FINITE ELEMENT MODELLING OF BOREHOLE SEISMIC RESPONSES IN LAYERED ANISOTROPIC FORMATIONS AND ITS USE FOR ELASTIC INVERSION

摘要

A METHOD OF SIMULATING A BOREHOLE ACOUSTIC RESPONSE IN AN ANISOTROPIC FORMATION OF THE CRUST OF THE EARTH, THE METHOD COMPRISING: FORMULATING A GEOMETRIC MODEL OF THE FORMATION, THE GEOMETRIC MODEL COMPRISING A PLURALITY OF LAYERS DEFINABLE IN A CYLINDRICAL COORDINATE SYSTEM DEFINED BY AN AXIAL DIRECTION NORMAL TO EACH OF THE LAYERS, A RADIAL DIRECTION RELATIVE TO THE AXIAL DIRECTION, AND A CIRCUMFERENTIAL DIRECTION RELATIVE TO THE AXIAL DIRECTION; FORMULATING A COMPUTATIONAL MODEL OF WAVE PROPAGATION IN THE FORMATION, THE COMPUTATIONAL MODEL COMPRISING ONE OR MORE FIELD VARIABLES AND A WAVE EQUATION DESCRIBING A BEHAVIOR OF THE ONE OR MORE FIELD VARIABLES, WHEREIN THE ONE OR MORE FIELD VARIABLES ARE REPRESENTED AS RESPECTIVE FOURIER SERIES EXPANSIONS OF PERIODIC HARMONICS IN THE CIRCUMFERENTIAL DIRECTION, AND NUMERICALLY SOLVING THE COMPUTATIONAL MODEL. FIGURE 1