Reply to comment by F. A. Dahlen and G. Nolet on ‘On sensitivity kernels for ‘wave-equation’ transmission tomography’

Abstract

We thank Dahlen & Nolet for the comments (DN05) on our paper (HH05). There are many points of agreement, as we think is clear from HH05, but we respectfully continue to differ in opinion on some fundamental aspects of the finite frequency sensitivity kernels known as ‘banana doughnut’ kernels—hereinafter BDKs, as per the original nomenclature of Dahlen et al.—and their benefit to global tomography. In contrast to DN05’s summary statement, HH05’s main concern about BDKs is not the effect of uncertainty in the earthquake source signature or origin time. HH05 argue that (i) the evaluation of sensitivity kernels in simple media has limitations for the interpretation of broad-band signals by means of (linearized) finite frequency tomography; (ii) finite frequency kernels are (indeed) oscillatory, but in general heterogeneity their structure will be complex and different from BD features; (iii) the resolved length scales of model variations are induced by the spectral scales present in the data, which makes the notion of ‘hole’ irrelevant; and (iv) with the need for ‘damping’ (regularization) and without a basis that matches properly the multi-scale aspects of finite frequency sensitivity, ray theory or finite frequency theory inversions are likely to yield results that are practically the same.