Interpretation of hydrocarbon microtremors as pore fluid oscillations driven by ambient seismic noise

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Interpretation of hydrocarbon microtremors as
pore fluid oscillations driven by ambient seismic
noise
Marcel Frehner ETH Zurich, Switzerland,
frehner_at_erdw.ethz.ch Stefan M. Schmalholz ETH
Zurich, Switzerland Reto Holzner Spectraseis
Technologies Inc., Switzerland Yuri
Podladchikov University of Oslo, Norway
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Observation in microtremor signals ? Starting
point

• Continuous velocity-measurements of
  microtremor( Passive method)
• Fourier transformation
• Low frequencyspectral anomalies

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Low frequency spectral anomalies ? Explained as
pore fluid oscillations

• One possible explanation forlow frequency
  spectral anomalies
• Resonant oscillation of pore fluids
• Is the resonant movement of the pore fluids
  strong enough to be transferred to the elastic
  solid?
• Synthetic case study
• Reproduction of low-frequency anomaly

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Resonance of trapped oil blobs ? Resonance is
important
Hilpert et al, Geophysics, 2000 We investigate
the excitation by sound waves of capillary
trapped oil blobs. We derive approximate,
analytical expressions for the resonance of oil
blobs in capillary tubes . Based upon these
simple model systems, we conclude that resonance
of oil blobs is signi?cant for coarse-grained but
not ?ne-grained media.
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Resonance of trapped oil blobs ? Oil in a pore
can be treated as oscillator
Beresnev, Geophysics, 2006 Quantitative dynamics
of a non-wetting ganglion of residual oil
entrapped in a pore constriction and subjected to
vibrations of the pore wall can be approximated
by the equation of motion of an oscillator moving
under the effect of the external pressure
gradient, inertial oscillatory force, and
restoring capillary force.
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Resonance of trapped oil blobs ? Numerical
simulation

• Ongoing research of ASCOMP Ltd., Switzerland

• Full Navier-Stokes equations
• Surface tension taken into account
• One simulation for each frequency
• Calculate response of centerof mass of oil blob

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1D coupled wave-oscillator model ? Motivation

• A simple idea
• Observed low frequency anomalies at the surface
  are caused by oscillations of pore fluids in the
  reservoir.
• Question
• Is it possible to transfer the fluid oscillations
  to the solid?
• Can the eigenfrequency of these oscillations be
  observedin the spectrum of the solid velocity?
• Requirements
• Mathematical description of coupling
  betweenmicro-scale oscillations and macro-scale
  wave propagation

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1D coupled wave-oscillator model ? Model
equations

• Linear elastic solid
• Linear oscillator

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1D coupled wave-oscillator model ? Model
equations

• Coupled equations

• w0 has to be determined from pore fluid and pore
  geometry.
• For the moment it is assumed that w0 lies in the
  low frequency range under consideration.

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1D coupled wave-oscillator model ? Numerical code

• Explicit 1D finite differences
• Staggered grid in space(Virieux, 1986)
• Predictor-corrector method in time
• Non-reflecting boundaries(Ionescu Igel, 2003)
• Written in MATLAB
• Code checked vs. analytical solution of
  model-equations
• Energy conservation satisfiedEntropy inequality
  in progress

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1D coupled wave-oscillator model ? Test of
numerical code

• Energy conservation

Solid velocityFluid velocity
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Synthetic case study ? Homogeneous media
Eigenfrequency w0 of pore oscillations3 Hz
Monochromatic external source with 0.3Hz
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Synthetic case study ? Observations

• The model equations are truly linear
• Both boundaries are non-reflecting,ie. no
  two-way reflections occur
• The only input frequency is the 0.3Hz frequency
  of the external source
• Nevertheless the eigenfrequency of the pore fluid
  oscillations (3Hz) is clearly visible in the
  solid spectra
• The pore fluid seems to develop an oscillation
  with its eigenfrequency and transfer this motion
  to the solid

??? HOW IS THIS POSSIBLE ???
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Synthetic case study ? Discussion
Absolute velocities
Relative velocity
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Synthetic case study ? Discussion

• Decay of low frequency anomalies

Eigenfrequency w0 of pore oscillations3 Hz
Black spectra short time signal Red long
time signal
Monochromatic external source with 0.3Hz
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Synthetic case study ? Reservoir thickness
variation

• Layered model

No oscillation
Reservoir with 3Hz oscillators
No oscillation
0.3Hz external source
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1D coupled wave-oscillator model ? Comparison to
nature / Outlook

• Linear model

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Low frequency spectral anomalies explained as
pore fluid oscillations ? Conclusions / Summary

• Although no other frequencies than the 0.3Hz of
  the external source is put into the system, the
  pore fluid starts to oscillate with its
  eigenfrequency.
• Incidence of monochromatic wave is enough to
  excite oscillations of the pore fluid with its
  eigenfrequency.
• Under the conditions shown the 3Hz eigenfrequency
  of the pore fluid oscillations is transferred to
  the elastic solid
• The time evolution of the low frequency anomaly
  could contain information of the reservoir
  thickness.

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Thank you