Building subsurface velocity models is essential to our goals in utilizing seismic data for Earth discovery and exploration, as well as monitoring. With the dawn of machine learning, these velocity models (or, more precisely, their distribution) can be stored accurately and efficiently in a generative model. These stored velocity model distributions can be utilized to regularize or quantify uncertainties in inverse problems, like full waveform inversion. However, most generators, like normalizing flows or diffusion models, treat the image (velocity model) uniformly, disregarding spatial dependencies and resolution changes with respect to the observation locations. To address this weakness, we introduce VelocityGPT, a novel implementation that utilizes Transformer decoders trained autoregressively to generate a velocity model from shallow subsurface to deep. Owing to the fact that seismic data are often recorded on the Earth's surface, a top-down generator can utilize the inverted information in the shallow as guidance (prior) to generating the deep. To facilitate the implementation, we use an additional network to compress the velocity model. We also inject prior information, like well or structure (represented by a migration image) to generate the velocity model. Using synthetic data, we demonstrate the effectiveness of VelocityGPT as a promising approach in generative model applications for seismic velocity model building.

翻译：构建地下速度模型对于实现利用地震数据进行地球探测、勘探及监测的目标至关重要。随着机器学习的兴起，这些速度模型（或其分布）能够被准确高效地存储在生成模型中。这些存储的速度模型分布可用于正则化或量化反演问题（如全波形反演）中的不确定性。然而，大多数生成器（如归一化流或扩散模型）对图像（速度模型）进行均匀处理，忽略了空间依赖性及相对于观测位置的分辨率变化。为克服此缺陷，我们提出VelocityGPT——一种利用自回归训练的Transformer解码器从浅层地下至深层生成速度模型的新颖实现。鉴于地震数据通常在地表记录，自上而下的生成器可利用浅层反演信息作为生成深层结构的指导（先验）。为实现该方案，我们采用额外网络对速度模型进行压缩，并注入先验信息（如以井数据或偏移图像表示的地质构造）以生成速度模型。通过合成数据实验，我们验证了VelocityGPT作为地震速度模型构建生成模型应用的前沿方法的有效性。