Publisher Summary This chapter focuses on elastic wave propagation in stratified media. The development of the theory of elastic wave propagation in stratified media has been strongly influenced by the problems of seismic wave propagation and the nature of the seismograms recorded from earthquakes. For purely analytic developments of elastic wave propagation, the level of manageable algebraic complexity is reached in a model with one or two uniform layers overlying a uniform half space. This chapter shows how the excitation of elastic waves, within a horizontally stratified structure, can be conveniently developed in terms of reflection and transmission matrices. This procedure has allowed the construction of the full response of the medium or approximations with desired properties so that theoretical seismograms may be calculated for realistic distributions of elastic parameters. Although this development has been for isotropic media, nearly all the results apply directly to the case of full anisotropy if 3 × 3 reflection and transmission matrices allowing coupling between all wave types are employed. This development of the wavefield for both source and receiver within the stratification may be used for other classes of wave propagation.

Seismic Wave Propagation in Stratified Media

The two volumes which make up The Seismic Wavefield provide a comprehensive guide to the understanding of seismograms in terms of physical propagation processes within the Earth The focus is on the observation of earthquakes and man-made sources on all scales, for both body waves and surface waves Volume I provided a general introduction and a development of the theoretical background for seismic waves This material is exploited in Volume II to look at the way in which observed seismograms relate to the propagation processes Volume II discusses local and regional seismic events, global wave propagation, and the three-dimensional Earth The combination of observation and theoretical development with a strong visual focus will greatly appeal to graduate students in seismology The two volumes will also be valuable to researchers and professionals in academia and the petroleum industry

The seismic wavefield

A vertical tomogram is constructed for the mantle between Tonga and Hawaii. Using a complete Gaussian-Bayesian approach, we inverted a data set comprising 304 ScS reverberation travel times with Frechet kernels computed by the paraxial ray approximation and 1122 frequency-dependent phase delays of turning and surface waves with Frechet kernels calculated by a normal-mode coupling algorithm. The model parameters include shear speed variations, perturbations to shear wave radial anisotropy in the uppermost mantle, and the topographies of the 410- and 660- km discontinuities. Tests demonstrate that the data set resolves lateral structures in the upper mantle with scale lengths of several hundred kilometers and greater. The most significant feature in our model is a well resolved regular pattern of high and low shear velocities in the upper mantle. These variations have a horizontal wavelength of 1500 km, a vertical dimension of 700 km, and an amplitude of about 3%, and they show a strong positive correlation with seafloor topography and geoid height variations. The geoid highs correspond to a series of northwest trending swells associated with the major hotspots of the Society, Marquesas, and Hawaiian Islands. Where these swells cross the corridor, they are underlain by high shear velocities throughout the uppermost mantle, so it is unlikely that their topographies are supported by thermal buoyancy. Although chemical buoyancy generated by basaltic volcanism and the formation of its low-density peridotitic residuum can explain the positive correlation between topography and velocity variation at the shallow depth, an additional mechanism is needed to account for the shear velocity pattern at depths greater than 200 km. It is therefore hypothesized that the central Pacific is underlain by a system of Richter-type convective rolls that are oriented subparallel to the absolute plate velocity, have unit aspect ratio transverse to this orientation, and are confined above the 660-km discontinuity. This convection pattern appears to be strongly correlated with the locations of the Tahitian, Marquesan, and Hawaiian hotspots, which raises interesting questions for Morgan's hypothesis that these hotspots are the surface manifestations of deep mantle plumes.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JB00504

High‐resolution, two‐dimensional vertical tomography of the central Pacific mantle using ScS reverberations and frequency‐dependent travel times

Summary The generalized ray method in a vertically inhomogeneous model is formulated without any approximation by homogeneous layers. The solution is obtained as an infinite series in multiply ‘ reflected ’ waves. Each term can be solved using the exact method or the plane-wave, firstmotion or geometrical approximations. It is shown that the firstmotion approximation of the series converges rapidly, the ratio of successive terms in the infinite series being - (21+ 1)(21)(6/n)’. In addition it is shown that the first-motion approximation, which reduces to the geometrical approximation when the latter is valid, is a useful alternative to geometrical ray theory, being more generally valid and being almost as simple to compute.

Exact and Approximate Generalized Ray Theory in Vertically Inhomogeneous Media

This article describes a three-dimensional Gaussian beam model for calculating transducer-generated ultrasonic wave fields in inhomogeneous anisotropic media. The model is based on a formulation presented recently for homogeneous anisotropic materials. The inhomogeneity is modeled by dividing the material into several homogeneous layers, the approach accounting for the propagation through the various layers and the reflection/refraction processes at the interfaces. It thus calculates ultrasonic field patterns, including proper amplitude information and allows a quick evaluation of the sound fields. Application of the model in view of ultrasonic nondestructive testing of layered composite material and of austenitic steel components is addressed. In the latter case, examples are given for various weldment structures, wherein ultrasonic inspection using commercial angle beam transducers is of interest.

Modeling of transducer fields in inhomogeneous anisotropic materials using Gaussian beam superposition

Numerical Methods of Ray Generation in Multilayered Media

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

F. Hron

Author Tools

Chat about Author

Papers

Numerical Methods of Ray Generation in Multilayered Media