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.