Usage

Here are some simple examples on how to use the package. This only requires a CHAOS model mat-file, e.g. “CHAOS-6-x7.mat” in the current working directory. The model coefficients can be downloaded here.

Computing the field components on a grid

Use ChaosMagPy to compute the magnetic field components of the different sources that are accounted for in the model. For example, the time-dependent internal field:

import numpy as np
import chaosmagpy as cp

# create full grid
radius = 3485.  # km, core-mantle boundary
theta = np.linspace(0., 180., num=181)  # colatitude in degrees
phi = np.linspace(-180., 180., num=361)  # longitude in degrees

phi_grid, theta_grid = np.meshgrid(phi, theta)
radius_grid = radius*np.ones(phi_grid.shape)

time = cp.data_utils.mjd2000(2000, 1, 1)  # modified Julian date

# load the CHAOS model
model = cp.load_CHAOS_matfile('CHAOS-6-x7.mat')

# compute field components on the grid using the Gauss coefficients
B_radius, B_theta, B_phi = model.synth_values_tdep(coeffs, radius_grid, theta_grid, phi_grid)

When using a regular grid, consider grid=True option for speed. It will internally compute a grid in theta and phi similar to numpy.meshgrid() in the example above while saving time with some of the computations (note the usage of, for example, theta instead of theta_grid):

B_radius, B_theta, B_phi = model.synth_values_tdep(time, radius, theta, phi, grid=True)

The same computation can be done with other sources described by the model:

Source

Type

Method in CHAOS class

internal

time-dependent

synth_values_tdep() (see example)

static

synth_values_static()

external

time-dep. (GSM)

synth_values_gsm()

time-dep. (SM)

synth_values_sm()

Computing timeseries of Gauss coefficients

ChaosMagPy can also be used to synthesize a timeseries of the spherical harmonic coefficients. For example, in the case of the time-dependent internal field:

import numpy as np
import chaosmagpy as cp

# load the CHAOS model from the mat-file
model = cp.load_CHAOS_matfile('CHAOS-6-x7.mat')

print('Model timespan is:', model.model_tdep.breaks[[0, -1]])

# create vector of time points in modified Julian date from 2000 to 2004
time = np.linspace(0., 4*365.25, 10)  # 10 equally-spaced time instances

# compute the Gauss coefficients of the MF, SV and SA of the internal field
coeffs_MF = model.synth_coeffs_tdep(time, nmax=13, deriv=0)  # shape: (10, 195)
coeffs_SV = model.synth_coeffs_tdep(time, nmax=14, deriv=1)  # shape: (10, 224)
coeffs_SA = model.synth_coeffs_tdep(time, nmax=9, deriv=2)  # shape: (10, 99)

# save time and coefficients to a txt-file: each column starts with the time
# point in decimal years followed by the Gauss coefficients in
# natural order, i.e. g(n,m): g(1,0), g(1, 1), h(1, 1), ...

dyear = cp.data_utils.mjd_to_dyear(time)  # convert mjd2000 to decimal year

np.savetxt('MF.txt', np.concatenate([dyear[None, :], coeffs_MF.T]), fmt='%10.5f', delimiter=' ')
np.savetxt('SV.txt', np.concatenate([dyear[None, :], coeffs_SV.T]), fmt='%10.5f', delimiter=' ')
np.savetxt('SA.txt', np.concatenate([dyear[None, :], coeffs_SA.T]), fmt='%10.5f', delimiter=' ')

The same can be done with other sources accounted for in CHAOS. However, except for the time-dependent internal field, there are no time derivatives available.

Source

Type

Method in CHAOS class

internal

time-dependent

synth_coeffs_tdep() (see example)

static

synth_coeffs_static()

external

time-dep. (GSM)

synth_coeffs_gsm()

time-dep. (SM)

synth_coeffs_sm()

Converting time formats in ChaosMagPy

The models in ChaosMagPy only accept modified Julian date. But sometimes it is easier to work in different units such as decimal years or Numpy’s datetime. For those cases, ChaosMagPy offers simple conversion functions. First, import ChaosMagPy and Numpy:

import chaosmagpy as cp
import numpy as np

From Modified Julian Dates

Convert to decimal years (account for leap years) with chaosmagpy.data_utils.mjd_to_dyear():

>>> cp.data_utils.mjd_to_dyear(412.)
    2001.1260273972603

Convert to Numpy’s datetime object with chaosmagpy.data_utils.timestamp():

>>> cp.data_utils.timestamp(412.)
    numpy.datetime64('2001-02-16T00:00:00.000000')

To Modified Julian Dates

Convert from decimal years (account for leap years) with chaosmagpy.data_utils.dyear_to_mjd():

>>> cp.data_utils.dyear_to_mjd(2001.25)
    457.25

Convert from Numpy’s datetime object with chaosmagpy.data_utils.mjd2000():

>>> cp.data_utils.mjd2000(np.datetime64('2001-02-01T12:00:00'))
    397.5

Note also that chaosmagpy.data_utils.mjd2000() (click to see documentation) accepts a wide range of inputs. You can also give the date in terms of integers for the year, month, and so on:

>>> cp.data_utils.mjd2000(2002, 1, 19, 15)  # 2002-01-19 15:00:00
    749.625

Plotting maps of the time-dependent internal field

Here, we make a map of the first time-derivative of the time-dependent internal part of the model. We will plot it on the surface at 3485 km (core-mantle boundary) from the center of Earth and on January 1, 2000:

import chaosmagpy as cp

model = cp.load_CHAOS_matfile('CHAOS-6-x7.mat')

radius = 3485.0  # km, here core-mantle boundary
time = 0.0  # mjd2000, here Jan 1, 2000 0:00 UTC

model.plot_maps_tdep(time, radius, nmax=16, deriv=1)  # plots the SV up to degree 16
_images/plot_maps_tdep.png

Secular variation at the core-mantle-boundary up to degree 16 in January 1, 2000 0:00 UTC.

Save Gauss coefficients of the time-dependent internal (i.e. large-scale core) field in shc-format to a file:

model.save_shcfile('CHAOS-6-x7_tdep.shc', model='tdep')

Plotting maps of the static internal field

Similarly, the static internal (i.e. small-scale crustal) part of the model can be plotted on a map:

import chaosmagpy as cp

model = cp.load_CHAOS_matfile('CHAOS-6-x7.mat')
model.plot_maps_static(radius=6371.2, nmax=85)
_images/plot_maps_static.png

Static internal small-scale field at Earth’s surface up to degree 85.

and saved

model.save_shcfile('CHAOS-6-x7_static.shc', model='static')