Stratigraphic coordinates, a coordinate system tailored to seismic interpretation

Introduction

In certain seismic data processing and interpretation tasks, such as spiking deconvolution, tuning analysis, impedance inversion, spectral decomposition, etc., it is commonly assumed that the vertical direction is normal to reflectors. This assumption does not hold true in the case of dipping layers and may therefore lead to inaccurate results (Guo and Marfurt, 2010). Mallet (2004) defined a mathematical framework, called GeoChron, for transforming the geologic space into a new space in which all horizons appear flat, and faults, if any, disappear. In this paper, we propose the stratigraphic coordinate system, in which geometry follows the shape of each reflector and the vertical direction corresponds to normal reflectivity .

Flattening post-stack seismic data is an immediate use of the proposed coordinate system. Flattened seismic images facilitate the interpreter's ability to extract detailed stratigraphic information from the seismic data. In interpretational applications, several different algorithms for image flattening have been developed by different authors. The idea of seismic image flattening by extracting stratal slices was introduced by Zeng et al. (1998). Automatic picking of horizons using local shifts was studied by Bienati and Spagnolini (1999) and Stark (2005). Lomask et al. (2006) and Parks (2010) presented inversion methods in which horizons are calculated on the basis of local slopes and are then used to flatten seismic events. Fomel (2010) proposed the method of predictive painting that uses the prediction operators extracted by plane-wave destruction to spread information inside the seismic volume recursively.

Conventionally, seismic image flattening is performed by shifting samples in the original image up or down - in other words, differentially stretching and squeezing the original image in order to flatten the reflection events. Luo and Hale (2013) proposed a method for image flattening that uses the vector shift field instead of the scalar field of vertical shifts to define deformations in the image. Flattening by vector shift uses either vertical shear or rotation or a combination of the two, depending on the type of geologic deformation.

The stratigraphic coordinate system, introduced in this paper, represents a new framework for seismic interpretation and processing. To construct stratigraphic coordinates, we combine predictive painting with an upwind finite-difference scheme (Franklin and Harris, 2001) for solving relevant gradient equations. The stratigraphic coordinate system is semi-orthogonal; i.e., picked horizons that are level sets of the first axis are orthogonal to the other two axes. In other words, stratigraphic coordinates are aligned with horizons, and the vertical direction in stratigraphic coordinates corresponds to the direction normal to the major reflection boundaries. Application of the stratigraphic coordinate system is not limited to seismic image flattening and may be extended to many data processing and interpretation tasks in which the vertical direction is commonly assumed to be normal to reflection boundaries: a crude assumption in all structures but flat geology. In the following sections, we start by describing a constructive algorithm for generating stratigraphic coordinates. We then illustrate applications of the stratigraphic coordinate system to seismic image flattening and spectral decomposition using synthetic and field data examples.

Stratigraphic coordinates, a coordinate system tailored to seismic interpretation