This chapter addresses the eigenvalue problem (EVP) with a focus on its application to describing standing waves or stationary quantum systems. A numerical method known as the shooting method is introduced to solve the EVP. Using a cylindrical waveguide (e.g., optical fibre) as a system model, the normal modes of a scalar wave are explored. The wave equation is examined, with considerations made for axial symmetry, boundary conditions, and the influence of refraction coefficients. A significant part of the study is devoted to finding the normal modes and associated wave numbers in an optical fibre. The latter part of the chapter presents the shooting method, a recursive technique to ascertain the eigenvalue in numerical calculations. The applicability of this method is further examined in the context of a quantum well. This chapter offers a thorough exploration of the EVP, highlighting its relevance to real-world research and introducing a robust numerical method for its resolution.

This chapterreviews the development of “conventional” towed streamer marine seismic work from 2D through 3D, its shortcomings, and its continuing development into so-called “broadband” seismic. It describes and explains the recent trend towards ocean-bottom recording, currently mostly executed using nodes (OBN), whose market share has expanded from around 10% in 2013 to an estimated 25% in 2020. It covers the increasing requirement for higher quality seismic data to enable imaging of the very problematic subsurface structures such as subsalt plays, which require more extensive shooting geometries and extra low-frequency bandwidths. “Blended” sources are bringing costs down, and practical research includes the use of autonomous underwater vehicles (AUVs), possibly even deployed as intelligent “swarms.” Cost comparisons of the current techniques are included.