Attenuation of diffracted multiples with an apex-shifted tangent-squared radon transform in image space

Earth Sciences Research Journal, Dec, 2006 by Gabriel Alvarez, Biondo Biondi, Antoine Guitton

ABSTRACT

In this paper, a method to attenuate diffracted multiples with an apex-shifted tangent-squared Radon transform in angle domain common image gathers (ADCIG) is proposed. Usually, where diffracted multiples are a problem, the wavefield propagation is complex and the moveout of primaries and multiples in data space is irregular. The method handles the complexity of the wave field by migration, providing reasonably accurate migration velocities. As a result, the moveout of the multiples is well behaved in the ADCIGs. For 2D data, the apex-shifted tangent-squared Radon transform maps the 2D space image into a 3D space-cube model whose dimensions are depth, curvature and apex-shift distance.

Well-corrected primaries map to or near the zero curvature plane and specularly-reflected multiples map to or near the zero apex-shift plane. Diffracted multiples map elsewhere in the cube according to their curvature and apex-shift distance. Thus, specularly reflected as well as diffracted multiples can be attenuated simultaneously. This approach is illustrated with a segment of a 2D seismic line over a large salt body in the Gulf of Mexico. It is shown that ignoring the apex shift compromises the attenuation of the diffracted multiples, whereas the approach proposed attenuates both the specularly-reflected and the diffracted multiples without compromising the primaries.

Key Words: diffracted multiples, ADCIG, Gulf of Mexico

RESUMEN

En este articulo, proponemos un metodo para atenuar reflexiones multiples difractadas (o simplemente multiples difractadas). El metodo consiste en la aplicacion de una transformada de Radon parametrizada en terminos del angulo de reflexion (angulo de apertura), y de la posicion del apice de la curva del multiple en el dominio de las imagenes de angulo comun. Usualmente, donde las multiples difractadas son un problema, la propagacion del campo de onda es compleja y la curva del multiple en el espacio de los datos (CMPs) deja de ser hiperbolica y es imposible de predecir analiticamente. Como consecuencia, el metodo usual de aplicar una transformada de Radon hiperbolica o parabolica para atenuar las multiples, produce pobres resultados. Nuestro metodo maneja la complejidad de la propagacion del campo de onda mediante una migracion preapilado en profundidad con la ecuacion de onda, en la medida en que las velocidades de migracion sean razonablemente precisas. En dos dimensiones, nuestra transformada de Radon "mapea" las imagenes de angulo comun en un modelo tridimensional que es funcion de la profundidad, la curvatura (moveout) y la posicion del apice de la curva del multiple en las imagenes de angulo comun.

Las reflexiones primarias (o simplemente primarias) se mapean cerca del plano de cero curvatura por cuanto fueron migradas con la velocidad correcta. Las multiples especulares se mapean en el plano de apice cero con curvaturas que dependen de la diferencia entre las velocidades de migracion de los primarios y las multiples. Por su parte, las multiples difractados se mapean en el resto del cubo alejados de los planos de cero curvatura y cero apice. De esta manera, en el dominio de Radon, las primarias, las multiples especulares y las multiples difractadas, se separan. Esta separacion permite recuperar las primarias atenuando tanto las multiples especulares como las difractadas. Nosotros ilustramos el metodo aplicandoselo a una linea sismica del Golfo de Mexico. En particular, mostramos que si se ignora la componente que discrimina la posicion apice del multiple en las imagenes de angulo comun, la atenuacion de las multiples difractadas se deteriora sensiblemente. Cuando incluimos esta componente, logramos atenuar tanto las multiples especulares como las difractadas sin afectar notoriamente las primarias.

Key Words: Multiples difractados, ADCIG, Golfo of Mexico

INTRODUCTION

Surface-related multiple elimination (SRME) uses the recorded seismic data to predict and iteratively subtract the multiple series (Verschuur et al., 1992). 2D SRME can deal with all kinds of 2D multiples, provided enough data are recorded given the offset limitations of the survey line. Diffracted multiples from scatterers with a cross-line component cannot be predicted by 2D SRME but in principle can be predicted by 3D SRME as long as the acquisition is dense enough in both in-line and cross-line directions. With standard marine streamer acquisition, the sampling in the cross-line direction is too coarse and diffracted multiples need to be removed by other methods (Hargreaves et al., 2003) or the data need to be interpolated and extrapolated to a dense, large aperture grid (van Dedem and Verschuur, 1998; Nekut, 1998; Biersteker, 2001). In general, multiples may not have their moveout apex at zero offset on a CMP gather. Peg-leg multiples "split" into independent events when reflectors dip. These events look similar to diffracted multiples and may similarly hamper standard Radon demultiple and velocity analysis. Hargreaves et al. (2003) proposed a shifted hyperbola approach to attenuate split or diffracted multiples in CMP gathers. This approach, however, relies on the moveout of the multiples to be well approximated by hyperbolas in data space, which is problematic in complex media. A similar apex-shifted Radon transform was proposed by Trad (2002) for data interpolation.