# Volume Loss Assessment with MT-InSAR during Tunnel Construction in the City of Naples (Italy)
## Appendix A Proof of V\({}^{*}\)\({}_{\rm L}\) = V\({}_{\rm L}\). Consider the functions w(x) and d\({}_{\rm v}\)(x). The integral of the first function (w(x)) is a fraction (namely volume loss, V\({}_{\rm L}\)) of the excavated volume per unit of length:  
\[\int\text{w(x)}\cdot\text{dx}=V_{\rm L}\cdot\pi\cdot\text{D}^{2}/4. \tag{1}\]  
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