The incoherent gradient echo (gradient spoiled) type of sequence uses a continuous shifting of the RF pulse to spoil the remaining transverse magnetization. The transverse magnetization is destroyed by a magnetic field gradient. This results in a T1 weighted image. Spoiling can be accomplished by RF or a gradient.
Gradient spoiling occurs after each echo by using strong gradients in the slice-select direction after the frequency encoding and before the next RF pulse. Because spins in different locations in the magnet thereby experience a variety of magnetic field strengths, they will precess at differing frequencies; as a consequence they will quickly become dephased. Magnetic field gradients are not very efficient at spoiling the transverse steady state. To be effective, the spins must be forced to precess far enough to become phased randomly with respect to the RF excitation pulse. In clinical MRI machines, the field gradients are set up in such a way that they increase and decrease relative to the center of the magnet; the magnetic field at the magnet 'isocenter' does not change.
The T1 weighting increases with the flip angle and the T2* weighting increases with echo time (TE). Typical repetition time (TR) are 30-500 ms and TE less than 15 ms.

See also Ernst Angle.

The k-space is an extension of the concept of Fourier space that is well known in imaging. In MR imaging the k-space is a temporary memory of the spatial frequency information in two or three dimensions of an object; the k-space is defined by the space covered by the phase and frequency encoding data.
The relation between K-space data and image data is the Fourier Transformation. The data acquisition matrix contains raw image data before the image processing. In 2 dimensional Fourier transformation imaging, a line of data corresponds to the digitized MRI signal at a particular phase encoding level. The position in k-space is directly related to the gradient across the object being imaged. By changing the gradient over time, the k-space data are sampled in a trajectory through Fourier space at each point until it is filled.

See also Spatial Frequency and Raw Data.

Quick Overview
Please note that there are different common names for this artifact.

Patient motion is the largest physiological effect that causes artifacts, often resulting from involuntary movements (e.g. respiration, cardiac motion and blood flow, eye movements and swallowing) and minor subject movements.
Movement of the object being imaged during the sequence results in inconsistencies in phase and amplitude, which lead to blurring and ghosting. The nature of the artifact depends on the timing of the motion with respect to the acquisition. Causes of motion artifacts can also be mechanical vibrations, cryogen boiling, large iron objects moving in the fringe field (e.g. an elevator), loose connections anywhere, pulse timing variations, as well as sample motion. These artifacts appear in the phase encoding direction, independent of the direction of the motion.

Motion artifacts can be flipped 90° by swapping the phase//frequency encoding directions.
The artifacts can be reduced by using breath holding, cardiac synchronization or respiratory compensation techniques: triggering, gating, retrospective triggering or phase encoding artifact reduction. Flow effects can be reduced by using gradient moment nulling of the first order of flow, gradient moment rephasing or flow compensation, depending of the MRI system.
Peristaltic motion can be reduced with the intravenous injection of an anti-spasmodic (e.g. Buscopan).
By using multiple averages, respiratory motion can be reduced in the same way that multiple averages increase the signal to noise ratio. Noticeable motion averaging is seen when four averages are obtained, six averages are often as good as respiratory compensation techniques and higher averages will continue to improve image quality.
In some cases will help a presaturation of the anatomy that was generating the motion.

See also Phase Encoded Motion Artifact.

(MEDIC) MEDIC is a heavily T2* weighted spoiled gradient echo sequence with multiple echoes. MEDIC uses a series of identically phase encoded gradient echoes, sampled per line in k-space. Unipolar frequency encoding gradients are used to achieve flow compensation and to avoid off resonance effects. For each echo the magnitude images are reconstructed and postprocessed by using a sum of squares algorithm to improve the signal to noise ratio. The increased receiver bandwidth reduces the T2* effects and impairment of the spatial resolution.
The multi echo data image combination sequence is potentially useful in imaging of cartilage in joints.