I am interested in applied and computational mathematics, especially in application to geophysical problems. Very broadly, this includes aspects of numerical analysis, scientific computing, optimization, signal processing, imaging, and inversion.
In October 2017, I was invited on the podcast Undersampled Radio, a podcast about machine learning and geoscience. You can listen to discussions about my undergraduate research, amongst a few other things, on Episode 60: Game, Set, Match.
My undergraduate honors thesis advisor is Dr. Sergey Fomel, and I began working with him midway through my sophomore year (January 2016).
Here are some projects I've worked on during that time.
My undergraduate honors thesis, "A data matching algorithm and its application in seisic data analysis" can be found here.
Improving migration resolution by approximating the least-squares Hessian using non-stationary amplitude and frequency matching
Collaborated with Zhiguang Xue and Sergey Fomel
We propose using two non-stationary operators to represent the amplitude and frequency variations in the least-squares Hessian to account for the principal differences between conventional and least-squares migrated images. The calculation and application of these operators are computationally inexpensive when compared to one iteration of least-squares migration, and it increases the resolution and amplitude fidelity of the migrated image. Successful results are achieved on an application of reverse-time migration to the Sigsbee synthetic data set.
Matching and merging high-resolution and legacy seismic images
Collaborated with Sergey Fomel
When multiple seismic surveys are acquired over the same area using different technologies that produce data with different frequency content, it may be beneficial to combine these data to produce a broader bandwidth volume. In this paper, we propose a workflow for matching and blending seismic images obtained from shallow high-resolution seismic surveys and conventional surveys. The workflow consists of three distinct steps: (a) balancing the amplitudes and frequency content of the two images by non-stationary smoothing of the high-resolution image; (b) estimating and removing variable time shifts between the two images; and (c) blending the two images together by least-squares inversion. The proposed workflow is applied successfully to images from the Gulf of Mexico.
Balancing local frequency content in seismic data using non-stationary smoothing
Collaborated with Sergey Fomel
Seismic data can experience non-stationary frequency variations caused by attenuation. This problem is encountered when matching multiple data sets, such as in multicomponent image registration, because signals with differing frequency content are hard to correlate. In this paper, we propose a method to balance frequency content between data sets while taking into account non-stationary frequency variations. This method involves finding and applying a non-stationary smoothing operator to minimize the local frequency difference between data sets. Numerical examples demonstrate that the proposed method improves multicomponent image registration and matching images of differing resolution.