random_noise¶
- emg3d.surveys.random_noise(standard_deviation, mean_noise=0.0, ntype='white_noise')[source]¶
Return random noise for given inputs.
Different methods are implemented to create random noise for frequency-domain CSEM data. All methods generate random noise in the following way
\[d^\text{noise} = \varsigma \left[(1 + \text{i})\,u + \mathcal{R} \right] \, .\]where \(\varsigma\) is the standard deviation (see
emg3d.surveys.Survey.standard_deviation
), \(u\) is the mean value of the randomly distributed noise, and \(\mathcal{R}\) are the random realizations of the noise.Currently there are three methods (
ntype
) implemented.white_noise
Random uniform phases with constant amplitudes. This is the default implementation, and corresponds to white noise in the time-domain: a flat amplitude spectrum for all frequencies, with random phases:
\[\mathcal{R}_\text{wn} = \exp[\text{i}\,\mathcal{U}(0, 2\pi)] \, ,\]where \(\mathcal{U}(0, 2\pi)\) is the uniform distribution and its range.
Random Gaussian noise.
In the following, \(\mathcal{N}(0, 1)\) is the standard normal distribution of zero mean and unit standard deviation.
gaussian_correlated
Same realization added to real and imaginary part.
\[\mathcal{R}_\text{gc} = (1+\text{i})\,\mathcal{N}(0, 1) \, .\]gaussian_uncorrelated
Independent realizations added to real and imaginary part.
\[\mathcal{R}_\text{gu} = \mathcal{N}(0, 1) + \text{i}\,\mathcal{N}(0, 1) \, .\]
There are, of course, other possibilities. One could, e.g., make the non-zero mean itself random.
See the example random_noise_f_domain.html for more details about random noise in the frequency domain.
- Parameters
- standard_deviationndarray
Standard deviations of the data.
- mean_noisefloat, default: 0.0
Mean value of the random noise (as fraction of standard_deviation).
- ntypestr, default: white_noise
What type of noise. Options:
'white_noise'
: random uniform phases with constant amplitude.'gaussian_correlated'
: Same Gaussian random realizations added to Real and Imaginary part.'gaussian_uncorrelated'
: Independent Gaussian random realizations added to Real and Imaginary part.
- Returns
- noisendarray
Noise, a complex-valued ndarray of the same shape as standard_deviation.