The disclosure is directed to an apparatus and method for determining the bound-water-filled porosity of formations surrounding a borehole. Bound-water-filled porosity is the fraction of the formation unit volume (matrix plus fluid) which is occupied by bound water, bound water being the portion of the total water which is adsorbed or bound to, or impermeably held by, the matrix. In one embodiment, means are provided for deriving a first quantity which is a measure of the attenuation of microwave electromagnetic energy passed through the formations of interest. This first quantity may be, for example, the attenuation constant determined for the microwave electromagnetic energy passing through the formations. Means are provided for generating a second quantity which is substantially proportional to the square of the first quantity. The second quantity is indicative of the bound-water-filled porosity of the formations. In another embodiment of the invention, means are provided for deriving a third quantity which is representative of the total porosity of the formations. In this embodiment, a further means is provided for generating a fourth quantity as a function of the difference between the third quantity and the second quantity, the fourth quantity being indicative of the free fluid index of the formations.