Multiscale tomography of buried magnetic structures: its use in the localization and characterization of archaeological structures

We have previously developed a method for characterizing and localizing 'homogeneous' buried sources, from the measure of potential anomalies at a fixed height above ground (magnetic, electric and gravity). This method is based on potential theory and uses the properties of the Poisson kernel (real by definition) and the continuous wavelet theory. Here, we relax the assumption on sources and introduce a method that we call the 'multiscale tomography'. Our approach is based on the harmonic extension of the observed magnetic field to produce a complex source by use of a complex Poisson kernel solution of the Laplace equation for complex potential field. A phase and modulus are defined. We show that the phase provides additional information on the total magnetic inclination and the structure of sources, while the modulus allows us to characterize its spatial location, depth and 'effective degree'. This method is compared to the 'complex dipolar tomography', extension of the Patella method that we previously developed. We applied both methods and a classical electrical resistivity tomography to detect and localize buried archaeological structures like antique ovens from magnetic measurements on the Fox-Amphoux site (France). The estimates are then compared with the results of excavations.

[1]  I. Marson,et al.  Advantages of using the vertical gradient of gravity for 3-D interpretation , 1993 .

[2]  P. Mauriello,et al.  3D geoelectric tomography and archaeological applications 1 , 1998 .

[3]  Biwen Xu,et al.  Archaeological investigation by electrical resistivity tomography: a preliminary study , 1991 .

[4]  Matthias Holschneider,et al.  Identification of sources of potential fields with the continuous wavelet transform: Basic theory , 1999 .

[5]  I. W. Somerton,et al.  Magnetic interpretation in three dimensions using Euler deconvolution , 1990 .

[6]  D. Patella.  Introduction to ground surface self‐potential tomography , 1997 .

[7]  V. Lapenna,et al.  Tomographic analysis of self-potential data in a seismic area of Southern Italy , 2000 .

[8]  R. Parker.  Geophysical Inverse Theory , 1994 .

[9]  R. Blakely.  Potential theory in gravity and magnetic applications , 1996 .

[10]  G. Keller,et al.  The Geoelectrical Methods in Geophysical Exploration , 1994 .

[11]  D. T. Thompson,et al.  EULDPH: A new technique for making computer-assisted depth estimates from magnetic data , 1982 .

[12]  John W. Pritchett,et al.  Numerical simulation of electrokinetic potentials associated with subsurface fluid flow , 1996 .

[13]  Frédérique Moreau.  Méthodes de traitement de données géophysiques par transformée en ondelettes. , 1995 .

[14]  P. Sailhac,et al.  Characterization of geological boundaries using 1‐D wavelet transform on gravity data: Theory and application to the Himalayas , 2001 .

[15]  Matthias Holschneider,et al.  Wavelet analysis of potential fields , 1997 .

[16]  Richard Kronland-Martinet,et al.  Detection of abrupt changes in sound signals with the help of wavelet transforms , 1987 .

[17]  R. Parker,et al.  The inversion of magnetic anomalies in the presence of topography , 1974 .

[18]  F. Boschetti,et al.  Analysis of potential field data in the wavelet domain , 1999 .

[19]  Two-dimensional inversion filters in magnetic prospecting: Application to the exploration for buried antiquities , 1992 .

[20]  M. Nabighian.  Toward a three‐dimensional automatic interpretation of potential field data via generalized Hilbert transforms: Fundamental relations , 1984 .

[21]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[22]  A. Grossmann,et al.  DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE , 1984 .

[23]  Richard Kronland-Martinet,et al.  Extraction of Modulation laws of Elastic Shells by the use of the Wavelet Transform. , 1991 .

[24]  Gordon R. J. Cooper,et al.  EULDEP: a program for the Euler deconvolution of magnetic and gravity data , 1998 .

[25]  Philippe Labazuy,et al.  Localization of self-potential sources in volcano-electric effect with complex continuous wavelet transform and electrical tomography methods for an active volcano , 2004 .

[26]  R. Kronland-Martinet,et al.  Characterization of elastic shells by the use of the wavelet transform , 1990, IEEE Symposium on Ultrasonics.

[27]  Integrated geophysical methods in archaeological surveys , 1992 .

[28]  A. Grossmann,et al.  Wavelet Transforms and Edge Detection , 1988 .

[29]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[30]  A. Tarantola.  Inverse problem theory : methods for data fitting and model parameter estimation , 1987 .

[31]  D. Ravat.  Analysis of the Euler Method and Its Applicability in Environmental Magnetic Investigations , 1996 .

[32]  Pascal Sailhac,et al.  Analytic potentials for the forward and inverse modeling of SP anomalies caused by subsurface fluid flow , 2001 .

[33]  Stéphane Mallat,et al.  Singularity detection and processing with wavelets , 1992, IEEE Trans. Inf. Theory.

[34]  Y. Jeng,et al.  Integrated signal enhancements in magnetic investigation in archaeology , 2003 .

[35]  Gauthier Hulot,et al.  Worldwide wavelet analysis of geomagnetic jerks , 1996 .

[36]  Gauthier Hulot,et al.  Detection of geomagnetic jerks using wavelet analysis , 1995 .

[37]  Paolo Mauriello,et al.  Principles of probability tomography for natural‐source electromagnetic induction fields , 1999 .