Mogi-Yamakawa's model (or Mogi's model) has often been used to explain crustal deformation observed around volcanoes. This model is based on an analytical solution derived by Yamakawa (1955), which only holds good under the restricted condition that a small enough spherical pressure source exists at some depth within a semi-infinite homogeneous elastic body. However, there have been hardly any quantitative investigations of the application limit of this solution when
a/
D (
a : radius of the sphere,
D : depth of the sphere) increases. McTigue (1987) modified Yamakawa's solution so as to hold good even for large
a/
D. However, there have been no quantitative investigations of the application limit when
a/
D increases for this solution either. Therefore, we created large
a/
D numerical models using the finite element method (FEM) and found numerical solutions of surface deformation. Comparison with FE analyses clarified the limits of application of these two analytical solutions. For example, the values of
a/
D that agree with FE analyses within 1% are 0.22 for Yamakawa's solution and 0.45 for McTigue's solution. These two analytical solutions may hold precisely with smaller
a/
D values. However, the discrepancy between these two solutions and FE analysis gradually increases when
a/
D exceeds these values. In contrast, if
D and
a are determined by applying Yamakawa's solution to results of FE analyses,
D is found to be determined much shallower than the true value, while
a is determined with relative precision. Therefore, Δ
V (volume change of the spherical pressure source) may also be estimated with relative precision.
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