  Dialect variation is of considerable interest in linguistics and other social
sciences. However, traditionally it has been studied using proxies
(transcriptions) rather than acoustic recordings directly. We introduce novel
statistical techniques to analyse geolocalised speech recordings and to explore
the spatial variation of pronunciations continuously over the region of
interest, as opposed to traditional isoglosses, which provide a discrete
partition of the region. Data of this type require an explicit modeling of the
variation in the mean and the covariance. Usual Euclidean metrics are not
appropriate, and we therefore introduce the concept of $d$-covariance, which
allows consistent estimation both in space and at individual locations. We then
propose spatial smoothing for these objects which accounts for the possibly non
convex geometry of the domain of interest. We apply the proposed method to data
from the spoken part of the British National Corpus, deposited at the British
Library, London, and we produce maps of the dialect variation over Great
Britain. In addition, the methods allow for acoustic reconstruction across the
domain of interest, allowing researchers to listen to the statistical analysis.
