High Frequency Sonar Elastic Image Enhancements: Ray Theory

2001 ◽  
Author(s):  
Philip L. Marston
Keyword(s):  
High Frequency ◽  
Ray Theory ◽  
Image Enhancements

Dynamic properties of reflected and head waves near the critical point

1979 ◽  
Vol 16 (7) ◽  
pp. 1388-1401 ◽  
Author(s):  
Larry W. Marks ◽  
F. Hron
Keyword(s):  
Exact Solution ◽  
High Frequency ◽  
Classical Problem ◽  
Plane Boundary ◽  
Head Wave ◽  
Disk File ◽  
Ray Theory ◽  
Computational Point ◽  
Spherical Waves ◽  
Head Waves

The classical problem of the incidence of spherical waves on a plane boundary has been reformulated from the computational point of view by providing a high frequency approximation to the exact solution applicable to any seismic body wave, regardless of the number of conversions or reflections from the bottoming interface. In our final expressions the ray amplitude of the interference reflected-head wave is cast in terms of a Weber function, the numerical values of which can be conveniently stored on a computer disk file and retrieved via direct access during an actual run. Our formulation also accounts for the increase of energy carried by multiple head waves arising during multiple reflections of the reflected wave from the bottoming interface. In this form our high frequency expression for the ray amplitude of the interference reflected-head wave can represent a complementary technique to asymptotic ray theory in the vicinity of critical regions where the latter cannot be used. Since numerical tests indicate that our method produces results very close to those obtained by the numerical integration of the exact solution, its combination with asymptotic ray theory yields a powerful technique for the speedy computation of synthetic seismograms for plane homogeneous layers.

Comparison of seismic anisotropy of sedimentary strata at low- and high-frequency limits

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. MR1-MR10 ◽  
Author(s):  
Fuyong Yan ◽  
De-Hua Han ◽  
Tongcheng Han ◽  
Xue-Lian Chen
Keyword(s):  
High Frequency ◽  
Seismic Anisotropy ◽  
Sedimentary Rocks ◽  
Low Frequency ◽  
Layered Media ◽  
Ray Theory ◽  
Frequency Limit ◽  
Anisotropic Properties ◽  
Velocity Anisotropy ◽  
Backus Averaging

The layer-induced seismic anisotropy of sedimentary strata is frequency-dependent. At the low-frequency limit, the effective anisotropic properties of the layered media can be estimated by the Backus averaging model. At the high-frequency limit, the apparent anisotropic properties of the layered media can be estimated by ray theory. First, we build a database of laboratory ultrasonic measurement on sedimentary rocks from the literature. The database includes ultrasonic velocity measurements on sandstones and carbonate rocks, and velocity-anisotropy measurements on shales. Then, we simulate the sedimentary strata by randomly selecting a certain number of rock samples and using their laboratory measurement results to parameterize each layer. For each realization of the sedimentary strata, we estimate the effective and apparent seismic anisotropy parameters using the Backus average and ray theory, respectively. We find that, relative to Backus averaging, ray theory usually underestimates the Thomsen parameters [Formula: see text] and [Formula: see text], and overestimates [Formula: see text]. For an effective layered medium consisting of isotropic sedimentary rocks, the differences are significant. These differences decrease when shales with intrinsic seismic anisotropy are included. For the same sedimentary strata, the seismic wave should perceive stronger seismic anisotropy than the ultrasonic wave.

scholarly journals Asymptotics of near-cloaking

2020 ◽  
pp. 1-21
Author(s):  
J. R. OCKENDON ◽  
H. OCKENDON ◽  
B. D. SLEEMAN ◽  
R. H. TEW
Keyword(s):  
Asymptotic Analysis ◽  
Acoustic Waves ◽  
High Frequency ◽  
Ray Theory ◽  
Elastic Materials ◽  
Eigenfunction Expansions ◽  
Linear Elastic

This paper describes how asymptotic analysis can be used to gain new insights into the theory of cloaking of spherical and cylindrical targets within the context of acoustic waves in a class of linear elastic materials. In certain cases, these configurations allow solutions to be written down in terms of eigenfunction expansions from which high-frequency asymptotics can be extracted systematically. These asymptotics are compared with the predictions of ray theory and are used to describe the scattering that occurs when perfect cloaking models are regularised.

Use of ray theory to calculate high-frequency radiation from earthquake sources having spatially variable rupture velocity and stress drop

1984 ◽  
Vol 74 (6) ◽  
pp. 2061-2082
Author(s):  
Paul Spudich ◽  
L. Neil Frazer
Keyword(s):  
Stress Drop ◽  
High Frequency ◽  
Slip Velocity ◽  
Green’S Functions ◽  
Ground Motions ◽  
Spatial Variations ◽  
Body Waves ◽  
Ray Theory ◽  
Rupture Velocity ◽  
Ground Acceleration

Abstract We analyze the problem of calculating high-frequency ground motions (>1 Hz) caused by earthquakes having arbitrary spatial variations of rupture velocity and slip velocity (or stress drop) over the fault. We approximate the elastic wave Green's functions by far-field body waves, which we calculate using geometric ray theory. However, we do not make the traditional Fraunhofer approximation, so our method may be used close to large faults. The method is confined to high frequencies (greater than about 1 Hz) due to the omisson of near-field terms, and must be used at source-observer distances less than a few source depths, due to the omission of surface waves. It is easily used in laterally varying velocity structures. Assuming a simple parameterization of the slip function, the computational problem collapses to the evaluation of a series of line integrals over the fault, with one line integral per each time ti in the observer seismogram. The path of integration corresponding to observation time ti consists of only those points on the fault which radiate body waves arriving at the observer at exactly time ti. This path is an isochron of the arrival time function. An isochron velocity may be defined that depends on rupture velocity and resembles the usual directivity function. Observed ground motions are directly dependent upon this isochron velocity. Ground velocity is proportional to isochron velocity and ground acceleration is proportional to isochron acceleration in dislocation models of rupture. Ground acceleration may also be related to spatial variations of slip velocity on the fault, using the square of isochron velocity as a constant of proportionality. We show two rupture models, one with variable slip velocity and the other with variable rupture velocity, that cause the same ground acceleration at a single observer. The computational method is shown to produce reasonably accurate synthetic seismograms, compared to a method using complete Green's functions, and requires about 0.5 per cent of the computer time. It may be very effective in calculating ground motions in the frequency band 1 to 10 Hz at observers within a few source depths of large earthquakes, where most of the high-frequency motions may be caused by direct P and S waves. We suggest a possible method for inverting ground motions for both slip velocity and rupture velocity over the fault.

REFRACTION ALONG A LAYER

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 369-388 ◽  
Author(s):  
T. W. Spencer
Keyword(s):  
High Frequency ◽  
High Speed ◽  
Shear Mode ◽  
Ray Theory ◽  
Dominant Wavelength ◽  
Layer Depth ◽  
Time Intervals ◽  
Reflected Waves ◽  
Head Waves ◽  
Compressional Mode

High‐frequency geometric ray theory is used to investigate the refracted arrival from a high‐speed layer embedded in an infinite medium. The effect of changing the layer thickness to dominant wavelength ratio [Formula: see text] and the range to depth ratio (ρ/H) is analyzed for a point compressional source. The results approximate the exact solution when [Formula: see text]. The theory predicts shingling and shows that it is range‐limited. Factors which improve the resolution between reflected arrivals increase the range over which shingling occurs. As the range increases, the traveltime curves for all the multiply reflected rays which cross the layer the same number of times in the shear mode approach the same asymptote (regardless of the number of crossings in the compressional mode). When the layer is thick compared to the dominant wavelength, the refracted arrival may consist of a series of events separated by equal time intervals. Each event is produced by the superposition of reflected waves which cross the layer the same number of times in the shear mode. The amplitude of each event satisfies [Formula: see text], where H is the layer depth. Because the head waves decay like [Formula: see text], the reflected waves predominate at large ranges.

Advanced statistical energy analysis

1994 ◽  
Vol 346 (1681) ◽  
pp. 501-510 ◽  
Keyword(s):  
High Frequency ◽  
Energy Analysis ◽  
Frequency Theory ◽  
Theory Approach ◽  
Exact Results ◽  
Statistical Energy Analysis ◽  
Ray Theory ◽  
Structural Assembly ◽  
Residual Power ◽  
Higher Order Models

A high-frequency theory (advanced statistical energy analysis (ASEA)) is developed which takes account of the mechanism of tunnelling and uses a ray theory approach to track the power flowing around a plate or a beam network and then uses statistical energy analysis (sea) to take care of any residual power. ASEA divides the energy of each sub-system into energy that is freely available for transfer to other sub-systems and energy that is fixed within the sub-system. The theory allows for coupling between sub-systems that are physically separate and can be interpreted as a series of mathematical models, the first of which is identical to standard SEA and subsequent higher order models are convergent on an accurate prediction. Using a structural assembly of six rods as an example, ASEA is shown to converge onto the exact results, whereas SEA is shown to overpredict by up to 60 dB.

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