Readable survey of the theoretical core of the propagation of waves in solids offers a concise account of the classical theory, considers how this theory has been. The author gives a concise account of the classical theory necessary to an understanding of the subject, considers how this theory has been extended to solids. Download Citation on ResearchGate | Stress waves in solids / by H. Kolsky | Incluye índice }.
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The Kolsky basic model and modified model for attenuation and dispersion is the mathematical Q models that is most used in seismic applications. The basic Kolsky model is used for its simplicity in seismic data processing, however it does not rigorously satisfy the Minimum phase criterion and cannot satisfy the Kramers—Kronig relations. But then soluds Kolsky’s modified model comes to our rescue, producing an accurate representation of the velocity dispersion within the seismic frequency band.
Stress Waves in Solids (Dover Books on Physics) by Kolsky, H
The basic Kolsky model is presented in Kolsky’s book “Stress waves in solids” that are available as a Google book. This book is also available as a Google book: Seismic inverse Q filtering. The theoretical background for mathematical Q models can be found in the Wikipedia article: Here we found a function K solifs we can call a propagation constant in line with Futterman.
To obtain a solution that can be applied to seismic k w must be connected to a function that represent the way the seismic wave propagates in the seismic media.
Stress Waves in Solids
This functions can be regarded as a Q-model. In his outline Wang calls the Kolsky-Futterman model the Kolsky model.
Where c r and Q r are the phase velocity and the Q value at a reference frequency w r.
A requirement in the theory for materials satisfying the linear attenuation assumption is that the reference frequency w r is a finite arbitrarily small but nonzero cut-off on the absorption. According to Kolsky, we are free to choose w r following the phenomenological criterion that it be small compared with the lowest koksky frequency w in the frequency band.
They used the Kolsky model as a reference model. For each of the Q models Ursin B.
The Kolsky basic model and modified model for attenuation and dispersion – Wikipedia
The choice of w r as the lowest frequency in the frequency band will introduce phase errors wavee we use the Kolsky model as an inverse Q filter. This is very well documented in Wang Hz Then we can get a correct solution with inverse Q filtering with the Kolsky model.