plateflex.classes.RhocGrid(grid, dx, dy)

Basic grid class of plateflex for crustal density data that inherits from Grid

Additional Attributes

unitsstr: Units of Density (’\(kg/m^3\)’)
title: str: Descriptor for Density data

Note

This class should only be used to specify the density of the crust at each cell location. Although the Grid methods are still available, they are not useful in this context.

ZcGrid

class plateflex.classes.ZcGrid(grid, dx, dy)

Basic grid class of plateflex for crustal thickness data that inherits from Grid

Additional Attributes

unitsstr: Units of Crustal thickness (’\(m\)’)
title: str: Descriptor for Crustal thickness data

Note

This class should only be used to specify the thickness of the crust at each cell location. Although the Grid methods are still available, they are not useful in this context.

Project Class

This module further contains the class Project, which itself is a container of Grid objects (at least one each of TopoGrid and GravGrid). Methods are available to:

Add Grid or Project objects to the project
Iterate over Grid objects
Initialize the project
Perform the wavelet admittance and coherence between topography (TopoGrid object) and gravity anomalies (GravGrid object)
Plot the wavelet admnittance and coherence spectra
Estimate model parameters at single grid cell
Estimate model parameters at every (or decimated) grid cell
Plot the statistics of the estimated parameters at single grid cell
Plot the observed and predicted admittance and coherence functions at single grid cell
Plot the final grids of model parameters
Save the results to disk as .csv files

Project

class plateflex.classes.Project(grids=None)

Container for Grid objects, with methods to calculate the wavelet admittance and coherence and estimate flexural model parameters as well as plot various results.

Parameters:: grids (list of Grid, optional) – Initial list of PlateFlex Grid objects.

Default Attributes

gridsList: List of Grid objects
inversestr: Type of inversion to perform. By default the type is ‘L2’ for non-linear least-squares. Options are: ‘L2’ or ‘bayes’
maskArray: 2D array of boolean values determined independently
initializedBool: Whether or not the project has been initialized and is ready for the wavelet analysis and estimation steps. By default this parameter is False, unless the method init() has been executed.

Note

Can hold a list of any length with any type of Grid objects - however the wavelet calculations will only proceed if the project holds one each of TopoGrid and GravGrid (BougGrid or FairGrid) objects.

Examples

Create zero-valued square grid

>>> import numpy as np
>>> from plateflex import Grid, TopoGrid, BougGrid, GravGrid, Project
>>> nn = 200; dd = 10.
>>> topogrid = TopoGrid(np.random.randn(nn, nn), dd, dd)
>>> bouggrid = BougGrid(np.random.randn(nn, nn), dd, dd)
>>> isinstance(bouggrid, GravGrid)
True
>>> isinstance(bouggrid, Grid)
True

Assign project with list of grids

>>> Project(grids=[topogrid, bouggrid])
<plateflex.classes.Project object at 0x10c62b320>

Add Grid to project

>>> project = Project()
>>> project += topogrid
>>> project += bouggrid
>>> project.grids
[<plateflex.classes.TopoGrid object at 0x1176b4240>, <plateflex.classes.BougGrid object at 0x1176b42e8>]

Append Grid to project

>>> project = Project()
>>> project.append(topogrid)
<plateflex.classes.Project object at 0x1176b9400>
>>> project.grids[0]
<plateflex.classes.TopoGrid object at 0x1176b4240>

Initialize project

>>> project.init()

Exception if project does not contain exactly one TopoGrid and one GravGrid

>>> project = Project(grids=[topogrid, topogrid])
>>> project.init()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/Users/pascalaudet/Softwares/Python/plateflex-dev/PlateFlex/plateflex/classes.py", line 492, in wlet_admit_coh
    grids = self.grids + other.grids
Exception: There needs to be one GravGrid object in Project

Calculate wavelet admittance and coherence

>>> project = Project(grids=[topogrid, bouggrid])
>>> project.wlet_admit_coh()
 #loops = 17:  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17
 #loops = 17:  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17
 Calculation jackknife error on admittance and coherence

append(grid)

Append a single Grid object to the current :class:`~plateflex.classes.Project object.

Parameters:: grid (Grid) – object to append to project

Example

>>> import numpy as np
>>> from plateflex import Grid, Project
>>> nn = 200; dd = 10.
>>> grid = Grid(np.random.randn(nn, nn), dd, dd)
>>> project = Project()
>>> project.append(grid)

extend(grid_list)

Extend the current Project object with a list of Grid objects.

Parameters:: trace_list – list of Grid objects or Project.

Example

>>> import numpy as np
>>> from plateflex import Grid, Project
>>> nn = 200; dd = 10.
>>> grid1 = Grid(np.random.randn(nn, nn), dd, dd)
>>> grid2 = Grid(np.random.randn(nn, nn), dd, dd)
>>> project = Project()
>>> project.extend(grids=[grid1, grid2])

init()

Method to initialize a project. This step is required before calculating the wavelet admittance and coherence. The method checks that the project contains one each of TopoGrid and GravGrid. It also ensures that all grids have the same shape and sampling intervals. If Grids of type RhocGrid and/or ZcGrid are present, the project attributes will be updated with data from those grids to be used in the estimation part. The method further sets the water depth at each cell location (grid point) from the TopoGrid object.

Additional Attributes

water_depthndarray: Grid of water depth from topography data (shape (nx,ny))
nxint: Number of grid cells in the x-direction
nyint: Number of grid cells in the y-direction
ns int: Number of wavenumber samples
knp.ndarray: 1D array of wavenumbers
initializedbool: Set to True when method is called successfully

Optional Attributes

rhocndarray: Grid of crustal density data (shape (nx,ny))
zcndarray: Grid of crustal thickness data (shape (nx,ny))

Example

>>> project = Project[grids=[topogrid, fairgrid, zcgrid]]
>>> project.init()

wlet_admit_coh()

This method uses the module cpwt to calculate the wavelet admittance and coherence. The object needs to contain exactly two Grid objects, one of each of TopoGrid and GravGrid objects.

Note

If no wl_trans attribute is found for individual Grid objects, the method automatically calculates them first.

Stores the wavelet admittance, coherence and their errors as attributes

Additional Attributes

wl_admitndarray: Wavelet admittance (shape (nx,ny,ns))
ewl_admitndarray: Error of wavelet admittance (shape (nx,ny,ns))
wl_cohndarray: Wavelet coherence (shape (nx,ny,ns))
ewl_cohndarray: Error of wavelet coherence (shape (nx,ny,ns))

plot_admit_coh(kindex=None, mask=None, save=None, contours=None, **kwargs)

Method to plot grids of wavelet admittance and coherence at a given wavenumber index.

Parameters:

kindex (int) – Index of wavenumber array
mask (ndarray, optional) – Array of booleans for masking data points
title (str, optional) – Title of plot
save (str, optional) – Name of file for to save figure
clabel (str, optional) – Label for colorbar
contours (List) – List of contour lines obtained separately
kwargs (Keyword arguments) – Keyword arguments allowing more control on plots

estimate_cell(cell=(0, 0), alph=False, atype='joint', returned=False)

Method to estimate the parameters of the flexural model at a single cell location of the input grids. The type of estimation performed is set by the project attribute inverse. See Project` and estimate for details. The model parameters rhoc and zc are extracted from the corresponding RhocGrid and ZcGrid objects if they were initialized in the project.

Parameters:

cell (tuple) – Indices of cell location within grid
alph (bool, optional) – Whether or not to estimate parameter alpha
atype (str, optional) – Whether to use the admittance (‘admit’), coherence (‘coh’) or both (‘joint’)
returned (bool, optional) – Whether or not to return the estimates

Additional Attributes

traceMultiTrace: Posterior samples from the MCMC chains
summaryDataFrame: Summary statistics from Posterior distributions
map_estimatedict, optional: Container for Maximum a Posteriori (MAP) estimates
celltuple: Indices of cell location within grid

Results are stored as attributes of Project object.

estimate_grid(nn=10, alph=False, atype='joint', parallel=False)

Method to estimate the parameters of the flexural model at all grid point locations. It is also possible to decimate the number of grid cells at which to estimate parameters.

Parameters:

nn (int) – Decimator. If grid shape is (nx, ny), resulting grids will have shape of (int(nx/nn), int(ny/nn)).
alph (bool, optional) – Whether or not to estimate parameter alpha
atype (str, optional) – Whether to use the admittance (‘admit’), coherence (‘coh’) or both (‘joint’)

Additional Attributes

mean_Te_gridndarray: Grid with mean Te estimates (shape (nx, ny))
MAP_Te_gridndarray: Grid with MAP Te estimates (shape (nx, ny))
std_Te_gridndarray: Grid with std Te estimates (shape (nx, ny))
mean_F_gridndarray: Grid with mean F estimates (shape (nx, ny))
MAP_F_gridndarray: Grid with MAP F estimates (shape (nx, ny))
std_F_gridndarray: Grid with std F estimates (shape (nx, ny))

Optional Attributes

mean_a_gridndarray: Grid with mean alpha estimates (shape (nx, ny)). Only present if alph=True.
MAP_a_gridndarray: Grid with MAP alpha estimates (shape (nx, ny)). Only present if alph=True.
std_a_gridndarray: Grid with std alpha estimates (shape (nx, ny)). Only present if alph=True.
chi2_gridndarray: Grid with reduced chi-squared estimates (shape (nx, ny)). Only present if project.inverse='L2'
new_maskArray: New grid of masked (boolean) values, corresponding to decimated mask.

plot_bayes_stats(title=None, save=None)

Method to plot the marginal and joint distributions of samples drawn from the posterior distribution as well as the extracted statistics. Calls the function plot_stats() with attributes as arguments.

Parameters:

title (str, optional) – Title of plot
save (str, optional) – Name of file for to save figure

plot_functions(est='mean', title=None, save=None)

Method to plot observed and fitted admittance and coherence functions using one of mean or MAP estimates. The MAP is only available if the project attribute has been set to project='bayes'. Calls the function plot_functions() with attributes as arguments.

Parameters:

est (str, optional) – Type of inference estimate to use for predicting admittance and coherence
title (str, optional) – Title of plot
save (str, optional) – Name of file for to save figure

plot_results(mean_Te=False, MAP_Te=False, std_Te=False, mean_F=False, MAP_F=False, std_F=False, mean_a=False, MAP_a=False, std_a=False, chi2=False, mask=False, contours=None, save=None, filter=True, sigma=1, **kwargs)

Method to plot grids of estimated parameters with fixed labels and titles. To have more control over the plot rendering, use the function plot_real_grid() with the relevant quantities and plotting options.

Parameters:

mean/MAP/std_Te/F/a (bool) – Type of plot to produce. All variables default to False (no plot generated)
mask (bool) – Whether or not to plot the mask
contours (List) – List of contours with coordinate positions
filter (bool) – Whether or not to filter the resulting grid using a Gaussian filter
sigma (int) – Standard deviation of filter (in terms of adjacent cells), if set to True
kwargs (Keyword arguments) – Keyword arguments allowing more control on plots

Note

It is advisable to plot each grid separately using one call per grid, in order to have more control on plot parameters (e.g., colormap, min and max values of colorbar, etc.).

save_results(mean_Te=False, MAP_Te=False, std_Te=False, mean_F=False, MAP_F=False, std_F=False, mean_a=False, MAP_a=False, std_a=False, chi2=False, mask=False, contours=None, filter=True, sigma=1, prefix='PlateFlex_')

Method to save grids of estimated parameters with default file names.

Parameters:

mean/MAP/std_Te/F/a (bool) – Type of grid to save. All variables default to False (no grid saved)
mask (bool) – Whether or not to save the mask
contours (List) – List of contours with coordinate positions
filter (bool) – Whether or not to filter the resulting grid using a Gaussian filter
sigma (int) – Standard deviation of filter (in terms of adjacent cells), if set to True
prefix (str) – Prefix of file name.

Note

It is advisable to save each grid separately using one call per grid, in order to have more control on file names.