An apparatus for estimating at least one parameter in a downhole environment includes: an optical fiber configured to be disposed in a borehole, the optical fiber having a property that causes intrinsic backscattering of signals transmitted therein. The property varies along a length of the optical fiber to generate a variable intensity of the backscattering, the intensity of backscattering varying along the optical fiber as a function of distance from an end of the optical fiber. The apparatus also includes a light source configured to send an optical signal into the optical fiber; and a detector configured to receive a return signal including backscattered signals.