Mathematics – Logic
Scientific paper
Mar 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011geoji.184.1058n&link_type=abstract
Geophysical Journal International, Volume 184, Issue 3, pp. 1058-1068.
Mathematics
Logic
Wavelet Transform, Inverse Theory, Magnetic Anomalies: Modelling And Interpretation, Back-Arc Basin Processes
Scientific paper
Inversion of magnetic data is frequently used for geostructural investigations. Long airborne flight lines and dense sampling of magnetic field result to very large data sets, which in 3-D point of view become very difficult to be inverted by non-smooth inversions. As line spacings are far larger than sample intervals along the lines, normally more resolution is achieved along the line than aside the lines; using 2-D algorithms along the line (if the investigated structures allow) can make use of original observed data and will result in a better imaging of intersecting structures.
In this paper, we are looking for a 2-D blocky distribution of magnetic susceptibility inside the Earth; for this purpose the area under the profile is divided into a large number of infinitely long horizontal prisms with square cross-section and unknown susceptibility. Optimizing a suitably defined multiterm cost function based on edge-preserving penalty functions and an orthogonal transform gives rise to the unknown susceptibility vector. An L0 like norm of model derivative vector acts as the edge-preserving term in the cost function to prevent sharp transitions from being penalized. To make use of the reference model and to create geologically reasonable solutions an L2-norm of model vector is used in the cost function. An orthogonal transform that can be a discrete cosine or wavelet transform is used to compress the columns of sensitivity matrix and produce a sparse forward operator by thresholding small coefficients in the transform domain. This allows fast forward modelling by performing matrix-vector multiplications in the sparse domain without introducing additional cost to the algorithm.
The functionality of the algorithm is shown by inverting synthetic data and comparing the results with those of classical smooth inversion. Finally, we inverted a long airborne magnetic flight data in southeast Iran that intersects the Makran subduction zone and its related geological structures. Our results show a deep oceanic crust remnant, beneath the sedimentary cover located at Juzmurian depression, which makes a prominent role in reconstructing whole geological history of the area.
Gholami Azam
Hafizi M. A.
Namaki Loghman
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