As previously stated, ultrasonics is not something I have worked with. Please read the below with a grain of salt.
You will have omidirectional sound dispersion if your source is a point source. Amplitude will then experience so called spatial decay as the sphere to which sound spreads doubles it surface with every radial distance doubling, i.e. geometric decay is 6 dB/doubling of distance. This value will not change between new or old mortar as it is determined solely by geometry.
A plane compression wave has a decay rate of
12.8*eta db/wavelength ,
where eta is the material structural loss factor.
You can determine the value for eta by measuring response at multiple locations away from the source. In your case, I guess, this would translate into measuring at locations where the wave impinges with 1, 2, 3, etc number of bounces.
Firslty, thank you very much for the suggested article, it was very helpful.
When the total attenuation coefficient is calculated using the spectra (FFT) of the sinesweep pulses through the examination material, Is this attenuation coefficient measured in Nepers/unit length (Np/m), where a Neper (Np) is a dimensionless quantity OR expressed in terms of decibels/unit length (dB/m)? See joined PDF file bellow
Another way is to measure transfer functions, e.g. with the electric outputsignal as reference and to deteremine damping using Experimental Modal Analysis (EMA) or the half power bandwidth method.
The transfer function approach relies on a sufficent number of roundtrips for resonance to build up. It appears reasonable to assume that it should work in the thickness direction.
Material for self study on experimental modal analysis is found here