@article{HaynPanetDiamentetal.2012,
  author    = {Hayn, Michael and Panet, I. and Diament, M. and Holschneider, Matthias and Mandea, Mioara and Davaille, A.},
  title     = {Wavelet-based directional analysis of the gravity field evidence for large-scale undulations},
  series = {Geophysical journal international},
  volume    = {189},
  journal   = {Geophysical journal international},
  number    = {3},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0956-540X},
  doi       = {10.1111/j.1365-246X.2012.05455.x},
  pages     = {1430 -- 1456},
  year      = {2012},
  abstract  = {In the eighties, the analysis of satellite altimetry data leads to the major discovery of gravity lineations in the oceans, with wavelengths between 200 and 1400 km. While the existence of the 200 km scale undulations is widely accepted, undulations at scales larger than 400 km are still a matter of debate. In this paper, we revisit the topic of the large-scale geoid undulations over the oceans in the light of the satellite gravity data provided by the GRACE mission, considerably more precise than the altimetry data at wavelengths larger than 400 km. First, we develop a dedicated method of directional Poisson wavelet analysis on the sphere with significance testing, in order to detect and characterize directional structures in geophysical data on the sphere at different spatial scales. This method is particularly well suited for potential field analysis. We validate it on a series of synthetic tests, and then apply it to analyze recent gravity models, as well as a bathymetry data set independent from gravity. Our analysis confirms the existence of gravity undulations at large scale in the oceans, with characteristic scales between 600 and 2000 km. Their direction correlates well with present-day plate motion over the Pacific ocean, where they are particularly clear, and associated with a conjugate direction at 1500 km scale. A major finding is that the 2000 km scale geoid undulations dominate and had never been so clearly observed previously. This is due to the great precision of GRACE data at those wavelengths. Given the large scale of these undulations, they are most likely related to mantle processes. Taking into account observations and models from other geophysical information, as seismological tomography, convection and geochemical models and electrical conductivity in the mantle, we conceive that all these inputs indicate a directional fabric of the mantle flows at depth, reflecting how the history of subduction influences the organization of lower mantle upwellings.},
  language  = {en}
}
@article{GaciZaourarBriqueuetal.2011,
  author    = {Gaci, Said and Zaourar, Naima and Briqueu, Louis and Holschneider, Matthias},
  title     = {Regularity analysis applied to sonic logs data a case study from KTB borehole site},
  series = {Arabian journal of geosciences},
  volume    = {4},
  journal   = {Arabian journal of geosciences},
  number    = {1-2},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1866-7511},
  doi       = {10.1007/s12517-010-0129-y},
  pages     = {221 -- 227},
  year      = {2011},
  abstract  = {Borehole logs provide in situ information about the fluctuations of petrophysical properties with depth and thus allow the characterization of the crustal heterogeneities. A detailed investigation of these measurements may lead to extract features of the geological media. In this study, we suggest a regularity analysis based on the continuous wavelet transform to examine sonic logs data. The description of the local behavior of the logs at each depth is carried out using the local Hurst exponent estimated by two (02) approaches: the local wavelet approach and the average-local wavelet approach. Firstly, a synthetic log, generated using the random midpoints displacement algorithm, is processed by the regularity analysis. The obtained Hurst curves allowed the discernment of the different layers composing the simulated geological model. Next, this analysis is extended to real sonic logs data recorded at the Kontinentales Tiefbohrprogramm (KTB) pilot borehole (Continental Deep Drilling Program, Germany). The results show a significant correlation between the estimated Hurst exponents and the lithological discontinuities crossed by the well. Hence, the Hurst exponent can be used as a tool to characterize underground heterogeneities.},
  language  = {en}
}