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Paper IPM / Physic / 14437  


Abstract:  
This paper addresses an important fundamental question: the differences betweenwave propagation in fractured
porous media with a uniform matrix (constant bulk modulus) and those in which the matrix is heterogeneous
with its bulk modulus distributed spatially. The analysis of extensive experimental data [Phys. Rev. E 71, 046301
(2005)] indicated that such distributions are selfaffine and induce correlations at all the relevant length scales. The
comparison is important from a practical view point because in many of the traditional models of fractured rock,
particularly those that are used to study wave propagation or fit some data, the matrix is assumed to be uniform.
Using extensive numerical simulation of propagation of acoustic waves, we present strong evidence indicating
that the wavesï¿½?? amplitude in a fractured porous medium with a heterogeneous matrix decays exponentially with
the distance from the source. This is in sharp contrast with a fractured porous medium with a uniform matrix
in which not only the wavesï¿½?? amplitude decays with the distance as a stretched exponential function, but the
exponent that characterizes the function is also dependent upon the fracture density. The localization length
depends on the correlations in the spatial distribution of the bulk modulus, as well as the fracture density. The
mean speed of the waves varies linearly with the fracturesï¿½?? mean orientation.
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