Rock Physics: Basic Concepts

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Transcript of Rock Physics: Basic Concepts

  • Stanford Rock Physics Laboratory - Gary Mavko

    14

    Basic Geophysical Concepts

  • Stanford Rock Physics Laboratory - Gary Mavko

    15

    where density K bulk modulus = 1/compressibility shear modulus Lam's coefficient E Young's modulus Poisson's ratio M P-wave modulus = K + (4/3)

    P wave velocity

    S wave velocity

    E wave velocity

    In terms of Poisson's ratio we can also write:

    Relating various velocities:

    Body wave velocities have form: velocity= modulusdensity

    Moduli from velocities:

    = VS2 K = VP

    2 43

    VS

    2

    E = VE2M = VP

    2

    VP2

    VS2 =

    2 1v( )(12v)

    VE2

    VP2 =

    1+ v( )(12v)(1 v)

    v = VP2 2VS2

    2(VP2 VS

    2 )=VE2 2VS2

    2VS2

    VP2

    VS2 =

    4 VE2

    VS2

    3 VE2

    VS2

    VE2

    VS2 =

    3VP2

    VS2 4

    VP2

    VS2 1

    VP =K + (4 / 3)

    =

    + 2

    VS =

    VE =E

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    The reflection coefficient of a normally-incident P-wave on a boundary is given by:

    where V is the acoustic impedance. Therefore,anything that causes a large contrast in impedancecan cause a large reflection. Candidates include:Changes in lithologyChanges in porosityChanges in saturationDiagenesis

    We usually quantify Rock Physics relations interms of moduli and velocities, but in the fieldwe might look for travel time or Reflectivity

    R =2V21V12V2+1V1

    1V12V2

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    In an isotropic medium, a wave that is incident on aboundary will generally create two reflected waves (oneP and one S) and two transmitted waves. The total sheartraction acting on the boundary in medium 1 (due to thesummed effects of the incident an reflected waves) mustbe equal to the total shear traction acting on the boundary inmedium 2 (due to the summed effects of thetransmitted waves). Also the displacement of a point inmedium 1 at the boundary must be equal to the displace-ment of a point in medium 2 at the boundary.

    VP1, VS1, 1

    VP2, VS2, 2

    1

    1

    22

    Reflected P-wave

    Incident P-wave

    Reflected S-wave

    Transmitted P-wave

    Transmitted S-wave N.4

    AVOAmplitude Variation with Offset

    Recorded CMP Gather Synthetic

    Deepwater Oil Sand

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    AVO - Aki-Richards approximation:

    P-wave reflectivity versus incident angle:

    In principle, AVO gives us information aboutVp, Vs, and density. These are critical foroptimal Rock Physics interpretation. Wellsee later the unique role of P- and S-waveinformation for separating lithology,pressure, and saturation.

    Intercept Gradient

    R0 12

    VPVP

    +

    R() R0 +12

    VPVP

    2VS2

    VP2

    + 2 VSVS

    sin2

    +12

    VPVP

    tan2 sin2[ ]

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    Seismic AmplitudesMany factors influence seismic amplitude: Source coupling Source radiation pattern Receiver response, coupling, and pattern Scattering and Intrinsic Attenuation Sperical divergence Focusing Anisotropy Statics, moveout, migration, decon, DMO Angle of Incidence

    Reflection coefficient

    Source Rcvr

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    Intervals or Interfaces? Crossplots or Wiggles?

    Interval Vp vs. Vs

    A

    B

    Rock physics analysis is usually applied to intervals, wherewe can find fairly universal relations of acoustic properties tofluids, lithology, porosity, rock texture, etc.

    In contrast, seismic wiggles depend on interval boundariesand contrasts. This introduces countless variations ingeometry, wavelet, etc.

    Interval Vp vs. Phi

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    Convolutional ModelImpedancevs. depth

    Reflectivity

    ConvolveWith

    wavelet

    Normal IncidenceSeismic

    Normal incidence reflection seismograms can beapproximated with the convolutional model. Reflectivitysequence is approximately the derivative of theimpedance:

    Seismic trace is smoothed with the wavelet:

    R(t) 12ddtln V( )

    S(t) w(t)R(t)Be careful of US vs. European polarity conventions!

    Rock propertiesin each smalllayer

    Derivatives oflayerproperties

    Smoothed imageof derivative ofimpedance

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    Inversion

    Two quantitative strategies to link intervalrock properties with seismic:Forward modelingInversion

    We have had great success in applyingrock physics to interval properties.

    For the most part, applying RP directly tothe seismic wiggles, requires a modelingor inversion step.

    We often choose a model-based study,calibrated to logs (when possible) toDiagnose formation propertiesExplore situations not seen in the wellsQuantify signatures and sensitivities

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    The Rock Physics Bottleneck

    Seismic Attributes

    TraveltimeVnmoVp/VsIp,IsRo, GAI, EIQanisotropyetc

    Acoustic Properties

    VpVsDensityQ

    ReservoirProperties

    PorositySaturationPressureLithologyPressureStressTemp.Etc.

    At any point in the Earth, there are only 3(possibly 4) acoustic properties: Vp, Vs,density, (and Q).

    No matter how many seismicattributes we observe, inversions canonly give us three acoustic attributesOthers yield spatial or geometric information.

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    Problem of ResolutionLog-scale rock physics may be different

    than seismic scale

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    Seismic properties (velocity, impedance,Poisson Ratio, etc) depend on pore pressure and stress

    Units of Stress:

    1 bar = 106 dyne/cm2 = 14.50 psi

    10 bar = 1 MPa = 106 N/m2

    1 Pa = 1 N/m2 = 1.45 10-4 psi = 10-5 bar

    1000 kPa = 10 bar = 1 MPa

    Stress always has units of force/area

    Mudweight to Pressure Gradient

    1 psi/ft = 144 lb/ft3

    = 19.24 lb/gal

    = 22.5 kPa/m

    1 lb/gal = 0.052 psi/ft