 Total-field magnetic anomaly

The difference $\Delta T=|{\mathbf{B}}_0+\mathbf{b}|-|{\mathbf{B}}_0|$ between measured scalar field strength and a specified background. For $|\mathbf{b}|\ll |{\mathbf{B}}_0|$, it is approximately ${\hat{\mathbf{B}}}_0\cdot \mathbf{b}$, not an arbitrary fixed Cartesian component.