ContrasInver: Ultra-Sparse Label Semi-supervised Regression for Multi-dimensional Seismic Inversion

TL;DR

ContrasInver is the first data-driven approach yielding reliable results on the Netherlands F3 and Delft, using only three and two well logs, respectively, and is the first data-driven approach yielding reliable results on the Netherlands F3 and Delft, using only three and two well logs.

Abstract

The automated interpretation and inversion of seismic data have advanced significantly with the development of Deep Learning (DL) methods. However, these methods often require numerous costly well logs, limiting their application only to mature or synthetic data. This paper presents ContrasInver, a method that achieves seismic inversion using as few as two or three well logs, significantly reducing current requirements. In ContrasInver, we propose three key innovations to address the challenges of applying semi-supervised learning to regression tasks with ultra-sparse labels. The Multi-dimensional Sample Generation (MSG) technique pioneers a paradigm for sample generation in multi-dimensional inversion. It produces a large number of diverse samples from a single well, while establishing lateral continuity in seismic data. MSG yields substantial improvements over current techniques, even without the use of semi-supervised learning. The Region-Growing Training (RGT) strategy leverages the inherent continuity of seismic data, effectively propagating accuracy from closer to more distant regions based on the proximity of well logs. The Impedance Vectorization Projection (IVP) vectorizes impedance values and performs semi-supervised learning in a compressed space. We demonstrated that the Jacobian matrix derived from this space can filter out some outlier components in pseudo-label vectors, thereby solving the value confusion issue in semi-supervised regression learning. In the experiments, ContrasInver achieved state-of-the-art performance in the synthetic data SEAM I. In the field data with two or three well logs, only the methods based on the components proposed in this paper were able to achieve reasonable results. It's the first data-driven approach yielding reliable results on the Netherlands F3 and Delft, using only three and two well logs respectively.

Figures (9)

• Figure 1: This paper examines the data-driven impedance inversion task, utilizing the Netherlands F3 as an illustrative example. The figure demonstrates a complete seismic volume along with four well logs. The seismic data is denoted as $\textbf{D} \in \mathbb{R}^{t\times l_\text{i} \times l_\text{x}}$, where $t$ is the seismic trace length, $l_\text{i}$ is the inline length, and $l_\text{x}$ is the crossline length. The well log data (labels) are represented as $y_i \in \mathbb{R}^{\phi_i t \times1 \times 1}$, where $y_i$ is a vector of continuous values, $\phi_i$ is the ratio of well log to seismic traces. Each $y_i$ corresponds to a seismic trace $x_i$ within the seismic volume. As depicted in the figure, impedance inversion is a regression task where a 3D seismic volume learns from 1D continuous value labels.
• Figure 2: The complete framework of ContrasInver, and the roles assumed by the individual innovations (red boxes or letters). In the supervised component, samples are generated by MSG, and the network outputs a vector that is projected onto basis vectors to obtain impedance (IVP). The supervised part is responsible for guiding and constraining the direction of the impedance vector. In the unsupervised component, RGT is utilized to gradually diffuse well log information and perform unsupervised learning based on IVP. One of the functions of IVP is to filter out certain abnormal components from the labels, preventing the issue of value confusion in semi-supervised learning where the regression task learns from the teacher network.
• Figure 3: Each subfigure has a horizontal axis representing the number of steps. The vertical axis represents the feature dimensions of the impedance vector. All visualizations are performed using min-max normalization.
• Figure 4: (a) SEAM Phase I profile in grayscale. (b) GT. (c) Training and validation well locations with 4 logging wells. (d) Training and validation well locations with 9 logging wells. (e) Training and validation well locations with 16 logging wells. The red markings are for training logs and the blue are for validation logs.
• Figure 5: The figure shows the Delft seismic data along with its three impedance well logs, all three of which are inclined wells. This is a typical example of extreme label less.