Many of the transforms and attributes used in gravity and magnetic interpretation can be expressed as a 2D or 3D vector. The horizontal gradient and the 2D analytic signal are 2D vectors. The gravity or magnetic field, the 3D analytic signal, and the monogenic signal are defined by a 3D vector. In practice, we prefer to interpret the amplitude and/or phase of a 2D or 3D vector, but we often forget that a meaningful interpretation requires a magnetic reduction-to-the-pole operation when these techniques are applied to magnetic anomaly data and the source body is 3D. Furthermore, the gravity or magnetic anomaly has an unknown constant level that may affect the amplitude and phase. The horizontal gradient, the analytic signal, and the monogenic signal can be applied to not only the gravity or magnetic anomaly but also any nth-order derivative or a filtered version of the anomaly. They can be related to each other and to the magnetic field vector. We do not introduce new attributes. Instead, we have explained the relationships among different transforms (or vectors) and addressed precautions and requirements for their practical use.

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