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| Titel |
Inverse modeling of the overpressure distribution in an extension fracture with an arbitrary aperture variation: application to non-feeder dikes in the Miyake-jima Volcano, Japan |
| VerfasserIn |
Shigekazu Kusumoto, Nobuo Geshi, Agust Gudmundsson |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250039669
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| Zusammenfassung |
| We derived a solution for the overpressure distribution acting on the walls (surfaces) of an
extension fracture (a hydrofracture) with an arbitrary opening-displacement (or aperture)
variation. In the proposed model, we assume that the overpressure distribution can be
described by Fourier cosine series. We at first present a solution for the forward model giving
the fracture aperture when it is opened by an irregular overpressure variation obtained using
the Fourier cosine series. Next, by changing the form of the solution for the forward model,
we obtain a matrix equation that can be used to estimate the Fourier coefficients to obtain the
overpressure distribution from the fracture aperture variation. As simple examples of this
inverse analysis, we estimate the overpressure conditions from crack apertures given
analytically for two cases, namely, 1) the overpressure in the crack is constant, and 2) the
overpressure variation in the crack varies linearly from its center. The estimated
overpressure distributions were found to be correct, although a small “noise” was
present.
Since the method presented here gives the overpressure distribution as a Fourier series by
the aperture data measured at a finite number of points, the overpressure conditions for
forming the fracture can be determined for each wavelength. The Fourier coefficient of
n = 0 is an important coefficient that gives the average value of the overpressure
acting inside the crack. With the exception of n = 0, the Fourier coefficient of n
= 1 expresses the longest wavelength component of the irregular overpressure.
Thus, because this coefficient including the coefficient of n = 0 gives the longest
wavelength component in the irregular overpressure, the component may be an
important indicator of the overpressure condition that decides the basic form of the
crack.
We applied the solution for the inverse analysis to the thickness data of 19 non-feeder
dikes exposed in the caldera wall of the Miyake-jima Volcano, Japan. In the analysis, the
host-rock Young’s modulus and Poisson’s ratio were taken as 1 GPa and 0.25. The results
show that most of the estimated overpressures increase toward the tips of the dikes and reach
about 5 to 15 MPa (average was 8 MPa). In addition, results indicate host-rock fracture
toughnesses between 60 MPa m1-2 and 170 MPa m1-2 (average 100 MPa m1-2). For
comparison, we also estimated the magma overpressure by the least square method, assuming
constant overpressure. This method gives overpressure between 1.5 MPa and 4 MPa
(average 2.8 MPa). Similarly, the fracture toughnesses estimated in this way range
between 30 MPa m1-2 and 120 MPa m1-2 (average 55 MPa m1-2). These methods and
assumptions thus yield somewhat different results, as expected, but indicate the likely
ranges of the magma overpressures and host-rock fracture toughnesses both of which
are very reasonable and agree with earlier results obtained by different methods. |
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