Conformal Map on Rough Boundaries Application to Fracture

ABSTRACTA conformai mapping technique is presented which allows to solve efficiently harmonic and bi-harmonic problems in semi-infinite domains limited by a rough boundary. This technique is applied to obtain the statistical distribution of flux and elastic stress in the vicinity of a self-affine boundary. This computation justifies the occurence of Weibull statistics for the strength of glass fibers, with Weibull modulus depending on the roughness amplitude. Another application concerns the determination of the local mode III stress intensity factor ahead of a rough crack. Extension of the method to surface stress-corrosion, and interfacial crack propagation are discussed.

TELLURIC FIELD AND APPARENT RESISTIVITY OVER AN INCLINED NORMAL FAULT

The telluric field and apparent resistivity anomalies caused by an inclined normal fault are calculated along a profile perpendicular to the strike of the fault. The method of conformai mapping is used to obtain an analytic solution of the boundary value problem. Numerical results are presented in the form of a series of graphs. It is concluded that the angle of inclination for a basement fault can be determined quantitatively for a large throw or qualitatively for a moderate throw.The effect of anisotropic strata on the anomaly curves is discussed.