Fourier reconstruction is basically a linear inverse problem that attempts to recover the Fourier spectrum of the seismic wave-field from irregularly sampled data along the spatial coordinates. The estimated Fourier coefficients are then used to reconstruct the data in a regular grid via a standard inverse Fourier transform (IDFT or IFFT). Unfortunately, this kind of inverse problem is usually under-determined and illconditioned. For this reason the Fourier reconstruction with minimum norm (FRMN) adopts a weighted damped least-squares inversion to retrieve a unique and stable solution. In this work we show how damping can introduce deleterious artifacts on the reconstructed 3D data. To quantitatively describe this issue, we introduce the concept of extended resolution matrix (ERM) and we formulate the reconstruction problem as an appraisal problem. Through the simultaneous analysis of the ERM and of the noise term, we can assess the validity of the reconstructed data and verify the possible bias introduced by the inversion process. Also, we can guide the parametrization of the forward problem to minimize the occurrence of unwanted artifacts. Real data from a 3D marine common shot gather are used to discuss our approach and to show the results of FMNR reconstruction.

3D fourier reconstruction of irregularly sampled seismic Gathers : analysis of the extended model resolution matrix / F. Ciabarri, M. Mazzotti, E. Stucchi - In: Extended Abstracts 74th EAGE Conference & Exhibition[s.l] : European Association of Geoscientists and Engineers, 2012 Jun. - ISBN 9789073834279. - pp. 5231-5235 (( Intervento presentato al 74. convegno EAGE Conference & Exhibition incorporating SPE EUROPEC tenutosi a Copenhagen nel 2012 [10.3997/2214-4609.20148680].

3D fourier reconstruction of irregularly sampled seismic Gathers : analysis of the extended model resolution matrix

E. Stucchi
Ultimo
2012

Abstract

Fourier reconstruction is basically a linear inverse problem that attempts to recover the Fourier spectrum of the seismic wave-field from irregularly sampled data along the spatial coordinates. The estimated Fourier coefficients are then used to reconstruct the data in a regular grid via a standard inverse Fourier transform (IDFT or IFFT). Unfortunately, this kind of inverse problem is usually under-determined and illconditioned. For this reason the Fourier reconstruction with minimum norm (FRMN) adopts a weighted damped least-squares inversion to retrieve a unique and stable solution. In this work we show how damping can introduce deleterious artifacts on the reconstructed 3D data. To quantitatively describe this issue, we introduce the concept of extended resolution matrix (ERM) and we formulate the reconstruction problem as an appraisal problem. Through the simultaneous analysis of the ERM and of the noise term, we can assess the validity of the reconstructed data and verify the possible bias introduced by the inversion process. Also, we can guide the parametrization of the forward problem to minimize the occurrence of unwanted artifacts. Real data from a 3D marine common shot gather are used to discuss our approach and to show the results of FMNR reconstruction.
Settore GEO/11 - Geofisica Applicata
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/223379
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