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Simulate InSAR tropospheric noise

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Simulate tropospheric noise for InSAR data


To simulate one turbulence image, you can specify the shape:

from troposim import turbulence
noise = turbulence.simulate(shape=(500, 500))

or add a 3rd dimension to simulate a stack of images

noise = turbulence.simulate(shape=(10, 500, 500))

The beta argument is the slope of the log10(power) vs log10(frequency) graph. The default is to use a single linear slope of $\beta = 2.5$:

$$ P(f) = \frac{1}{f^\beta} $$

For smaller-scale turbulence, you can use a different beta:

flatter_noise = turbulence.simulate(beta=2.2)

Since real InSAR data typically have a power spectrum that is not a single slope, you can estimate the spectrum from an image and use that to simulate new data:

from troposim.turbulence import Psd
psd = Psd.from_image(noise)
new_noise = psd.simulate()

Here the psd object has the following attributes:

  • p0: the power at the reference frequency freq0
  • beta: a numpy Polynomial which was fit to the log-log PSD

The two attributes psd.freq and psd.psd1d are the radially averaged spectrum values. You can see these with the .plot() method.

# assuming maptlotlib is installed

# Or, to plot a side-by-side of image and 1D PSD
from troposim import plotting 
plotting.plot_psd(noise, freq=freq, psd1d=psd1d)
# Or just the PSD plot, no image
plotting.plot_psd1d(freq, psd1d)

To simulate a stack of new values, you can pass the estimated p0 and beta back to simulate:

noise = turbulence.simulate(shape=(10, 400, 400), p0=p0, beta=beta)

Note that the default fit will use a cubic polynomial. To request only a linear fit,

psd = Psd.from_image(noise, deg=1)

You can also save the PSD parameters for later use:"my_psd.npz")
# Later, reload from this file
psd = Psd.load(outfile)



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