In addition to their utility in geochronology, radiogenic isotope systems can preserve information regarding the isotopic signature of the source region of a magma or detritus at the time of formation. If the system has remained closed since this time, it is possible to age-correct, or back calculate, the measured present-day isotopic ratio of the sample (sedimentary, igneous or even metamorphic) to the time of formation of the rock. It is then possible to compare this age-corrected ratio with that of potential source regions in order to constrain whether the sample in question was derived from one region of the lithosphere or mantle rather than another. Such isotopic tracing is potentially a very powerful tool, and is commonly used in igneous petrogenesis and detrital sedimentary studies. However, as with all tools, such approaches are severely limited by our understanding of the nature of the source region with which we are comparing our sample – often we are forced to make assumptions regarding (for example) the nature of the mantle a particular sample might have been derived from, or the source terrane for detritus may have been entirely eroded away, leaving no other record of its existence. Therefore radiogenic (and indeed stable) isotopic tracing requires a full understanding of the geological context of the samples in question, and cannot be applied blindly to ‘solve’ questions of source for samples. There is no magic bullet in understanding whether a particular magma or fluid was derived from the crust or mantle (say), but a weight-of-evidence approach through multiple chemical and isotopic studies can lead to a high degree of confidence in such interpretations when applied in an integrated manner.

The following section attempts to set out the commonly applied tools applied to tracing the when and where of mass transfer within and across the (dominantly) solid earth. The principles are directly transferable to, and indeed often are intimately linked with, the hydro- and atmospheres. They can also be scaled down from a whole-earth geochemical reservoir approach to that of piecing together the evolution of individual cratons and terranes (and terrains!), to the local scale when testing for contamination and assimilation. This chapter outlines the general tools that are used and their mathematical underpinnings.