Full wave modelling of microseismic waves

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Full wave modelling of microseismic waves

• Mark Hildyard
• (Acknowledgements Paul Young, John Napier,
  Laura Pyrak-Nolte, Will Pettitt, Lindsay Linzer,
  Alex Milev, Steve Spottiswoode)

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Outline

• Representing fracturing (explicit fractures)
• Full wave modelling of waves through fractures
• Laboratory experiments
• Stress effects on seismic waves
• In situ waveforms and interpretation of fracture
  sizes
• Quantifying Frequency effects
• Frequency-dependent velocity and attenuation due
  to fracture assemblies
• Testing microseismic inversions and mechanisms
• Some examples from mining research
• Possible contributions to BUMPS

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1. Representing Fractures
1. Representation
Effective vs Explicit

• Effective - modify properties in material
  (equivalent med.) OR
• Explicit fracture surfaces (or discrete)

• Explicit fractures
• Advantages full frequency range full fracture
  stiffness range control over conditions on
  fracture surfaces non-linear behaviour useful
  for other studies (e.g. fault slip)
• Main Disadvantage angled (non-grid-aligned)
  fractures difficult in FD staggered grid also
  cannot represent fractures smaller than a few
  elements.
• Explicit fractures (for WAVE) described in
  (Cundall, 1992 Hildyard et al, 1995 Hildyard,
  2001 Hildyard Young, 2002)

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Explicit fractures (2 surfaces with contacts)
1. Representation

• NOTE
• Can also represent non-linear effects
• Frictional sliding
• Tensile opening
• Closure
• Non-linear stiffness
• But effects shown here occur with simple linear
  fractures

• From single incident wave
• 4 wave-fronts(2 transmitted 2 reflect)
• Fracture tips (Diffracted P and S waves)
• Multiple fractures quickly yield complicated
  wave-fields

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2a. Modelling Laboratory Experiments
2. Waves thru fractures

• Ultrasonic Experiments simulating waves through
  Multiple parallel fractures
• Taken from (Pyrak-Nolte et al., 1990)
• Fractures in experiment modelled as displacement
  discontinuities with linear normal and shear
  contact stiffness

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Models of P- and S- wave experiments
2a Lab
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Wave propagation parallel to the fractures
2a Lab

• SO something is working ...
• Correct behaviour i.t.o wave-speeds, frequency
  content, amplitudes, the full wave-forms.

P-wave
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Wave propagation across the fractures
2a Lab

• SO something is wrong!!
• Correct behaviour fractures slow and attenuate
  the waves Freq. effects are similar.
• BUT not the degree of attenuation or slowing!
• ALL attenuation and slowing is from a form of
  scattering
• Does it need another damping mechanism in the
  fractures?

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2b. Stress effects on seismic waves
2. Waves thru fractures
Stress distribution(Normal to the fractures)
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Stress-dependent fracture stiffness
2b Stress
Stress distribution(Normal to the fractures)
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2b Stress
Change in wave patterns, arrivals and amplitudes
due to non-uniform stress
1. Full waveform analysis important. Previous
analyses did not recognise stress effects in
these results 2. Increased attenuation does not
necessarily require inherent dissipation to
explain. Simple linear fracture stiffness can
cause large attenuation, while stress variation
can vary its effect. 3. A general useful approach
to capture the effect of stress and stress
changes on waveforms 4. Changes wave patterns,
arrivals-time, and amplitudes. Practically very
important, if any reason to suspect a non-uniform
stress-field
Uniform stress-field
Non-Uniform stress-field
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2c. Waves through in situ micro-cracks (and
interpretation of fracture size)
2. Waves thru fractures
Waveforms from velocity scans from an underground
AE experiment at URL (Carlson and Young, 1992)
Cross-hole
Cross-section through underground tunnel
Model of 8x8 array
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Elastic model shows up anisotropy
2c in situ
Paths parallel to tunnel
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Elastic model shows up anisotropy
2c in situ
Paths parallel to tunnel
Paths oblique to tunnel
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Addition of random micro-cracks
2c in situ
MAIN RESULTS 1. Orientation (primarily parallel
to tunnel) 2. Crack density (lt 0.1) 3. Open crack
sizes (lt 22mm)
Paths parallel to tunnel
Paths oblique to tunnel
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Why relevant to BUMPS?
2. Waves thru fractures

• So far, about waves through fractures. But
  relevant to micro-seismics for the meaningful
  interpretation of the medium from velocities,
  amplitudes, attenuation, frequency content,
  shear-wave splitting, etc even for location.

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Outline

• Representing fracturing (explicit fractures)
• Full wave modelling of waves through fractures
• Laboratory experiments
• Stress effects on seismic waves
• In situ waveforms and interpretation of fracture
  sizes
• Quantifying Frequency effects
• Frequency-dependent velocity and attenuation due
  to fracture assemblies
• Testing microseismic inversions and mechanisms
• Some examples from mining research
• Possible contributions to BUMPS

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3. Quantifying Frequency variation due to
assemblies/ networks of fractures
3. Freq
Record waveforms (e.g. varying crack density)
Very Carefully construct random fracture models
- record at two spatial positions
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3. Freq
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Phase Velocity and Attenuation Function(For
increasing crack density, 11.3 m cracks)
3. Freq
Attenuation
11.3 m fractures
Phase Velocity
Atten.per 100m
Wave-speed
Frequency (kHz)
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3. Freq
3. Quantifying Frequency variation in assemblies
of fractures
Characterise frequency effects of variations in
- Fracture size - Fracture stiffness -
Combined orientations - Size distributions -
Stress P-wave results to date, but potential
to study shear waves, shear-wave splitting
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4. Microseismic mechanisms and inversions
Small micro-seismic network for monitoring
failure of a CRUSH pillar in a platinum mine.
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4 mechanisms
4. Modelling Microseismic mechanisms
Lesson 1 Geometry effect huge! Model a thick
reef geometry. Sx size large near-field
interactions.
Lesson 2 Location in h/w, reef or f/w has huge
effect (yet lt 1.5m, i.e. source size!)
Lesson 3 Location (which pillar edge) has large
effect
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Models as Tests on Microseismic inversions

• Simple models effect of stope
• Perfect spherical coverage
• Far-field, 320 m from source
• Finite size source (20mx20m)
• Rupture propagation, 50 MPa
• Small stope 60m x 60m

Model X m Y m Z m Error m Magn. MoP 109N.m MoS 109N.m Mo 109N.m
Crush, no stope 353.6 360.2 354.0 1.3 2.0 1160 529 740
Crush, with stope 352.6 360.2 352.5 1.4 2.2 5640 1990 3200
Shear, no stope 361.0 369.1 361.3 1.2 1.4 296 446 396
Shear, with stope 360.8 361.6 361.3 4.3 1.7 534 715 655
Model EnergyP MJ EnergyS MJ Energy MJ rP m rS m r m foP Hz foS Hz fo Hz ?s MPa
Crush, no stope 67.4 253.0 321.0 20.1 14.1 18.2 122.5 102.1 112.3 53.7
Crush, with stope 40.9 261.0 302.0 68.0 26.8 49.7 36.2 53.7 45.0 11.4
Shear, no stope 2.7 82.0 84.7 23.0 16.5 20.6 107.0 87.2 97.1 19.8
Shear, with stope 4.7 253.0 258.0 30.7 16.6 25.8 80.2 86.7 83.5 16.7
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Future Directions

• Representing fracturing
• Develop angled explicit fractures ( others)
• Comparisons explicit vs effective results
• Laboratory Experiments
• Existing new
• Laura Pyrak-Nolte (Purdue) Paul Young (uToronto)
• Quantifying Frequency effects
• Size distributions shape
• Shear waves and shear-wave splitting
• Microseismic inversions and mechanisms
• Relevance/ interest to BUMPS?

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Thank you Any Questions?