Introduction

Well-log properties can be extended to a volume using a 3D seismic image to obtain a global interpretation of the subsurface. Such integration of well log data and seismic images can be used to constrain the following seismic inversion. Beginning with tying well logs measured in depth to seismic data in two-way time (Wu and Caumon, 2016), the joint interpretation requires spatially interpolating and extrapolating the well logs using seismic data. Several authors have studied using post-stack seismic data together with other attributes to guide the interpolation (Hampson et al., 2001; Taner et al., 1994; Schultz et al., 1994), while assuming that the interpolated rock property conforms to seismic horizons.

However, picking seismic horizons can involve manual labor and subjectivity. Hale (2010) proposed the image-guided interpolation of borehole data without picking seismic horizons or faults using the blended neighbor interpolation method (Hale, 2009a). Rather than using only the seismic image structures, Karimi and Fomel (2015) proposed an approach based on predictive painting (Fomel, 2010) that utilizes both image structures and amplitudes to guide the interpolation of well logs.

Although predictive painting can guide the interpolation along conforming horizons, it encounters difficulties in painting across faults or unconformities. Therefore, it is necessary to limit the interpolation painting only within the range of conforming image structures.

In order to constrain well-log interpolation, seismic coherency attributes can be measured to enhance indistinguishable faults or other geological discontinuities (Chopra and Marfurt, 2005). Many methods were proposed to detect faults and measure fault attributes, including computing normalized cross-correlation (Bahorich and Farmer, 1995), eigenvalues of the local covariance matrix (Gersztenkorn and Marfurt, 1999), eigenvectors of the structure tensor (Hale, 2009b; Randen et al., 2000), and predictive coherency (Karimi et al., 2015). Phillips et al. (2016) proposed a modified Sobel filter that utilizes plane-wave destruction and plane-wave shaping. Wu (2017) recently used directional structure-tensor-based coherence to measure fault likelihood in seismic images.

We propose to apply the fault discontinuity attribute as an additional constraint to assist seismic-guided well-log interpolation. Using this attribute, we modify the distance between seismic traces across the fault, so that the interpolation will not be affected by well logs obscured by the fault but only the well logs that conformally paint at such location. We define geologic distance as the distance measured along seismic horizons. Because geologic distance can better represent the coherence level along seismic horizons than horizontal geometric distance, it provides a more accurate weight for spreading and interpolating well log information.