Open AccessResonance prediction of deep sediment valleys through an eigenvalue method
Author(s) -
Zhou Tiao,
Dravinski Marijan
Publication year - 1994
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1994.tb02467.x
Subject(s) - eigenvalues and eigenvectors , dimensionless quantity , boundary (topology) , mathematical analysis , boundary value problem , mode (computer interface) , resonance (particle physics) , plane (geometry) , space (punctuation) , electrical impedance , geometry , physics , mathematics , geology , mechanics , quantum mechanics , computer science , operating system
SUMMARY 2‐D resonance of different orders for a sediment valley embedded in a half‐space is studied for anti‐plane and plane‐strain models. It is found that the resonant frequencies are properties of the valley while the incident wavefield only affects the excitation of different modes. The dimensionless resonant frequencies are found to be independent of impedance contrast between the half‐space and the valley. Based on this property, an eigenvalue method is proposed to determine resonant frequencies of the valley. Resonant frequencies and mode shapes are obtained by solving an eigenvalue problem. The method is valid for valleys of arbitrary shape. The eigenvalue problem is solved numerically based on an indirect boundary integral method. The corresponding eigenfrequencies are identified as the resonant frequencies of the valley for all incident waves. The eigenvalue method results are verified by a spectral‐search method. The method is found to be numerically much more efficient than the spectral‐search method.