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Velocity model building using shape optimization applied to level sets. SEP-175 (2019)



Chapter 1

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

Chapter 2

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

Chapter 3

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

Chapter 4

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

Chapter 5

In order to prove the efficacy of this method, I demonstrate on a 3D ocean-bottom 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

Appendix A

The first step of pre-processing 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

Appendix B

The second step of pre-processing 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

Taylor Dahlke
Publication Date
April 1, 2019