Joint work with Jaideva Goswami.
Nuclear Magnetic Resonance (NMR) has been in use for many years in chemistry and biochemistry laboratories to analyze the molecular structure of compounds. In the last few years, NMR measurements have become an important part of oilfield well-logging to identify and quantify oil and gas reservoirs. One of the major difficulties in the measurement process is that the NMR signal is weak and therefore affected strongly by the noise. The magnitude of the resulting NMR signal is proportional to the number of nuclei which precess in resonance with the RF frequency ω. Since this Larmor frequency (i.e., rotational frequency of the spins which precess around the external magnetic field) involves the strength of the applied static magnetic field and is expressed as γ B0, where γ is a constant (gyromagnetic ratio) which is specific to each isotope's nucleus, and B0 designates the static magnetic field strength, a more spatially homogeneous static magnetic field should produce a bigger volume of the nuclei in resonance. Therefore such an homogeneous static field produces a bigger NMR signal in the receiver. In consequence, the most important issue in designing an NMR spectrometer is to produce a strong and homogeneous static magnetic field over a large volume sample of the formation. This task is a challenge for a magnet-designer since the sample (earth formation) is outside the sensor. In this talk, we will show an application of the optimal control technique for a specific magnet design in an NMR well-logging tool.