Least-squares horizons with local slopes and multigrid correlations

Abstract

Most seismic horizon extraction methods are based on seismic local reflection slopes that locally follow seismic structural features. However, these methods often fail to correctly track horizons across discontinuities such as faults and noise because the local slopes can only correctly follow laterally continuous reflections. In addition, seismic amplitude or phase information is not used in these methods to compute horizons that follow a consistent phase (e.g., peaks or troughs). To solve these problems, we have developed a novel method to compute horizons that globally fit the local slopes and multigrid correlations of seismic traces. In this method, we first estimate local reflection slopes by using structure tensors and compute laterally multigrid slopes by using dynamic time warping (DTW) to correlate seismic traces within multiple laterally coarse grids. These coarse-grid slopes can correctly correlate reflections that may be significantly dislocated by faults or other discontinuous structures. Then, we compute a horizon by fitting, in the least-squares sense, the slopes of the horizon with the local reflection slopes and multigrid slopes or correlations computed by DTW. In this least-squares system, the local slopes on the fine grid and the multiple coarse-grid slopes will fit a consistent horizon in areas without lateral discontinuities. Across laterally discontinuous areas where the local slopes fail to correctly correlate reflections and mislead the horizon extraction, the coarse-grid slopes will help to find the corresponding reflections and correct the horizon extraction. In addition, the multigrid correlations or slopes computed by dynamic warping can also assist in computing phase-consistent horizons. We apply the proposed horizon extraction method to multiple 2D and 3D examples and obtain accurate horizons that follow consistent phases and correctly track reflections across faults.

Does shallow geological knowledge help neural-networks to predict deep units?

“…Here we introduce another method, different from data augmentation of regularization, to train networks with greater prediction power. The core idea is as follows: there are often one or more shallow geological units that can be delineated from just one or a few seed points, accurately and fast, using auto-tracking algorithms that are not based on learning, e.g., [Wu and Fomel, 2018]. While these shallower geological units are not the targets of interest, they do carry information about the subsurface.…”

Building realistic structure models to train convolutional neural networks for seismic structural interpretation

“…To assist in seismic horizon interpretation, various methods such as phase-unwrapping (Stark, 2003;Wu and Zhong, 2012), waveform classification (Figueiredo et al, 2007(Figueiredo et al, , 2014(Figueiredo et al, , 2015, slope-based methods (Lomask et al, 2006;Fomel, 2010;Parks, 2010;Wu andHale, 2013, 2015;Zinck et al, 2013;Monniron et al, 2016), and multigrid correlation (Wu and Fomel, 2018b) have been proposed to automate the horizon mapping from a seismic image. These methods, however, face a common challenge of dealing with complex structures such as intensive crossing faults and complicated folding, which requires a globally optimal correlation of all the structure elements in a seismic image.…”

Automatic extraction of dislocated horizons from 3D seismic data using nonlocal trace matching

“…In the past few decades, different computational and computerassisted horizon extraction methods have been introduced as alternatives to the process of manually picking seed points, aiming to further automate the seismic interpretive workflow, process multidimensional data concurrently, and reduce the need for user interaction. Some of the more interesting horizon-extraction methods are based on local reflection slopes (e.g., Bakker, 2002;Lomask et al, 2006), unwrapped instantaneous phase (e.g., Stark, 2003Stark, , 2005Wu and Zhong, 2012), and dynamic time warping (DTW) (e.g., Wu and Hale, 2016a;Wu and Fomel, 2018) Local reflection slope methods involve using structure tensors and an iterative least-squares fitting of horizon slopes with local reflections slopes (Bakker, 2002;Lomask et al, 2006). In general, horizon tracking using local reflection slopes effectively tracks coherent seismic horizons but is sensitive to faults and other discontinuities.…”

“…In geophysics, DTW has proven useful to correlate well-to-well logs (e.g., Anderson and Gaby, 1983;Lineman et al, 1987) and to match seismic traces (e.g., Wu and Fomel, 2018). Hale (2013) presents a method for dynamic warping of seismic images to estimate fault throws in seismic images, and to estimate registration (alignment) of PP and PS images.…”

“…More recently, Wu and Fomel (2018) proposed to extract horizons by fitting, in the least-squares sense, the local slopes and multigrid correlations of seismic traces. In this method, the local slopes, computed from structure tensors (Hale, 2009;Wu and Janson, 2017), are helpful to fit a horizon that smoothly and consistently follows local reflection structures in areas without structural discontinuities.…”