Knowing the near-surface structure is of major importance for engineering and construction projects. Improved confidence directly results in reduced risks and associated costs. Seismic surface wave sample that region well and can be routinely acquired.
A large number of methods is being exploited for this purpose. Many of them use approximations of the wave equation to tame algorithmic complexity and computational costs. Utilizing the full wavefield can naturally retrieve more information from the data and Salvus, from the ground up, has been designed to tackle these types of problems.
Full seismic waveform inversion (FWI) is the natural evolution of approximate surface wave dispersion methods. For this case study we'll apply Salvus' FWI capabilities to a vibroseis field study using real data and highlight a few benefits of using Salvus:
Data processing can often be the most time consuming part of the full waveform inversion process. Salvus ships with a large number of built-in processing functionality for common aspects. Furthermore, since the whole user-interface is exposed as a Python library, the full power of the world leading data-science Python stack is readily available to attack even the most cutting edge use cases.
Aside from the actual processing being simplified with Salvus, using the full wavefield also directly reduces the need to process in the first place. In fact, for this project, the processing consists only of these four steps, all of which can be performed without manual intervention:
A single function call for example triggers 3-D data to be converted into its 2-D counterpart. For line deployments this greatly reduces the computational costs because the data can be analyzed with a 2-D digital twin.
FWI using waveform differences classically suffers from the cycle skipping problem demanding very good starting models. Using different misfit functionals can alleviate that. Salvus comes with a range of user-selectable misfit functions and, in addition, users can define their own misfit measures and directly integrate them into Salvus' inversion machinery.
State-of-the-art research offers several alternatives, one of them being optimal transport in graph-space pioneered in this work. Salvus contains an implementation and it readily enables the usage of the whole trace without worrying about muting the late arrivals.
Salvus offers a workflow to perform full waveform inversion on all scales ranging from ultrasonic applications all the way to global seismology. A direct consequence is that every aspect must be highly configurable while still being able to run in a fully automatic fashion.
This is achieved via a Python based user-interface that allows fine-grained control and comes with a comprehensive suite of visualizations. Most images on this page are in fact screenshots of Salvus in action.
We ran a heavily regularized visco-elastic inversion for 56 iterations with a trust-region L-BFGS optimization method starting from a very rough 1-D model. The misfit drops significantly and the final model is able to explain all major features of the observed data while the model stays free from obvious over-fitting artifacts.
This page naturally omits a lot of details. If you want to learn more please head over to Salvus' documentation for details regarding the technical and scientific background.