Signal processing for field and experimental data for earthquake engineering

## eqsig

A Python package for seismic signal processing.

### Features

This package provides common functions for computing ground motion parameters and performing signal processing. The functions are implemented on either numpy arrays or on a signal object that uses caching to avoid expensive recalculation of widely used parameters.

• Compute the acceleration response spectrum and elastic response time series using the fast Nigam and Jennings (1968) algorithm.

• Compute the Fourier amplitude spectrum (using the scipy.signal.fft algorithm)

• Compute the smooth Fourier amplitude spectrum according to Konno and Ohmachi (1998)

• Compute velocity and displacement from acceleration time series

• Compute peak ground motion quantities (PGA, PGV, PGD)

• Compute common ground motion intensity measures (Arias intensity, CAV, CAV_dp5, significant duration, bracketed duration, dominant period)

• Compute signal features (zero crossings, global peaks, local peaks)

• Compute rotated ground motion or intensity measure from two ground motion components

• Resampling of ground motion through interpolation or periodic resampling

• Butterworth filter (using scipy), running average, polynomial fitting

• Fast loading of, and saving of, plain text to and from Signal objects

### How to Use

#### Examples

##### Generate response spectra
import numpy as np
import matplotlib.pyplot as plt
import eqsig.single

bf, sub_fig = plt.subplots()
dt = 0.005  # time step of acceleration time series
periods = np.linspace(0.2, 5, 100)  # compute the response for 100 periods between T=0.2s and 5.0s
record = eqsig.AccSignal(a * 9.8, dt)
record.generate_response_spectrum(response_times=periods)
times = record.response_times

sub_fig.plot(times, record.s_a, label="eqsig")
plt.show()
##### Generate Stockwell transform
import numpy as np
import matplotlib.pyplot as plt
import eqsig

from matplotlib import rc
rc('font', family='Helvetica', size=9, weight='light')
plt.rcParams['pdf.fonttype'] = 42

dt = 0.01
time = np.arange(0, 10, dt)
f1 = 0.5
factor = 10.
f2 = f1 * factor
acc = np.cos(2 * np.pi * time * f1) + factor / 5 * np.cos(2 * np.pi * time * f2)

asig = eqsig.AccSignal(acc, dt)

asig.swtf = eqsig.stockwell.transform(asig.values)

bf, ax = plt.subplots(nrows=2, sharex=True, figsize=(5.0, 4.0))

ax[0].plot(asig.time, asig.values, lw=0.7, c='b', label='Signal')

in_pcm = eqsig.stockwell.plot_stock(ax[1], asig)
ax[1].set_ylim([0.0, 10])
ax[0].set_xlim([0, 10])

ax[0].set_ylabel('Amplitude [$m/s^2$]', fontsize=8)
ax[1].set_ylabel('$\it{Stockwell}$\nFrequency [Hz]', fontsize=8)
ax[-1].set_xlabel('Time [s]', fontsize=8)

from mpl_toolkits.axes_grid1.inset_locator import inset_axes
cbaxes = inset_axes(ax[1], width="20%", height="3%", loc='upper right')
cbaxes.set_facecolor([1, 1, 1])
cb = plt.colorbar(in_pcm, cax=cbaxes, orientation='horizontal')
cb.outline.set_edgecolor('white')
cbaxes.tick_params(axis='both', colors='white')

ax[0].legend(loc='upper right')
for sp in ax:
sp.tick_params(axis='both', which='major', labelsize=8)

plt.tight_layout()
plt.show()

### Contributing

#### How do I get set up?

1. Run pip install -r requirements.txt

#### Package conventions

• A function that calculates a property that takes a Signal object as an input, should be named as calc_<property>, if the calculation has multiple different implementations, then include the citation as author and year as well calc_<property>_<author>_<year>

• If the function takes a raw array then it should contain the word array (or values or vals).

#### Testing

Tests are run with pytest

• Locally run: pytest on the command line.

• Tests are run on every push using travis, see the .travis.yml file

#### Deployment

To deploy the package to pypi.com you need to:

1. Push to the pypi branch. This executes the tests on circleci.com

2. Create a git tag and push to github, run: trigger_deploy.py or manually:

git tag 0.5.2 -m "version 0.5.2"
git push --tags origin pypi

#### Documentation

Built via Sphinx following: https://codeandchaos.wordpress.com/2012/07/30/sphinx-autodoc-tutorial-for-dummies/

For development mode

1. cd to docs

2. Run make html

Docstrings follow numpy convention (in progress): https://numpydoc.readthedocs.io/en/latest/format.html

To fix long_description in setup.py: pip install collective.checkdocs, python setup.py checkdocs

#### Release instructions

On zenodo.org use the github integration tool, click on the eqsig package and click create new release.

### History

#### 1.2.10 (2020-11-24)

• Adjusted eqsig.stockwell.plot_stock, since min freq was out by factor of 0.5.

#### 1.2.5 (2020-11-24)

• Added gen_ricker_wavelet_asig to create an acceleration signal that is a Ricker wavelet

• Added eqsig.sdof.calc_input_energy_spectrum to compute the input energy into an SDOF

• Can now load a Signal with a scale factor by passing in the keyword m=<scale factor>

• The left interpolation function interp_left now returns the same size as x, which can be a scalar, and if y is None then assumes index (0,1,2,…,n)

#### 1.2.4 (2020-07-20)

• Fixed issue with computation of surface energy spectra

• Support for numpy==1.19

#### 1.2.3 (2020-05-05)

• Fixed docs for generation of FAS, changed kwarg n_plus to p2_plus since this adds to the power of 2.

#### 1.2.2 (2020-05-05)

• Switched to numpy for computing the Fourier amplitude spectrum

#### 1.2.1 (2020-05-05)

• Added response_period_range to AccSignal object initial inputs to define response periods using an upper and lower limit

• Improved speed of surface energy calculation calc_surface_energy and returns correct size based on input dimensions

• Removed global import of scipy - done at function level

• Added an interp_left function to interpolate an array and take lower value

• Fixed issue with inverse of stockwell transform stockwell.itransform, it no longer doubles the time step

• Increased speed of stockwell transform stockwell.transform.

• Added remove_poly function to remove a polynomial fit from an array

• Added option to access fa_frequencies and smooth_fa_frequencies as fa_freqs and smooth_fa_freqs.

• Added option for computing smoothed FAS with extra zero padding

• Added function for computing smoothed fas using a custom smoothing matrix.

#### 1.2.0 (2019-11-03)

• Added interp2d fast interpolation of a 2D array to obtain a new 2D array

• No longer raises warning when period is 0.0 for computing response spectrum

• Fixed issue with computation of smoothed response spectrum for dealing with zeroth frequency

• Increased speed ofgenerate_smooth_fa_spectrum

• Can now directly set AccSignal.smooth_fa_frequencies

• Deprecated AccSignal.smooth_freq_points and AccSignal.smooth_freq_range will be removed in later version

#### 1.1.2 (2019-10-31)

• More accuracy in calc_surface_energy - now interpolates between time steps. More tests added.

#### 1.1.1 (2019-10-29)

• Fixed issue in get_zero_crossings_array_indices where it would fail if array did not contain any zeros.

• Added calculation of equivalent number of cycles and equivalent uniform amplitude using power law relationship as intensity measures

• Added function get_n_cyc_array to compute number of cycles series from a loading series

• Added intensity measure im.calc_unit_kinetic_energy() to compute the cumulative change in kinetic energy according to Millen et al. (2019)

• Added surface.py with calculation of surface energy and cumulative change in surface energy time series versus depth from surface

#### 1.1.0 (2019-10-08)

• Fixed issue with second order term in sdof response spectrum calculation which effected high frequency response, updated example to show difference

#### 1.0.0 (2019-07-01)

• First production release

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