Velocity model building using shape optimization applied to level sets

Before
After
Taylor Dahlke, April 1 2019
This chapter introduces the problems surrounding the modeling of salt, why level sets offer an answer, what has already been done in this field, and what this thesis contributes. PDF  Source code
I describe the mathematics behind level sets and shape optimization. I begin with the basic definitions of the model space and objective function, and derive the gradient and Hessian. I demonstrate salt boundary updating on a simple 2D model. PDF  Source code
Radial basis functions (RBFs) can be used as a means to represent the implicit surface. I describe the new operator neccessary to this parameterization, and compare the results of inversion using RBFs and without using RBFs. PDF  Source code
The implicit surface can be exploited as a means to embed information related to the certianty of the salt boundary position. In this chapter, I describe how this type of interpreter guidance can be incorporated into the inversion workflow, and compare inversion that use guidance and that do not use guidance. PDF  Source code
In order to prove the efficacy of this method, I demonstrate on a 3D oceanbottom node (OBN) data set provided by Shell Exploration & Production. I describe the inversion algorithm and practical steps taken. With the resulting inverted model, I create new seismic images that I compare with the old, finding improvement in the images in the region below the updated area of the model. PDF  Source code
The first step of preprocessing the OBN data is to perform designature. The intuition and mathematics behind calculating the instrument response is described here, along with code examples. PDF  Source code
The second step of preprocessing the OBN data is to perform PZ summation (to isolate the upgoing and downgoing events). After, a shaping filter is used to help remove the bubble from the data and ready it for the inversion workflow. PDF  Source code
Copyright (c) 2019 Stanford Exploration Project. All rights reserved.