scholarly journals Computation of synthetic seismogram in real earth model by eigen function expansion

MAUSAM ◽  
2021 ◽  
Vol 67 (3) ◽  
pp. 659-668
Author(s):  
AJIT DE ◽  
A. ROY ◽  
M. MITRA ◽  
R. K. BHATTACHARYA
Keyword(s):  
Displacement Field ◽  
Source Model ◽  
Elastic Half Space ◽  
Earth Model ◽  
Dislocation Source ◽  
Transmission Coefficients ◽  
Runge Kutta Method ◽  
Function Expansion ◽  
Exact Evaluation ◽  
Eigen Function

The method of eigen function expansion has been used in the present study to compute synthetic or theoretical seismogram in layered elastic half-space of real earth model. Simple dislocation source model has been considered. The transverse (SH) or radial and vertical (P-SV) components of displacement field have been computed as summed modes and compared by using both exact and numerical techniques. The methods used in the study, include exact evaluation by propagator matrix approach using Reflection-Transmission coefficients as well as numerical computations using Runge-Kutta method of order 4. The specialty of the present study is to evaluate approximate displacement field for the earth models with homogeneous and / or inhomogeneous layers. The normalization technique has been used in the study to control the overflow errors. The study has an advantage to get an idea of earth structure or source model by an inverse iterative technique.  

scholarly journals Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 505-515 ◽  
Author(s):  
D. C. Gakenheimer ◽  
J. Miklowitz
Keyword(s):  
Exact Solution ◽  
Free Surface ◽  
Steady State ◽  
Wave Front ◽  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Point Load ◽  
Limit Case ◽  
Transient Waves

The propagation of transient waves in a homogeneous, isotropic, linearly elastic half space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are derived for the interior of the half space and for all load speeds. Wave-front expansions are obtained from the exact solution, in addition to results pertaining to the steady-state displacement field. The limit case of zero load speed is considered, yielding new results for Lamb’s point load problem.

A multipole representation of earthquake source mechanisms

1973 ◽  
Vol 63 (1) ◽  
pp. 211-225
Author(s):  
F. Richard Yeatts
Keyword(s):  
Test Site ◽  
Multipole Expansion ◽  
Source Model ◽  
Elastic Half Space ◽  
Nevada Test Site ◽  
Fault Movement ◽  
Source Mechanisms ◽  
The Relationship ◽  
Multipole Source ◽  
Finite Disturbance

abstract The static displacement field in an elastic half-space caused by a general, finite disturbance is derived in the form of an infinite series (multipole) expansion. The relationship between this theory and dislocation theory is discussed with the aid of examples. A multipole source model is derived for the strain-step field associated with the nuclear blast HANDLEY set off at the Nevada Test Site on March 26, 1970. The results suggest that there was significant fault movement associated with the detonation.

THE METHOD OF GENERALIZED REFLECTION AND TRANSMISSION COEFFICIENTS

Geophysics ◽  
1960 ◽  
Vol 25 (3) ◽  
pp. 625-641 ◽  
Author(s):  
T. W. Spencer
Keyword(s):  
Integral Representation ◽  
Wave Theory ◽  
Earth Model ◽  
Reflection And Transmission ◽  
Localized Source ◽  
Transmission Coefficients ◽  
The Laplace Transform ◽  
Normal Mode Theory ◽  
Ray Path ◽  
Irrotational Wave

The objective of this work is to provide a method for predicting the surface response of a stratified half space to the radiation from a localized source when neither the assumptions of the plane wave theory nor the assumptions of the normal mode theory are valid. The earth model consists of a finite number of perfectly elastic, homogeneous, isotropic layers separated by interfaces which are plane and parallel to one another. The method leads to an infinite series for the Laplace transform of the response function (displacement, velocity, stress, etc.) in a multi‐interface system. Each term in the series describes all the energy which traverses a particular generalized ray path between the source and the receiver. The specification of the mode of propagation across each stratum (either as an irrotational wave or as an equivoluminal wave) and of the sequence in which the strata are traversed serve to define a generalized ray path. A prescription is given for constructing the integral representation for the disturbance which has traversed such a path directly from the integral representation for the source radiation. The method therefore obviates the necessity for solving a tedious boundary value problem. The time function associated with each term can be obtained by using Cagniard’s method.

scholarly journals Deformation Source Revealed From Leveling Survey in Jigokudani Valley, Tateyama Volcano, Japan

2021 ◽  
Author(s):  
Kohei Hotta ◽  
Shigekazu Kusumoto ◽  
Hidenori Takahashi ◽  
Yuichi S Hayakawa
Keyword(s):  
Source Model ◽  
Deformation Source ◽  
Bench Mark ◽  
Interferometric Synthetic Aperture Radar ◽  
Dislocation Source ◽  
Grid Search Method ◽  
Current Maximum ◽  
Western Side ◽  
One Year ◽  
Gas Chamber

Abstract We modeled vertical deformation detected from leveling survey in Jigokudani valley, Tateyama volcano, central Japan. In Jigokudani valley, uplift of 4 cm/year was previously detected during the period from 2007 to 2010 by Interferometric Synthetic Aperture Radar (InSAR). To confirm whether this inflation has continued to the present, we conducted leveling survey in Jigokudani valley since 2015. Most bench marks showed subsidence up to 5.6 cm during the four-year period from October 2016 to September 2020, while a bench mark locates at the center of the leveling route uniquely showed uplift of 1.6 cm. We applied a dislocation source model to the deformation using a grid search method. A crack with a length of 350 m, a width of 100 m, a strike of N117°E and a dip of 61° is located at a depth of 50 m near the center of Jigokudani valley (Koya jigoku and the new fumarolic area) where highly activating recently. Closing of the crack of 344 cm yields volume decreases of 120,400 m3. Striking direction of the crack is parallel to the line of which are old explosion craters (Mikurigaike and Midorigaike ponds) and corresponds to current maximum compressive stress field in the region of Hida Mountains including Tateyama volcano. The deformation source of the previous period from 2007 to 2010 detected from InSAR was estimated to be at a depth of 50 m and a gas chamber was correspondingly found from the audio-frequency magnetotelluric (AMT) survey. The estimated crack in this study is also located at a similar position of the gas chamber which was also identified from AMT survey. During the period from 2015 to 2016, the crack opened (i.e., inflated) and the inflation stopped during the next one-year period from 2016 to 2017. During the period from 2017 to 2020, the crack turned to closing (i.e., deflation), probably because of the increase in emission of volcanic fluid or gas with a formation of a new crater at the western side of Jigokudani valley (Yahata jigoku) during the period from 2017 to 2018.

Transformation of the earthquake displacement field for spherical earth—Static case

1971 ◽  
Vol 61 (4) ◽  
pp. 861-874
Author(s):  
Hans R. Wason ◽  
Sarva Jit Singh
Keyword(s):  
Displacement Field ◽  
Spherical Surface ◽  
Homogeneous Medium ◽  
Addition Theorem ◽  
Polar Coordinate System ◽  
Earth Model ◽  
Static Case ◽  
Spherical Earth ◽  
Polar Coordinate ◽  
Internal Sources

abstract Explicit expressions for the static displacement field for a Volterra dislocation and a center of compression in an infinite homogeneous medium are obtained. Using an addition theorem, the field is transformed to a polar coordinate system with origin at the center of the Earth. Expressions for the discontinuity in the motion stress vector across the concentric spherical surface through the source are then obtained. These results can be used in studying the deformation of a multilayered spherical earth model induced by internal sources by the Thomson-Haskell matrix method which has so far been mostly applied to dynamic problems.

Body waves in a “real Earth”. Part I

1973 ◽  
Vol 63 (1) ◽  
pp. 145-156 ◽  
Author(s):  
A. Cisternas ◽  
O. Betancourt ◽  
A. Leiva
Keyword(s):  
Exact Solution ◽  
Theoretical Analysis ◽  
Power Series ◽  
Arbitrary Number ◽  
Body Waves ◽  
Reflection And Transmission Coefficients ◽  
Earth Model ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Earth

abstract A theoretical analysis of body waves in a “real Earth” is presented. The earth model consists of an arbitrary number of spherical liquid and solid layers. The algebraic part of the analysis deals with the way to obtain generalized rays out of the exact solution. It is shown that the Rayleigh matrix, and not the Rayleigh determinant, should be used to expand the solution into a power series of modified reflection and transmission coefficients in order to obtain rays.

A mechanism-based homogenization of a dislocation source model for bending

2019 ◽  
Vol 164 ◽  
pp. 663-672 ◽  
Author(s):  
Severin Schmitt ◽  
Markus Stricker ◽  
Peter Gumbsch ◽  
Katrin Schulz
Keyword(s):  
Source Model ◽  
Dislocation Source
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