  Conventional seismic techniques for detecting the subsurface geologic
features are challenged by limited data coverage, computational inefficiency,
and subjective human factors. We developed a novel data-driven geological
feature detection approach based on pre-stack seismic measurements. Our
detection method employs an efficient and accurate machine-learning detection
approach to extract useful subsurface geologic features automatically.
Specifically, our method is based on kernel ridge regression model. The
conventional kernel ridge regression can be computationally prohibited because
of the large volume of seismic measurements. We employ a data reduction
technique in combination with the conventional kernel ridge regression method
to improve the computational efficiency and reduce memory usage. In particular,
we utilize a randomized numerical linear algebra technique, named Nystr\"om
method, to effectively reduce the dimensionality of the feature space without
compromising the information content required for accurate detection. We
provide thorough computational cost analysis to show efficiency of our new
geological feature detection methods. We further validate the performance of
our new subsurface geologic feature detection method using synthetic surface
seismic data for 2D acoustic and elastic velocity models. Our numerical
examples demonstrate that our new detection method significantly improves the
computational efficiency while maintaining comparable accuracy. Interestingly,
we show that our method yields a speed-up ratio on the order of $\sim10^2$ to
$\sim 10^3$ in a multi-core computational environment.
