Abstract: Various embodiments include a method for generating a pulse for use in nuclear magnetic resonance (NMR) logging. One such method generates the pulse by adjusting one or more of pulse parameters including a pulse shape, a pulse amplitude, a pulse phase, and/or a pulse frequency. The generated pulse produces a substantially uniform nuclear spin saturation or nuclear spin inversion response from a fluid. A wait time between the pulse transmission and an echo that indicates spin equilibrium has been achieved is substantially equal to a T1 time indicating characteristics of the fluid.

Abstract: A magnetic resonance method includes providing a pulse sequence that affects different measurement regions in presence of a magnetic field gradient, the pulse sequence having multiple pulse shapes and multiple characteristic interecho intervals (TEs).

Abstract: NMR logging of hydrocarbon formations may be performed with a gradient multi-frequency NMR technique using an increased packing density of the sensitive volumes such that the radiofrequency (RF) pluses for adjacent sensitive volumes interfere. An exemplary method may include applying first and second sequences of RF pulses at first and second frequencies, respectively, the second sequence being applied at a time interval following the first sequence; acquiring the NMR relaxation data from first and second sensitive volumes corresponding to the first and second frequencies, respectively; and selecting the first and second frequencies and the time interval to allow for interference between the first sequence of RF pulses and the NMR relaxation data from the second sensitive volume in order to increase a signal-to-noise ratio and a signal-to-noise ratio per square root of time of the NMR relaxation data.

Abstract: An example pulse sequence for performing phase coherence order selection within a single transient acquisition includes an excitation pulse with a tip angle of 90° and phase ?A, followed by a train of N refocusing pulses with tip angles of 180°, with the center of the first refocusing pulse occurring time ? after the center of the excitation pulse, and the center of the nth refocusing pulse occurring at time (2n+1)? after the center of the excitation pulse. This causes a train of echoes to form at times 2nt after the center of the excitation pulse. In this example, the first refocusing pulse has phase ?B, where \?B??A\=90°, and each successive refocusing pulse (304) has a phase ?? greater than the last refocusing pulse. This incremental change in pulse phase over the course of the echo train has the effect of aiabatically “dragging” the echo phase around the unit circle in a predictable manner corresponding to the phase coherence order of the relevant signals.

Abstract: NMR logging of hydrocarbon formations may be performed with a gradient multi-frequency NMR technique using an increased packing density of the sensitive volumes such that the radiofrequency (RF) pluses for adjacent sensitive volumes interfere. An exemplary method may include applying first and second sequences of RF pulses at first and second frequencies, respectively, the second sequence being applied at a time interval following the first sequence; acquiring the NMR relaxation data from first and second sensitive volumes corresponding to the first and second frequencies, respectively; and selecting the first and second frequencies and the time interval to allow for interference between the first sequence of RF pulses and the NMR relaxation data from the second sensitive volume in order to increase a signal-to-noise ratio and a signal-to-noise ratio per square root of time of the NMR relaxation data.

Abstract: A magnetic resonance method includes providing a pulse sequence that affects different measurement regions in presence of a magnetic field gradient, the pulse sequence having multiple pulse shapes and multiple characteristic interecho intervals (TEs).

Abstract: An example pulse sequence for performing phase coherence order selection within a single transient acquisition includes an excitation pulse with a tip angle of 90° and phase ?A, followed by a train of N refocusing pulses with tip angles of 180°, with the center of the first refocusing pulse occurring time ? after the center of the excitation pulse, and the center of the nth refocusing pulse occurring at time (2n+1)? after the center of the excitation pulse. This causes a train of echoes to form at times 2nt after the center of the excitation pulse. In this example, the first refocusing pulse has phase ?B, where \?B??A\=90°, and each successive refocusing pulse (304) has a phase ?? greater than the last refocusing pulse. This incremental change in pulse phase over the course of the echo train has the effect of aiabatically “dragging” the echo phase around the unit circle in a predictable manner corresponding to the phase coherence order of the relevant signals.

Abstract: A method for approximating a plurality of digital signals or images using compressed sensing. In a scheme where a common component xc of said plurality of digital signals or images an innovative component xi of each of said plurality of digital signals each are represented as a vector with m entries, the method comprises the steps of making a measurement yc, where yc comprises a vector with only ni entries, where ni is less than m, making a measurement yi for each of said correlated digital signals, where yi comprises a vector with only ni entries, where ni is less than m, and from each said innovation components yi, producing an approximate reconstruction of each m-vector xi using said common component yc and said innovative component yi.

Abstract: A method for approximating a plurality of digital signals or images using compressed sensing. In a scheme where a common component xc of said plurality of digital signals or images an innovative component xi of each of said plurality of digital signals each are represented as a vector with m entries, the method comprises the steps of making a measurement yc, where yc comprises a vector with only ni entries, where ni is less than m, making a measurement yi for each of said correlated digital signals, where yi comprises a vector with only ni entries, where ni is less than m, and from each said innovation components yi, producing an approximate reconstruction of each m-vector xi using said common component yc and said innovative component yi.

Abstract: A method for approximating a plurality of digital signals or images using compressed sensing. In a scheme where a common component xc of said plurality of digital signals or images an innovative component xi of each of said plurality of digital signals each are represented as a vector with m entries, the method comprises the steps of making a measurement yc, where yc comprises a vector with only ni entries, where ni is less than m, making a measurement yi for each of said correlated digital signals, where yi comprises a vector with only ni entries, where ni is less than m, and from each said innovation components yi, producing an approximate reconstruction of each m-vector xi using said common component yc and said innovative component yi.

Abstract: A method for approximating a plurality of digital signals or images using compressed sensing. In a scheme where a common component xc of said plurality of digital signals or images an innovative component xi of each of said plurality of digital signals each are represented as a vector with m entries, the method comprises the steps of making a measurement yc, where yc comprises a vector with only ni entries, where ni is less than m, making a measurement yi for each of said correlated digital signals, where yi comprises a vector with only ni entries, where ni is less than m, and from each said innovation components yi, producing an approximate reconstruction of each m-vector xi using said common component yc and said innovative component yi.