Fast programs for layered half-space problems

1967 ◽  
Vol 57 (6) ◽  
pp. 1299-1315
Author(s):  
M. J. Randall
Keyword(s):  
Half Space ◽  
Matrix Method ◽  
Transfer Functions ◽  
Synthetic Seismograms ◽  
Time Function ◽  
Source Time Function ◽  
Fast Computer ◽  
The Matrix ◽  
Crustal Reflection ◽  
Layered Half Space

Abstract Knopoff's matrix method for the solution of P-SV problems has been somewhat simplified and modified to take account of oceanic structures. Advantage has been taken of a method of separating the frequency-dependent operations from the matrix multiplications to obtain very fast computer programs for calculating Rayleigh dispersion, crustal reflection functions, and crustal transfer functions. Applications include Rayleigh dispersion inversion, QitR, inversion, crustal investigations using pP, crustal transfer corrections to amplitude observations, and the construction of synthetic seismograms for investigation of the source time-function.

scholarly journals The dispersion of Rayleigh waves in orthotropic layered half-space using matrix method

2016 ◽  
Vol 38 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Tran Thanh Tuan ◽  
Tran Ngoc Trung
Keyword(s):  
Numerical Calculation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Matrix Method ◽  
Secular Equation ◽  
Material Parameters ◽  
Rayleigh Surface Waves ◽  
The Matrix ◽  
Dimensionless Variables ◽  
Layered Half Space

In this paper, the secular equation of Rayleigh surface waves propagating in an orthotropic layered half-space is derived by the matrix method.  All the layers and the half-space are assumed to have identical principle axes. The explicit form of the matrizant for each layer is obtained by the Sylvester's theorem. The derived secular equation takes only real values and depends only on the dimensionless variables and dimensionless material parameters. Hence, it is convenient in numerical calculation.

scholarly journals Mathematical Modelling and Simulation of Band Pass Filters using the Floating Admittance Matrix Method

2021 ◽  
Vol 20 ◽  
pp. 208-214
Author(s):  
Sanjay Kumar Roy ◽  
Kamal Kumar Sharma ◽  
Cherry Bhargava ◽  
Brahmadeo Prasad Singh
Keyword(s):  
Mathematical Modeling ◽  
Matrix Method ◽  
Transfer Functions ◽  
Large Network ◽  
Admittance Matrix ◽  
The Matrix ◽  
Band Pass ◽  
Time And Energy ◽  
Mathematical Modelling And Simulation ◽  
Partitioning Technique

This article aims to develop a band pass filter's mathematical model using the Floating Admittance Matrix (FAM) method. The use of the conventional methods of analysis based KCL, KVL, Thevenin's, Norton's depends on the type of the particular circuit. The proposed mathematical modeling using the floating admittance matrix method is unique, and the same can be used for all types of circuits. This method uses the partitioning technique for large network. The sum property of all the elements of any row or any column equal to zero provides the assurance to proceed further for analysis or re-observe the very first equation. This saves time and energy. The FAM method presented here is so simple that anybody with slight knowledge of electronics but understating the matrix maneuvering, can analyze any circuit to derive all types of transfer functions. The mathematical modeling using the FAM method provides leverage to the designer to comfortably adjust their design at any stage of analysis. These statements provide compelling reasons for the adoption of the proposed process and demonstrate its benefits

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