Saddle point nuclear magnetic resonance tool for measurements at multiple depths of investigation

A downhole tool for measuring properties of a geological formation, the downhole tool comprising:

• a nuclear magnetic resonance (NMR) sensor, wherein the NMR sensor comprises:
• a first magnet disposed at a first radial distance from a radial center of the NMR sensor, wherein the first magnet is configured to generate a first magnetic moment that is along a first direction;
• a second magnet disposed at a second radial distance from the radial center of the NMR sensor, wherein the second magnet is configured to generate a second magnetic moment along a second direction, wherein a first angle between the first direction and the second direction is greater than 90 degrees;
• a third magnet disposed at a third radial distance from the radial center of the NMR sensor, wherein the third magnet is configured to generate a third magnetic moment along a third direction that is opposite of the first direction, and wherein a second angle between the third direction and the first direction is greater than 90 degrees;
• a fourth magnet disposed at a fourth radial distance from the radial center of the NMR sensor, wherein the fourth magnet is configured to generate a fourth magnetic moment along a fourth direction that is opposite of the first direction, and wherein a third angle between the fourth direction and the first direction is greater than 90 degrees;
• wherein the first magnet, the second magnet, the third magnet, and the fourth magnet are separate from each other, wherein a net magnetic field produced by the first magnet, the second magnet, and the third magnet has a magnetic field profile that is suitable for multiple depth of investigation measurements (DOI), wherein the first radial distance is greater than the second radial distance, the third radial distance, and the fourth radial distance;
• and
• an antenna configured to:
• generate a first set of NMR data from a first DOI at a first frequency;
• and
• generate a second set of NMR data from a second DOI at a second frequency.

A method of manufacturing a nuclear magnetic resonance (NMR) sensor for a downhole tool, comprising:

• providing an antenna configured to generating at least one set of NMR data;
• providing a first magnet at a first radial distance from a radial center of the NMR sensor, wherein the first magnet is configured to generate a first magnetic moment that is along a first direction;
• and
• providing a second magnet at a second radial distance from the radial center of the NMR sensor, wherein the second magnet is configured to generate a second magnetic moment along a second direction, wherein a first angle between the first direction and the second direction is greater than 90 degrees;
• providing a third magnet at a third radial distance from the radial center of the NMR sensor, wherein the third magnet is configured to generate a third magnetic moment along a third direction that is opposite of the first direction, and wherein a second angle between the third direction and the first direction is greater than 90 degrees;
• providing a fourth magnet at a fourth radial distance from the radial center of the NMR sensor, wherein the fourth magnet is configured to generate a fourth magnetic moment along a fourth direction that is opposite of the first direction, and wherein a third angle between the fourth direction and the first direction is greater than 90 degrees, wherein the first radial distance is greater than the second radial distance, the third radial distance, and the fourth radial distance.