Comparison of wave equation migration in logpolar and elliptic coordinates
- PDF / 674,894 Bytes
- 9 Pages / 595.276 x 790.866 pts Page_size
- 15 Downloads / 178 Views
ORIGINAL PAPER
Comparison of wave equation migration in logpolar and elliptic coordinates Diako Hariri Naghadeh & Mohamad Ali Riahi
Received: 1 February 2012 / Accepted: 23 August 2012 # Saudi Society for Geosciences 2012
Abstract We extend Riemannian wavefield extrapolation to pre- and post-stack migration using 2D logpolar coordinate system in order to enhance imaging of subsurface structures with imaging of dipping reflectors and turning waves. The logpolar coordinate is a coordinate system adequate for propagating both the source and receiver wavefields. The logpolar extrapolation wavenumber introduces an isotropic slowness model stretch to the single square root operator that enables the use of Cartesian finite-difference extrapolators for propagating wavefields in logpolar meshes. Wavefield extrapolation in this coordinate does not require any ray tracing at all and it can be readily extended to high-order finite-difference schemes since it is an analytic extrapolation operator. Two migration examples illustrate the advantages of the logpolar coordinate for imaging complex geological structures. We compared results of post- and pre-stack depth migration in logpolar and elliptic coordinate systems and we found that steeply dipping events can be better imaged in logpolar coordinate than in elliptic coordinate. Keywords Riemanian . Logpolar . Pre-stack migration . Post-stack migration
Introduction Several extrapolation operators in different domains as downward continuation methods (Gazdag 1978; Berkhout 1981; Gazdag and Sguazzero 1984; Stoffa et al. 1990; Kessinger 1992; Ristow and Rühl 1994; Huang and Wu 1996a, b; Fehler and Huang 1998; Margrave and Ferguson D. Hariri Naghadeh (*) : M. A. Riahi Department of Geophysics, Science and Research Branch Islamic Azad University, Tehran, Iran e-mail: [email protected]
1999; Ferguson and Margrave 2002; Huang et al. 1998, 1999a, b, c; Huang and Fehler 2000a, 2001; Hale 1991) have been proposed in the literature. Downward continuation (Claerbout 1985) is accurate, robust, and capable of handling models with large and sharp velocity variations. This method naturally handles the multipathing that occurs in complex geology (Sava and Fomel 2005) but Kirchhoff-type methods are far less reliable in complex velocity models (Gray et al. 2001). Downward continuation is based on waves that propagate mainly in the vertical direction therefore with increasing angle between extrapolation axis and wave propagation direction, we will lose further reflection energy and this method cannot rebuild steeply dipping events in the migration process. In order to mitigate dip limitation in downward continuation techniques, we can use following solutions: Methods from the Fourier finite difference family (Ristow and Ruhl 1994; Biondi 2002), Gaussian beam (Hill 2001), the generalized screen propagator family (de Hoop 1996; Huang and Wu 1996), wavefield extrapolation in tilted coordinate systems (Etgen 2002), hybridization of wavefield and raybased techniques (Cˇerveny´ 2001; Hill 1990, 200
Data Loading...
