# Quantitative and Qualitative Seismic Imaging and Seismic Inversion

## TL;DR

This paper discusses seismic imaging and inversion, classifying methods into quantitative and qualitative approaches, emphasizing the importance of processing in time and exploring non-differentiable solutions.

## Contribution

It introduces a classification framework for seismic imaging methods, highlighting the roles of topology, semigroup methods, and non-differentiable solutions.

## Key findings

- Quantitative methods approximate seismic data with numerical solutions.
- Qualitative methods involve topology, semigroup, and non-differentiable solutions.
- Processing in time is crucial alongside depth-based imaging.

## Abstract

We consider seismic imaging to include seismic inversion. Imaging could use approximate operator or time instead of depth. Processing in time is an important part of seismic imaging as well as processing in depth. We can classify seismic imaging as quantitative versus qualitative methods. Quantitative method uses numerical methods to find the solution whose modeled seismic data approximates the input seismic records. Then we will progress to qualitative methods which have three aspects. The first aspect will be topology and geometry. The second aspect is semigroup method. The third aspect is to use non-differentiable solution.