First, because the set stage pole used for computing flowlines is calculated to fit the trend of the Hawaiian-Emperor seamount chain, the clear ‘X’ on the image of cumulative volcano amplitude (CVA), which marks the location of the Hawaiian hotspot, is a normal consequence of geometry. To say that the ‘X’ illustrates the power of the technique is a tautology.

Second, Wessel and Kroenke2 underestimate the effect of interference. If we plot the crustal flowline of each volcano (Fig. 1a), the biggest and brightest CVA maxima shown in their image are obtained by the intersection of flowlines issued mainly from different alignments that are not related. To avoid these problems, flowlines must not be plotted beyond the age of volcanoes, but this seriously reduces the usefulness of the hotspot method.

Figure 1: Analysis of the hotspotting technique.
figure 1

a, Crustal flowlines for a selection of alignments. The brightest CVA maxima (from Fig. 6 of ref. 1) are the dotted thick contours labelled A-G. The Rarotonga CVA maximum (A) is mainly the result of the intersection of crustal flowlines of the Samoa (from 10 Myr to 0 Myr ago)7 and the Cretaceous Marshall-Gilberts Islands (which does not present any age progression)8. The Mehetia CVA maximum (B) and Macdonald CVA maximum (C) are both underlined by the flowlines from the midCretaceous Phoenix islands9. The Fatuhiva CVA maximum (D) occurs at the intersection of flowlines from the Northern Line islands, the Central Basin Ridge and the Marquesas alignment. The Emperor Chain flowlines produce two CVA maximum artefacts (E and F) with, respectively, the Northern Line islands and the Central Basin Ridge flowlines. Age and/or direction constraints demonstrate that there is no possible genetic relationship between those hotspots and the respective alignments. b,Small circles calculated with the most recent pole in ref. 1 (25° N, 27° W). This pole fails to describe most of the alignments less than 5 Myr old (highlighted in yellow). Instead, using conventional backtracking, we propose a pole (260° W, 57° N)10 that locates the Louisville hotspot at 50.9° S, 137.6° W, near a 0.5-Myr-old volcano11 known to have a Louisville isotope signature12. Oceanic plateaux (orange) and volcanoes (red) are digitized from the gravity map in ref. 13.

Third, any non-hotspot alignment created, for instance, within a fracture zone parallel to a small circle described by the Hawaiian-Emperor chain, for instance, will converge at a single point of maximum focus. Some Pacific alignments also present two or more periods of volcanic activity3,5. It is not possible to discriminate between the diagenetic volcanoes other than by measuring their age: they will contribute to the same CVA simply because they are on the same trend. Moreover, the pole reported by Wessel and Kroenke1 fits the recent bend of the Hawaiian trend but fails to describe most Pacific alignments that are more than 5 million years old (Fig. 1b). Furthermore, it relocates the present Louisville hotspot to the Hollister Ridge, south of the Eltanin fracture zone, which is not consistent with geochemical constraints6.

Finally, Wessel and Kroenke1 say that the hotspotting concept can be used to refine absolute plate motions by seeking pertubations to the initial stage poles that will focus the CVA image. One of the problems is to define criteria that can be used to focus the image. Refining criteria based on statistics restricted to Hawaii and Louisville sea-mounts is not an easy task, as it is not possible to modify one stage pole and keep a good fit on both alignments without modifying the other poles.

We think these examples show that hotspotting is a flawed technique. Its application is not age-independent in practice, and it has no advantage over the classical technique of backtracking. Indeed, using the few existing dated volcanoes, it is possible to ‘pseudodate’ most Pacific volcanoes by backtracking and linking the co-genetic alignments.

Reply - Wessel and Kroenke