Refocussing pulse having an incremental phase

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 ϕA, followed by a train of N refocusing pulses with tip angles of 180°, with the center of the first refocusing pulse occurring time τ after the center of the excitation pulse, and the center of the nth refocusing pulse occurring at time (2n+1)τ 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 ϕB, where \ϕB−ϕA\=90°, and each successive refocusing pulse (304) has a phase ϕδ 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.

This application is a U.S. National Stage of International Application No. PCT/US/2013/075148, filed Dec. 13, 2013.

TECHNICAL FIELD

This invention relates to magnetic resonance measurements, and more particularly to pulse sequences used therein.

BACKGROUND

In the field of nuclear magnetic resonance (NMR), spin echo-based sequences are used to measure many material properties such as relaxivity and diffusivity. These sequences are used in a variety of contexts such as medical imaging, chemical analysis and particularly the characterization of heterogeneous media. Spin echo sequences are particularly valuable when making “ex-situ” measurements, as they tend to be robust in the presence of strong gradients. These sequences are often used in the field of logging (e.g., wireline logging, logging while drilling (LWD) and measurement while drilling (MWD), NMR tools have been used to explore the subsurface based on magnetic interactions with subsurface material. Some downhole NMR logging tools include a magnet assembly that produces a static magnetic field, and an antenna assembly that generates radio-frequency (RF) control signals and detects magnetic resonance phenomena in the subsurface material.

DETAILED DESCRIPTION

Nuclear magnetic resonance (NMR) is used in a variety of contexts, for instance in the fields of medicine and science for the characterization of heterogeneous media, or in the field of well logging (e.g., wireline logging, logging while drilling (LWD) and measurement while drilling (MWD)) to explore the subsurface of the earth. In the description below, embodiments are disclosed that relate to the use of NMR for well logging. However, it should be understood the implementations described here and not limited only to well logging applications, and may be broadly applicable to other applications in which NMR is used to characterize an unknown sample.

Referring toFIG. 1A, NMR is used to observe properties of a well system100a. The well system100aincludes an NMR logging system108and shows a subterranean region120beneath a ground surface106. In general, well systems can include additional or different features that are not shown inFIG. 1A. For example, well systems may include additional drilling system components, wireline logging system components, etc.

The subterranean region120can include all or part of one or more subterranean formations or zones. The example subterranean region120shown inFIG. 1Aincludes multiple subsurface layers122and a wellbore104penetrated through the subsurface layers122. The subsurface layers122can include sedimentary layers, rock layers, sand layers, or combinations of these other types of subsurface layers. One or more of the subsurface layers can contain fluids, such as brine, oil, gas, etc. Although the example wellbore104shown inFIG. 1Ais a vertical wellbore, the NMR logging system108can be implemented in other wellbore orientations. For example, the NMR logging system108may be adapted for horizontal wellbores, slant wellbores, curved wellbores, vertical wellbores, or combinations of these.

The example NMR logging system108includes a logging tool102, surface equipment112, and a computing subsystem110. In the example shown inFIG. 1A, the logging tool102is a downhole logging tool that operates while disposed in the wellbore104. The example surface equipment112shown inFIG. 1Aoperates at or above the surface106, for example, near the well head105, to control the logging tool102and possibly other downhole equipment or other components of the well system100. The example computing subsystem110can receive and analyze logging data from the logging tool102. An NMR logging system can include additional or different features, and the features of an NMR logging system can be arranged and operated as represented inFIG. 1Aor in another manner.

In some instances, all or part of the computing subsystem110can be implemented as a component of, or can be integrated with one or more components of, the surface equipment112, the logging tool102or both. In some cases, the computing subsystem110can be implemented as one or more discrete computing system structures separate from the surface equipment112and the logging tool102.

In some implementations, the computing subsystem110is embedded in the logging tool102, and the computing subsystem110and the logging tool102can operate concurrently while disposed in the wellbore104. For example, although the computing subsystem110is shown above the surface106in the example shown inFIG. 1A, all or part of the computing subsystem110may reside below the surface106, for example, at or near the location of the logging tool102.

The well system100acan include communication or telemetry equipment that allow communication among the computing subsystem110, the logging tool102, and other components of the NMR logging system108. For example, the components of the NMR logging system108can each include one or more transceivers or similar apparatus for wired or wireless data communication among the various components. For example, the NMR logging system108can include systems and apparatus for wireline telemetry, wired pipe telemetry, mud pulse telemetry, acoustic telemetry, electromagnetic telemetry, or a combination of these other types of telemetry. In some cases, the logging tool102receives commands, status signals, or other types of information from the computing subsystem110or another source. In some cases, the computing subsystem110receives logging data, status signals, or other types of information from the logging tool102or another source.

NMR logging operations can be performed in connection with various types of downhole operations at various stages in the lifetime of a well system. Structural attributes and components of the surface equipment112and logging tool102can be adapted for various types of NMR logging operations. For example, NMR logging may be performed during drilling operations, during wireline logging operations, or in other contexts. As such, the surface equipment112and the logging tool102may include, or may operate in connection with drilling equipment, wireline logging equipment, or other equipment for other types of operations.

In some implementations, the logging tool102includes a magnet assembly, which may be arranged to enhance the static magnetic field in a volume of interest. The logging tool102can also include one or more antenna assemblies. The antenna assemblies can produce polarized excitation in a subterranean volume and acquire a response from the volume by quadrature detection.

In some examples, NMR logging operations are performed during wireline logging operations.FIG. 1Bshows an example well system100bthat includes the NMR logging tool102in a wireline logging environment. In some example wireline logging operations, a the surface equipment112includes a platform above the surface106is equipped with a derrick132that supports a wireline cable134that extends into the wellbore104. Wireline logging operations can be performed, for example, after a drilling string is removed from the wellbore104, to allow the wireline logging tool102to be lowered by wireline or logging cable into the wellbore104.

In some examples, NMR logging operations are performed during drilling operations.FIG. 1Cshows an example well system100cthat includes the NMR logging tool102in a logging while drilling (LWD) environment. Drilling is commonly carried out using a string of drill pipes connected together to form a drill string140that is lowered through a rotary table into the wellbore104. In some cases, a drilling rig142at the surface106supports the drill string140, as the drill string140is operated to drill the wellbore104to penetrate the subterranean region120. The drill string140may include, for example, a kelly, drill pipe, a bottom hole assembly, and other components. The bottom hole assembly on the drill string may include drill collars, drill bits, the logging tool102, and other components. The logging tools may include measuring while drilling (MWD) tools, LWD tools, and others.

In some example implementations, the logging tool102includes an NMR tool for obtaining NMR measurements from the subterranean region120. As shown, for example, inFIG. 1B, the logging tool102can be suspended in the wellbore104by a coiled tubing, wireline cable, or another structure that connects the tool to a surface control unit or other components of the surface equipment112. In some example implementations, the logging tool102is lowered to the bottom of a region of interest and subsequently pulled upward (e.g., at a substantially constant speed) through the region of interest. As shown, for example, inFIG. 1C, the logging tool102can be deployed in the wellbore104on jointed drill pipe, hard wired drill pipe, or other deployment hardware. In some example implementations, the logging tool102collects data during drilling operations as it moves downward through the region of interest during drilling operations. In some example implementations, the logging tool102collects data while the drilling string140is moving, for example, while it is being tripped in or tripped out of the wellbore104.

In some example implementations, the logging tool102collects data at discrete logging points in the wellbore104. For example, the logging tool102can move upward or downward incrementally to each logging point at a series of depths in the wellbore104. At each logging point, instruments in the logging tool102perform measurements on the subterranean region120. The measurement data can be communicated to the computing subsystem110for storage, processing, and analysis. Such data may be gathered and analyzed during drilling operations (e.g., during logging while drilling (LWD) operations), during wireline logging operations, or during other types of activities.

The computing subsystem110can receive and analyze the measurement data from the logging tool102to detect properties of various subsurface layers122. For example, the computing subsystem110can identify the density, material content, or other properties of the subsurface layers122based on the NMR measurements acquired by the logging tool102in the wellbore104.

In an example downhole NMR experiment, a static magnetic field, B0, and second radio frequency (RF) magnetic field, B1, are used to create and manipulate nuclear magnetization of a sample. NMR experiments can give insight to a variety of properties of the downhole environment, for example diffusion, viscosity, porosity (i.e., amount of fluid in an underground formation), and permeability, among others. These properties can be measured from the transient NMR response, which measures the T1recovery time (i.e., the recovery time of magnetization in the longitudinal direction) and T2decay time of the magnetization (i.e., the recovery time of magnetization in the transverse plane).

The magnetic fields B0and B1can be generated in a variety of ways. For instance, referring toFIG. 2, magnetic fields B0and B1can be generated by an NMR logging tool102. NMR logging tool102includes a magnet module202, an antenna module204, and a data processing module206.

Magnet module202can be used to induce the magnetic field B0in an NMR experiment. For example, magnet module202can include a permanent magnetic or electromagnetic that that directs magnetic flux outward from logging102in order to induce a magnetic field within the subterranean region120.

Antenna module204can be used to induce an RF magnetic field B1in an NMR experiment, and can be used to measure the NMR signal in response to the induced fields. For example, antenna module204can include an antenna element defined by a path of electrically conductive material. When a current is applied to the antenna element, current flows through the path and induces a magnetic flux within the subterranean region120. Current can be applied to induce a series of pulses (frequently referred to as “pulse sequences”), creating a time-varying magnetic field B1that aligns and/or otherwise manipulates the nuclear spins of the subterranean region120.

In a similar manner, antenna module204can be used to detect changes in magnetism in the surrounding environment. For instance, in an example NMR experiment, nuclear magnetization within subterranean region120can be manipulated by a pulse sequence such that it initially aligns with the B0field, is tipped towards the B1field, and relaxes back towards the B0field. Antenna module204can be used to measure this NMR response through electromagnetic induction, and can be used to produce transient electric signals in response to the changing nuclear magnetism.

While magnetic fields B0and B1can be generated by the above described logging tool, these magnetic fields can also be generated in other ways. For instance, in some implementations, magnetic fields B0and B1can be generated by a separate tools that are used in conjunction to conduct an NMR experiment. In some implementations, magnetic field B0can be generated by a hyperpolarization method, or magnetic field B0may be an ambient field (e.g., the earth's magnetic field).

An NMR experiment can be designed to manipulate nuclear spins in a sample, so as to produce a particular frequency spectrum. Information regarding the sample can then be determined based on this frequency spectrum. However, in some circumstances, different components of an NMR signal may respond differently to changes in the phase of a pulse (i.e., the transmitter phase) and/or changes in the phase from which they are observed (i.e., the receiver phase), with many NMR signals containing components with various phase coherence values (i.e., the degrees to which the nuclear spins of a sample are coherent). As a result, the obtained spectrum may contain resonances other than those intended when the experiment was designed. In some circumstances, these spurious resonances can result in a variety of unwanted effects. For instance, in some cases, these resonances can introduce additional information to the spectrum that can obscure the wanted resonance peaks and lead to ambiguities of interpretation.

In some implementations, these unwanted resonances can be lessened through a procedure known as phase cycling, a method by which the transmitter and/or receiver phases are varied in an NMR experiment in order to eliminate unwanted signals on the basis of their phase response properties. Phase cycling can be used to separate out components of an NMR signal by their response to a change in transmitter and/or receiver phases, and can be used to remove undesirable resonances. In an example implementation, phase cycling can be used to selectively lessen or remove instrumental artifacts such as ringing, channel imbalances and signal offsets.

Phase cycling can be performed in a variety of ways. For example, in some circumstances, phase cycling can be achieved by repeating NMR experiments to produce several transient NMR responses. Each NMR experiment can be conducted with different values of the transmitter and receiver phase in order to separate out signals with different phase coherences. In an example, a set of NMR experiments can be designed such that each NMR experiment has a different transmitter and receiver phase pair. In this example, transmitter and receiver phases is selected such that the relative phase between each pair of phases remains the same, and such that when the NMR signals are averaged, components of an NMR signal with similar phase coherences are additively combined, while those of difference phase coherences cancel. In this manner, only signals of a particular phase coherence are isolated. In some implementations, instrumental artifacts are independent of the transmitter phase, while the NMR signal response depends linearly on the transmitter phase, and this technique can be used to isolate the NMR response signal from the instrumental artifacts. However, this approach may be undesirable in certain circumstances, as repeating an NMR experiment multiple times can increase the minimum duration of the experiment. This approach may also be problematic in circumstances, for instance when the logging tool is in motion during the NMR experiments, as each successive measurement is from a different position.

In some circumstances, phase cycling can be achieved by conducting a single NMR experiment to produce a single transient NMR response. An example pulse sequence300for conducting a single-transient phase cycling is shown inFIG. 3. Pulse sequence300is a variant of the Carr Purcell Meiboom Gill (CPMG) pulse sequence, and includes an excitation pulse302with a tip angle of 90° and phase ϕA, followed by a train of N refocusing pulses304with tip angle 180°, with the center of the first refocusing pulse304occurring time τ after the center of the excitation pulse302, and the center of the nthrefocusing pulse occurring at time (2n+1)τ after the center of the excitation pulse302. This causes a train of echoes306to form at times 2nτ after the center of the excitation pulse.

In this example, the first refocusing pulse has phase ϕB, where |ϕB−ϕA|=90°, and each successive refocusing pulse304has a phase ϕδgreater than the last refocusing pulse. This incremental change in pulse phase over the course of the echo train has the effect of adiabatically “dragging” the echo phase around the unit circle in a predictable manner corresponding to the phase coherence order of the relevant signals. In an example, for an excitation pulse302with a tip angle of 90° and refocusing pulses304with tip angles of 180°, the phase of NMR signal with phase coherence of 1 at the nthecho is nϕδ+1 on odd echoes, and nϕδon even echoes, showing up in a quadrature signal as a wave with frequency ϕ/(4πτ). In some implementations, in the presence of a gradient large enough that the bandwidth of the refocusing pulses304are selecting only a slice from the wider sample volume, echoes can form at phase nϕδfor all values of n. For example, referring toFIGS. 4A-F, when the pulse phase402of each refocusing pulse is incremented by 20°, the phase404of the resulting echoes is incremented by 40° for each odd-even pair of echoes. Accordingly, a linear phase increment of the refocusing pulses can have the effect of adiabatically dragging the phase of the echoes along with it.

After the NMR signal has been separated by phase coherence, unwanted artifacts can be removed. For example, in some implementations, the components of the signal can separated in Fourier space, allowing artifacts to be filtered away using a high-pass filter or bandpass filter. In some implementations, the phase of the receiver can be chosen during the experiment to follow the expected phase of the echoes, and a low-pass filter can be used to filter out unwanted components.

While the above example illustrates the use of a CPMG pulse sequence having an excitation pulse302with a tip angle of 90° and refocusing pulses304with tip angles of 180°, single-transient phase cycling can be performed in conjunction with other pulse sequences. For example, in some implementations, refocusing pulses304can have tip angles other than 180° (e.g., 90° and 135°). In some implementations, the excitation pulse302can have a tip angle other than 90°. In addition, the number of echoes can vary. For instance, in some implementations, pulse sequence300can have any number of echoes greater than two (e.g., three, four, five, six, and so forth).

An example method500of single-transient phase cycling with N echoes is shown inFIG. 5. Method500begins after the nuclear spins of a particular sample volume have been polarized (e.g., by an applied magnetic field, hyperpolarization techniques, or natural polarization along an ambient field). First, an excitation pulse is applied having a phase ϕA(502), and an index k is set to zero. After waiting for a duration τ (504), a refocusing pulse with phase ϕB+kϕδis applied to the sample volume (506) in order to induce a corresponding echo. After waiting for a duration τ (508), the NMR signal corresponding to the induced echo is acquired with a receiver phase ϕC, where ϕC=D+kϕδ(510), where D is a constant. Constant D may be selected such that it is equal to the phase of the initial refocusing pulse (i.e., D=ϕB), or equal to a phase value other than ϕB.

After the NMR signal is acquired for the induced echo, the index k is incremented by one, and the value of k is compared to the desired number of echoes N (512). If k is less than N, steps504,506,508,510, and512are repeated. If k equals to N, then a band-pass filter is applied to the data (514), where the filter has a width selected in order to eliminate the artifacts from the desired NMR signal.

An example of filtering is shown inFIGS. 6A-B. Referring toFIG. 6A, plot600shows example simulated NMR signals obtained using a single-transient pulse sequence without phase increment (602), a single-transient pulse sequence with phase increment (e.g., as described above) (604), and the “true” signal (606), representing an ideal NMR signal without artifacts. In this simulated example, the signal obtained using a single-transient pulse sequence without phase increment (602) is offset from the true signal606, and does not provide an accurate representation of the true signal. In addition, the signal obtained using a single-transient pulse sequence with phase increment (604) contains numerous frequency components (i.e., artifacts) that are not present in the true signal. Referring to plot610inFIG. 6B, by applying an appropriately selected low-pass filter to the signal obtained using a single-transient pulse sequence with phase increment604, the resulting signal612can accurately represent the true signal606.

In the example method500, the phase of the receiver can be chosen during the experiment to follow the expected phase of the echoes. However, this need not be the case. In some implementations, echoes acquired using a constant receiver phase, and the acquired signals components can be separated in Fourier space, allowing artifacts to be filtered away using a high-pass filter or bandpass filter. An example method700of single-transient phase cycling with N echoes is shown inFIG. 7. As above, method700begins after the nuclear spins of a particular sample volume have been polarized (e.g., by an applied magnetic field, hyperpolarization techniques, or natural polarization along an ambient field). First, an excitation pulse is applied having a phase ϕA(702), and an index k is set to zero. After waiting for a duration τ (704), a refocusing pulse with phase ϕB+kϕδis applied to the sample volume (706) in order to induce a corresponding echo. After waiting for a duration τ (708), the NMR signal corresponding to the induced echo is acquired with a receiver phase ϕC(710), where ϕC=D (510), where D is a constant. Constant D may be selected such that it is equal to the phase of the initial refocusing pulse (i.e., D=ϕB), or equal to a phase value other than ϕB.

After the NMR signal is acquired for the induced echo, the index k is incremented by one, and the value of k is compared to the desired number of echoes N (712). If k is less than N, steps704,706,708,710, and712are repeated. If k equals to N, then the data is Fourier transformed and an appropriate filter is selected to isolate the desired signal (714).

An example of filtering is shown inFIG. 8, in which a plot800shows an example simulated spectrum802of a Fourier transformed NMR signal. The spectrum802contains a first signal peak804, representing the desired signal, and a second signal peak806, representing artifacts. An appropriate filter can be selected to isolate the desired signal from the artifacts, such that the resulting signal accurately represents the true signal.

Various values can be used for the phase increment ϕδ. In some implementations, ϕδis selected based on the degree to which an NMR signal decays as a result of the phase increment. For example,FIGS. 9A-Bcompare NMR signals induced by a pulse sequence having a single excitation pulse with a tip angle of 90°, and a train of refocusing pulses having a tip angle of 135° (FIG. 9A) or 180° (FIG. 9B) with a phase increment of ϕδ. As shown in plots900and940, changes in the phase increment ϕδup to approximately 20° does not significantly affect the magnitude of the NMR signal, and has a relatively small effect on the signal other than the introduction of a echo phase oscillation at a frequency ϕ/4πτ. Referring to plots920and960, the effect on the phase-shifted signal (wherein the receiver phase is made to follow the drift), is that after one or two echoes, some signal is destroyed, then T2decay occurs as normal afterwards. Accordingly, in some implementations, the phase increment ϕδis a value greater than 0° and approximately less than or equal to 20°. In some implementations, for example when the degradation of the NMR signal is less of a concern, the phase increment ϕδcan be greater than 20° (e.g., 30°, 40°, 50°, and so forth).

In some implementations, for example in a slice-selective condition, the amount of T2amplitude destroyed by the inclusion of a phase increment can be relatively independent of both gradient strength and pulse length. For instance, referring toFIG. 10, plot1000shows example NMR signals acquired using pulse sequences having different phase increments ϕδ, where τ is 5 ms. Referring toFIG. 11, least squares fittings of example signals obtained using refocusing pulses having tip angles of either 135° (plot1102) or 180° (plot1104) both indicate that the signal strength decays approximately according to cosine. In other implementations, the amount of T2amplitude destroyed by the inclusion of a phase increment can depend on both gradient strength and pulse length. For example, when the pulse bandwidth is wider than the gradient across the sample, artifacts may be introduced in the event of non-ideal pulse lengths.

Referring toFIG. 12, in some implementations, the coefficient of determination (i.e., R2) values of the T2fits tend to decay rapidly after approximately 55° for signals obtained using refocusing pulses having tip angles of 135° (plot1202), and after approximately 100° for signals obtained using refocusing pulses having tip angles of 180° (plot1204). However, referring toFIG. 13, despite the decay in the amplitude, the fitted T2decay rate for signals obtained using refocusing pulses having tip angles of either 135° (plot1302) or 180° (plot1304) is relatively unchanged as a function of the phase drift, indicating that if the phase drift is known and can be taken into account, T2measurements are unlikely to be severely distorted by its presence.

In the above examples, simulated data has been used to illustrate various implementations of single-transient phase cycling. In some implementations, experimental data corresponds fairly well to the simulations, and the two are in good agreement, qualitatively, and primarily differ in the magnitude of the effects. In an example,FIGS. 14A-Bshow comparisons of various simulated and experimental echo train magnitudes for 135° pulses (plots1402,1404, and1406ofFIG. 14A) and 180° pulses (plots1408,1410, and1412ofFIG. 14B) in the presence of a magnetic field gradient, and plots1502,1504,1506, and1508ofFIG. 15show comparisons of various simulated and experimental amplitudes of T2fits as a function of phase drift per pulse.

In some implementations, phase cycling can used to separate out signals from coupled spins, which will respond to phase according to ϕn, where ϕ is the phase and n is a function of the number of coupled spins and the nature of their coupling and can take values n=N−2 k for values k∈, [0,N]. In a multi-transient approach, where the phase of the receiver and transmitter are varied according to an appropriate scheme, the number of transients acquired determines the extent of the aliasing, and a sequence selecting phase n will also select at minimum all coherences n+jN where j∈, [0,∞]. In a single-transient phase cycling approach, for example an implementation described above, because the phase of the magnetic field B pulses are continuously varied during the sequence, the resolution in the phase-coherence domain is proportional not to the number of transients, but rather to the number of echoes. In some implementations, this can provide an improvement in resolution, for instance an improvement by 2-3 orders of magnitude.

One or more of the above described implementations may provide a variety of benefits. For example, in some implementations, single-transient phase cycling can be performed by inducing a single transient. In contrast, a multi-transient approach may require two or more transients, and thus may require more time to conduct measurements, and may require averaging at multiple positions.

In some implementations, single-transient phase cycling has a very large cycle number, which can correspond to high frequency resolution. In contrast, in some multi-transient methods the resolution may be limited not by the number of pulses but by the number of transients.

In some implementations, single-transient phase cycling may not significantly affect the signal-to-noise ratio of the measurement, and is robust to pulse errors. Accordingly, in some implementations, single-transient phase cycling is suitable for use in a magnetic field gradient.

In some implementations, single-transient phase cycling does not require a moving average, which can remove fast-relaxing components from the measured NMR signals.

In some implementations, the resolution of measurements may be sufficiently high to observe a phase coherence spectrum in a single scan, and does not necessarily average out all but the selected components of the phase coherence spectrum.

In some implementations, single-transient phase cycling is used in combination with existing methods, for instance a phase alternated Carr Purcell (PACP) sequence (e.g., as described in PCT/US2005/020585), for greater artifact cancellation.

A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. For example, in some implementations, the above described phase incrementing pulse sequences can be used in conjunction with phase-alternating-pair (PAP) methodologies. In an example, implementation, multiple NMR experiments can be conducted with a phase incrementing pulse sequence, as described above, with each experiment having a different set of values for ϕA, ϕB, and ϕδ. The resulting acquired signals can be averaged together, for example to further remove artifacts and/or to further isolate signal from a single phase coherence order.

Further, while the above examples describe the use of a phase increment in NMR pulse sequences in order to perform single-transient phase cycling, phase increment can also be implemented in electron spin resonance (ESR) pulse sequences. In an example implementation, the use of a phase increment can be used in microwave CPMG pulse sequences in order to provide single-transient phase cycling in ESR applications.

Further still, while the above examples describe the use of single-transient phase cycling in the context of well logging, it should be understood the implementations described here are not limited only to well logging applications, may be broadly applicable to other applications in which NMR or ESR is used to characterize an unknown sample. For example, in some implementations, single-transient phase cycling can be used in other contexts, for instance for medical imaging applications (e.g., magnetic resonance imaging), chemical studies (e.g., NMR or ESR spectroscopy), or other applications of NMR or ESR.

Various aspects of the invention are summarized as follows.

In general, in an aspect, a method for performing magnetic resonance measurements of a sample includes applying an excitation pulse into a volume of polarized spins of a sample, the excitation pulse having a phase of ϕA, applying a sequence of n refocusing pulses, each kth refocusing pulse having a phase ϕB+kϕδ, detecting echoes from the volume induced by each kth refocusing pulse with a receiver phase of ϕCto determine signal information corresponding on the detected echoes, and determining information about the sample based on the signal information.

Implementations of this aspect may include one or more of the following features:

The sample is can be a subterranean region. The subterranean region can be proximate to a wellbore.

The method can further include applying a static magnetic field in the sample to obtain a volume of polarized nuclear spins.

ϕδcan be determined based on a T2 relaxation time of the volume of the sample. ϕδcan be greater than 0° and less than or equal to about 25°.

ϕBcan be equal to D+k*ϕδ, where D is a fixed constant.

Determining information about the sample can include band pass filtering the signal information.

The band-pass filter can have a width determined based on a T2 component of the signal information.

ϕδcan be a fixed constant.

The method can include performing a Fourier transform on the signal information.

The method can include removing information corresponding to artifacts from the signal information.

The method can include separating components of the signal information by phase coherence order.

The method can include obtaining multiple sets of signal information, each set of signal information corresponding to detected echoes associated with different excitation pulse phases, refocusing pulse phases, or receiver phases. The method can include removing artifacts from the sets of signal information by averaging the sets of signal information. The method can include isolating information corresponding to a single phase coherence order by averaging the sets of signal information.

The center of the excitation pulse and the center of a first refocusing pulse in the sequence of refocusing pulses can be separated by a time t.

The center of each refocusing pulse and the center of a corresponding acquisition period for detecting the echoes induced by each refocusing pulse can be separated by a time t.

The center of an acquisition period and a center of a subsequent refocusing pulse can be separated by a time t.

The excitation pulse can have a tip angle of 90°.

Each refocusing pulse can have a tip angle of about 180°. Each refocusing pulse can have a tip angle of about 135°.

The polarized spins can be polarized nuclear spins. The polarized spins can be polarized electron spins.

In general, in another aspect, a system for performing magnetic resonance measurements of a sample includes an antenna module and a data processing module. During use, the antenna module applies an excitation pulse into a volume of polarized nuclear spins of a sample, the excitation pulse having a phase of ϕA, applies a sequence of n refocusing pulses, each kth refocusing pulse having a phase ϕB+kϕδ, and detects echoes from the volume induced by each kth refocusing pulse with a receiver phase of ϕCto determine signal information corresponding on the detected echoes. During use, the data processing module determines information about the sample based on the signal information.

Implementations of this aspect may include one or more of the following features:

The sample can be a subterranean region. The subterranean region can be proximate to a wellbore.

The system can include a magnet module. During use, the magnet module can apply a static magnetic field in the sample to obtain a volume of polarized nuclear spins.

ϕδcan be determined based on a T2 relaxation time of the volume of the sample.

ϕδcan be greater than 0° and less than or equal to about 25°.

ϕCcan be equal to D+K*ϕδ, where D is a fixed constant.

Determining information about the sample can include band pass filtering the signal information.

The band-pass filter can have a width determined based on a T2 component of the signal information.

ϕδcan be a fixed constant.

During operation, the data processing module can perform a Fourier transform on the signal information. During operation, the data processing module can remove information corresponding to artifacts from the signal information. During operation, the data processing module can separate components of the signal information by phase coherence order. During operation, the data processing module can obtain multiple sets of signal information, each set of signal information corresponding to detected echoes associated with different excitation pulse phases, refocusing pulse phases, or receiver phases. During operation, the data processing module can remove artifacts from the sets of signal information by averaging the sets of signal information. During operation, the data processing module can isolate information corresponding to a single phase coherence order by averaging the sets of signal information.

The center of the excitation pulse and the center of a first refocusing pulse in the sequence of refocusing pulses can be separated by a time t.

The center of each refocusing pulse and the center of a corresponding acquisition period for detecting the echoes induced by each refocusing pulse can be separated by a time t.

The center of an acquisition period and a center of a subsequent refocusing pulse can be separated by a time t.

The excitation pulse can have a tip angle of 90°.

Each refocusing pulse can have a tip angle of about 180°. Each refocusing pulse can have a tip angle of about 135°.

The polarized spins can be polarized nuclear spins. The polarized spins can be polarized electron spins.