1/2 INVERSION OF DECAY TIME SPECTRA FROM SURFACE NMR DATA O. Mohnke , M. Braun and U. Yaramanci Technical University Berlin, Dept. of Applied Geophysics, Ackerstr. 71-76, 13355 Berlin, Germany INTRODUCTION The surface nuclear magnetic resonance (SNMR) method is a non-invasive geophysical method that allows direct determination of the water distribution in the subsurface. In SNMR the hydrogen protons in the pore water are excited with an artificial magnetic field, generated by an antenna loop on the surface. The loop is energized by an alternating current oscillating with the local Larmor frequency ϖ L of the protons. After termination of the exciting pulse, the magnetic field due to the relaxation of hydrogen protons is measured. The initial amplitude E 0 of the relaxation signal is directly proportional to the amount of free water. The decay time constant T (spin-spin-relaxation time) is linked to the effective pore size. The signal phase is related to the conductivity of the water bearing layers [1, 2]. Increasing the intensity of excita- tion, e.g. the pulse moment q, by raising the duration or strength of the exciting pulse in- creases the depth of investigation. INVERSION OF SNMR DATA So far SNMR is only used in sounding mode and the inversion of SNMR data mainly concen- trates on the interpretation of the water content distribution. Thereby, the inversion of the de- cay time T is done by fitting only a single relaxation constant (mono-exponential fit), e.g. as- suming a mean pore size for each inversion layer (strategy A) [3, 4]. The envelope amplitude E(t,q) of the SNMR relaxation signal is then expressed by ∫ ⊥ ⊥ - - = = V r T t q T t r d q r B r f r B M q E q t E L i 3 2 ) ( 0 ) ( 0 ) ) ( sin( ) exp( ) ( ) ( ) exp( ) ( ) , ( * 2 v v r v γ ϖ (1) where M 0 is the macroscopic magnetic dipole moment of the water molecules, f( r v ) is the wa- ter content for an unit volume at the point r v and B ⊥ ( r v ) is the component of the exciting field perpendicular to the earth’s magnetic field [4]. This approximation, however, often does not comply with the hydrogeophysical properties of the subsurface. In analogy to borehole and laboratory NMR we introduce a new approach to the inversion of SNMR data in terms of decay time spectra analysis, e.g. a multi-exponential fitting of the SNMR relaxation signals. This allows a more quantitative characterization of an aquifer with respect to the distribution of the pore radii. The total water content distribution is then given by the sum of N individual water content distributions, each correlating to a char- acteristic decay time constant T i within a given spectrum: [ ] [ ] ∫ ∑ ∑ ⊥ ⊥ = - = - = = V N i r T t i N i q T t r d q r B r f r B M q E q t E i L i i 3 2 1 ) ( 0 1 ) ( 0 ) ) ( sin( ) exp( ) ( ) ( ) exp( ) ( ) , ( v v v v γ ϖ (2) Both the initial amplitudes E 0i and the corresponding decay time constants T i can be inde- pendent variables in the curve fitting and inversion process (strategy B). Alternatively, using a fixed decay time spectrum, i.e. 20 sampling points with T i ranging from 10 to 1000 ms, only the corresponding amplitudes E 0i are optimized (strategy C). This yields individual SNMR sounding curves for each T i (q) reflecting a water content distribution within the corresponding pore size. When simultaneously fitting all measured relaxation curves of a SNMR sounding, the integral character of the method, e.g. smooth sounding curves, can be implemented in the inversion (regularization constraints). This reduces ambiguity and yields a geologically more plausible amplitude spectrum. The curve fitting is carried out using simulated annealing, a global optimization algorithm. The inversion is carried out using a block inversion software package for SNMR data [4]. TESTS WITH SYNTHETIC DATA The inversion scheme has been tested with synthetic data. Besides the conventional inversion of SNMR data (strategy A) two different strategies using variable (strategy B) and fixed (strategy C) spectral distributions of T have been employed and evaluated. Figure 1 shows a three layer model of an aquifer between 20 and 40 meters with 30% total water content asso- ciated with a main decay time of 250 ms ( ≈ medium sands). The content of free water within