Intensity bands (VH & VV)

Many applications are possible on amplitude bands (VH & VV), but
what are the practical applications of intensity bands (VH & VV) in sentinel 1 data?
what is their usage?

it’s the same information.
Amplitude * Amplitude = Intensity

More info: Difference between amplitude and intensity

By the multiplication of the amplitude, the contrasts in your image change: Bright areas become potentially brighter and the contrast in low-value areas decreases. This can be later addressed by applying the logarithm (after calibration) to translate the data int dB scale.

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Just to clarify:

The SAR measurement is a complex number (real and imaginary parts). To generate a detected product, the complex number is converted to intensity (i.e. i.i + q.q). To fit the dynamic range of the intensity data into the 16 bits of a product, the square root of the intensity values is applied - this is amplitude. So amplitude is just a convenient way of storing detected intensity data. For any measurements from detected data, the amplitude must be converted to intensity first. Also care should be taken when averaging over a region (e.g. a field) - convert to intensity first and then average.

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Thank you @peter.meadows and @ABraun
Can we consider a measured area of a region on the amplitude band as a proper measurement?
and does the calibration step in preprocessing of the image is converting amplitude to intensity?

Can we consider a measured area of a region on the amplitude band as a proper measurement?

It depends on how any average is performed - if it is just the average of amplitude values, then this is not a proper measurement.

and does the calibration step in preprocessing of the image is converting amplitude to intensity ?

I’m not familar with the code in SNAP and so cannot comment.

Amplitude data is not explicitly provided by SLC Sentinel 1, only as real (i) and imaginary (q) bands of each oriented polarization. To get amplitude would have to do:

Amplitude = sqrt(i²+q²)

or I can take the square root of the accommodated intensity band:
Amplitude = sqrt(Intensity)? this is correct? if not, why?