Determining bound and unbound fluid volumes using nuclear magnetic resonance pulse sequences

A method for measuring an indication of an attribute of a volume of earth formation with a borehole tool having means for producing static magnetic fields in a volume of a formation, means for producing oscillating magnetic fields in a volume of a formation, and means for measuring an induced magnetic signal, the method comprising:

• a) producing a static magnetic field in the volume of formation;
• b) producing oscillating magnetic fields according to a pulse sequence
• T.sub.r -90.degree..sub..+-.x -(t.sub.cp -180.degree..sub.y -t.sub.cp -echo.sub.j)
• where j=1, 2 . . . . N, and N is the number of echoes collected in a single Carr-Purcell-Meiboom-Gill (CPMG) sequence in order to induce signals in the volume which are measurable by the tool in the borehole;
• where T.sub.r is recovery time before a CPMG sequence, and
• where t.sub.cp is the Carr-Purcell spacing;
• c) using a linear operator to map a relaxation-time distribution to resulting spin echoes,
• d) producing a singular value decomposition (SVD) of the linear operator according to the pulse sequence;
• e) measuring with the tool the induced signals;
• and
• f) determining from the measured signals an indication of unbound fluid volume (UFV) of the volume of earth formation in light of the SVD.