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| Titel |
Wave velocity dispersion and attenuation in media exhibiting internal oscillations |
| VerfasserIn |
Marcel Frehner, Holger Steeb, Stefan M. Schmalholz |
| 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 |
250033822
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| Zusammenfassung |
| Understanding the dynamical and acoustical behavior of porous and heterogeneous rocks is
of great importance in geophysics, e.g. earthquakes, and for various seismic engineering
applications, e.g. hydrocarbon exploration. Within a heterogeneous medium oscillations with
a characteristic resonance frequency, depending on the mass and internal length of
the heterogeneity, can occur. When excited, heterogeneities can self-oscillate with
their natural frequency. Another example of internal oscillations is the dynamical
behavior of non-wetting fluid blobs or fluid patches in residually saturated pore spaces.
Surface tension forces or capillary forces act as the restoring force that drives the
oscillation. Whatever mechanism is involved, an oscillatory phenomena within a
heterogeneous medium will have an effect on acoustic or seismic waves propagating
through such a medium, i.e. wave velocity dispersion and frequency-dependent
attenuation.
We present two models for media exhibiting internal oscillations and discuss the
frequency-dependent wave propagation mechanism. Both models give similar results: (1) The
low-frequency (i.e. quasi-static) limit for the phase velocity is identical with the
Gassmann-Wood limit and the high-frequency limit is larger than this value and (2) Around
the resonance frequency a very strong phase velocity change and the largest attenuation
occurs.
(1) Model for a homogeneous medium exhibiting internal oscillations
We present a continuum model for an acoustic medium exhibiting internal damped
oscillations. The obvious application of this model is water containing oscillating gas
bubbles, providing the material and model parameters for this study. Two physically based
momentum interaction terms between the two inherent constituents are used: (1) A purely
elastic term of oscillatory nature that scales with the volume of the bubbles and (2) A viscous
term that scales with the specific surface of the bubble. The model is capable of taking into
account an arbitrary number of oscillators with different resonance frequencies. Exemplarily,
we show a log-normal distribution of resonance frequencies. Such a distribution changes the
acoustic properties significantly compared to the case with only one resonance frequency.
The dispersion and attenuation resulting from our model agree well with the dispersion and
attenuation (1) derived with a more exact mathematical treatment and (2) measured in
laboratory experiments.
(2) Three-phase model for residually saturated porous media
We present a three-phase model describing wave propagation phenomena in residually
saturated porous media. The model consists of a continuous non-wetting phase and a
discontinuous wetting phase and is an extension of classical biphasic (Biot-type) models. The
model includes resonance effects of single liquid bridges or liquid clusters with
miscellaneous eigenfrequencies taking into account a visco-elastic restoring force (pinned
oscillations and/or sliding motion of the contact line). In the present investigation, our aim is
to study attenuation due to fluid oscillations and due to wave-induced flow with a
macroscopic three-phase continuum model, i.e. a mixture consisting of one solid constituent
building the elastic skeleton and two immiscible fluid constituents. Furthermore, we study
monochromatic waves in transversal and longitudinal direction and discuss the resulting
dispersion relations for a typical reservoir sandstone equivalent (Berea sandstone). |
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