Quantitative measurement of two-dimensional distribution functions of diffusion and relaxation in grossly inhomogeneous fields

We demonstrate the quantitative extraction of multidimensional distribution functions in the presence of grossly inhomogeneous fields. Examples are shown for diffusion-T(2) distribution functions and T(1)-T(2) distribution functions. The pulse sequences consist of an initial editing sequence followed by a long series of nominal 180 degrees pulses. They are designed such that the kernels describing the relationships between the distribution functions and the measured data are separable. The required phase cycling is discussed. We analyze in detail the extra spin dynamics effects due to the strong field inhomogeneities including the effects on diffusion and relaxation. A recently developed algorithm is used to invert the data and extract stable multidimensional distribution functions in an efficient manner. We present examples for several applications of this new technique. Diffusion-relaxation distribution functions can be used for fluid identification and for the characterization of pore geometry of porous media based on the effects of restricted diffusion. We have also determined T(1)-T(2) distribution functions of water saturated sedimentary rock and find excellent agreement with previous measurements performed in homogeneous fields.