Rock Physics and Biot-Gassmann Equations Quiz

AVO = Amplitude Versus Offset CMP = Common Midpoint AVA = Amplitude Versus Angle AVO-analysis = Analysis of seismic amplitude variation with offset

Center pair of source-receiver = Zero-incidence Seismic CMP gather = Traces collected at Common Mid-Point Increasing offset = Increasing angles of incidence AVO phenomenon = Relationship between reflection coefficient and angle of incidence

Explore reasons for popularity of AVO = Discuss general steps of AVO-analysis workflow Basic theoretical background of AVO analysis = Methods that use AVO principles Seismic traces reflected from subsurface = Have increasing offset and angles of incidence θ Center pair with zero-incidence angle = Angle of incidence and reflected angle are both zero

<p>Reflected (upgoing) P-wave = Compression wave reflecting off an interface Transmitted (downgoing) P-wave = Compression wave passing through an interface Reflected (upgoing) S-wave = Shear wave reflecting off an interface Transmitted (downgoing) S-wave = Shear wave passing through an interface</p> Signup and view all the answers

<p>Bulk modulus K = Affects the compression of the rock Shear modulus 𝜇 = Determines the shear properties of the material Angle of incidence = Influences the reflection coefficients Density of layers above and below = Contributes to the reflection amplitude</p> Signup and view all the answers

<p>Bright spot = Event brighter than others at the same stratigraphic level Main parameters affecting reflection amplitudes = Angle of incidence, density, P and S-wave velocities Gas sands associated feature = Amplitudes changing with offset explaining bright spots Consistent amplitude with increasing offset = Contrast to bright spots in seismic data</p> Signup and view all the answers

<p>Shear modulus 𝜇 = Sole determinant of S-wave velocity Bulk modulus K = No effect on S-wave velocity due to inability to shear fluids Rock matrix elastic properties = Influences both elastic moduli K and 𝜇 Pore fluid properties = Described by Fritz Gassmann's 1951 paper</p> Signup and view all the answers

<p>Incident angle and velocity = Influence reflection coefficients in Zeoppritz equations Density of layers above and below = Contribute to amplitude variations in reflections Bulk modulus K = Affects compression of rock particles by P-waves Shear modulus 𝜇 = Determines shear properties affecting S-waves</p> Signup and view all the answers

<p>P-wave velocity = Used in traditional seismic surveys S-wave velocity = Helps separate rocks with different types of saturation Shear wave velocity = Utilized in AVO method for extracting S-wave type information from P-wave reflections Bulk modulus = Significantly affects P-wave velocity</p> Signup and view all the answers

<p>Gas saturant in pores = Reduces rock density and slightly increases S-wave velocity Introducing gas into pores = Causes a dramatic drop in P-wave velocity Brine-saturated rock = Has a higher bulk modulus than gas-saturated rock Water saturation dropping below 1 = Indicates introduction of gas into the pores</p> Signup and view all the answers

<p>Record converted S-waves using three-component receivers = Expensive but robust approach requiring careful data processing and interpretation Interpret amplitudes of P-waves as a function of offset or angle = Utilizes the AVO method to extract S-wave type information from P-wave reflections Utilize Zoeppritz equations = Contain theory for amplitudes of reflected and transmitted waves at an interface Use single component geophones or hydrophones = Traditionally used for recording P-wave data only in seismic surveys</p> Signup and view all the answers

<p>Poisson's ratio = Can be expressed in terms of Vp and Vs and used as a proxy for Vp/Vs ratio Acoustic Impedance = Can correspond to multiple lithologies if only Vp is known VP/VS ratio = Distinguishes different lithologies when known along with Vp or Vs Shear wave velocity = Enables easy differentiation between types of rocks when known along with Vp or Vs</p> Signup and view all the answers

<p>A = AVO intercept B = AVO slope C = Curvature D = Density contrast</p> Signup and view all the answers

<p>P-wave impedance contrast = Rp(0°) S-wave impedance contrast = Rs(0°) Density contrasts = RD Reflectivity terms = Physical parameters</p> Signup and view all the answers

<p>Aki-Richards equation = Shuey Aki-Richards rearranged = Fatti et al. Shuey approximation = Aki-Richards Fatti et al. formulation = Aki-Richards</p> Signup and view all the answers

<p>Intercept = Amplitude at zero angle Gradient = Rate of change of amplitude with offset Curvature = Significant in far range of angles Impedance contrast = Changes in impedance</p> Signup and view all the answers

<p>AVO effect extraction = A, B, C formulation of Aki-Richards Quantitative P and S reflectivity information extraction = Fatti et al. formulation Changes in impedance interpretation = Original Aki-Richards equation Empirical information extraction about AVO effect = B, the gradient</p> Signup and view all the answers

<p>Intercept A = Acoustic impedance variations across layer boundary Gradient B = Variations of VpVs P-impedance = Indication of reservoir discrimination VpVs ratio = Enhancing reservoir properties</p> Signup and view all the answers

<p>Negative intercept and negative gradient quadrant = Top of gas sand Positive intercept, positive gradient quadrant = Base of gas sand Negative intercept and positive gradient quadrant = Hard event underneath gas reservoir Positive intercept and negative gradient quadrant = Structure boundary</p> Signup and view all the answers

<p>AVO inversion = Enhance reservoir discrimination Wave equations or Zoeppritz equations = Calculate synthetic gathers for feasibility study Rock Physics Modelling = Prior to AVO modelling for understanding expected AVO response Analysis of partial stacks or AVO attributes = Direct methods for analysis</p> Signup and view all the answers

<p>P-wave velocity = Helps in separating rocks with different types of saturation S-wave velocity = Contributes to the elastic properties relationship in AVO Density = Affects the reflection coefficient and angle of incidence in AVO</p> Signup and view all the answers

<p>Gas saturated reservoir anomaly = Analyze Intercept A and Gradient B values Structure boundary anomaly = Cross-plot Intercept and gradient values for given time samples Hard event underneath gas reservoir anomaly = AVO inversion combined with petrophysical study Reservoir discrimination anomaly = Inverted P-impedance and Vp/Vs ratio cross-sections</p> Signup and view all the answers

<p>P-wave velocity = Input well log Density = Input well log S-wave velocity = Input well log Poisson's Ratio = Input well log</p> Signup and view all the answers

<p>Zoeppritz equations = Calculation of reflection coefficients Aki Richards two term equation = AVO curve computation Three term Fatti equation = AVO curve computation Biot-Gassmann equations = Computation of rock properties</p> Signup and view all the answers

<p>Gas Sand Model = Less deviation between two term and three term Fatti equation Wet Sand Model = Less deviation between two term and three term Aki Richards equation</p> Signup and view all the answers

<p>Intercept = Represents amplitude at sin2θ=0 Gradient = Represents change in amplitude with respect to sin2θ</p> Signup and view all the answers

<p>AVO Modeling = Process of creating synthetic data based on rock properties Reflection Coefficients = Values calculated for different incidence angles using Zoeppritz equations Synthetic Gather = Result of convolving reflection coefficients with a seismic wavelet AVO Attributes = Basic characteristics like Intercept and Gradient used to analyze AVO response</p> Signup and view all the answers

<p>Aki-Richards approximation = Expresses the magnitude of a reflection for a given angle in a linear equation with respect to three contrast variables Shuey approximation = An approximation derived from Aki-Richards, used in prestack seismic data interpretation Fatti approximation = Another approximation derived from Aki-Richards, widely used in the industry Koefoed approximation = An earlier approximation for the Zoeppritz equations not considered for practical implementation</p> Signup and view all the answers

<p>∆ρ = Changes in elastic properties of rocks across the layer boundary ∆Vp = Changes in P-wave velocity across the layer boundary ∆Vs = Changes in S-wave velocity across the layer boundary ρ = Average density of properties in two layers</p> Signup and view all the answers

<p>Aki-Richards approximation = Limited to interfaces with small contrasts and assumes small incident angles Shuey approximation = Limited by certain assumptions and conditions in seismic data interpretation Fatti approximation = Has specific constraints on the types of geological formations it can accurately model Koefoed approximation = Not suitable for AVO-analysis due to practical reasons</p> Signup and view all the answers

<p>Aki-Richards approximation = Interpreting amplitude variations with offset in terms of exploration seismic quantities Zoeppritz equations = Not always completely accurate in explaining real seismic responses Approximations to Zoeppritz equations = Designed to better show information conveyed by changes in amplitude Critical milestone methods of prestack seismic data interpretation = Developed based on approximations to Zoeppritz equations</p> Signup and view all the answers

<p>Aki and Richards approximation = Aligned within range of displayed angles of incidence but minor deviations at angles greater than 35 degrees Bortfeld approximation = Aligned within range of displayed angles of incidence but minor deviations at angles greater than 35 degrees Exact solution of Zoeppritz equations = Compared against Bortfeld and Aki-Richards approximations for a given model Chopra and Castagna figure = Shows comparison between Bortfeld, Aki and Richards approximations, and exact solution</p> Signup and view all the answers

<p>Zoeppritz coefficients limitations = Not always completely accurate but still helpful in practical exploration geophysics Various authors' derived approximations = Offer different versions depending on required accuracy or software implementation Effectiveness of Aki-Richards approximation = Significant role despite limitations to small contrasts and incident angles Usefulness of different approximations in software = Dependent on required accuracy or implementation</p> Signup and view all the answers

<p>Shuey approximation origin = Derived from Aki-Richards approximation Fatti approximation origin = Derived from Aki-Richards approximation Koefoed approximation origin = Given earlier by different authors but not considered for practical implementation Aki-Richards approximation origin = [Click] Provides a starting point for deriving practical AVO equations</p> Signup and view all the answers

<p>Using Aki-Richards for small contrasts and incident angles = [Click] Provides a significant role despite limitations Employing Koefoed for AVO-analysis practicality = [Click] Not considered due to practical reasons related to AVO-analysis Applying Fatti for specific geological formations modeling = [Click] Has constraints on accurately modeling certain geological formations</p> Signup and view all the answers

<p>Velocity ratio (VS/VP) = (VS/VP)^2 = 0.25 is assumed at a given time t Sin and Cosine of incident angles = Known values used to calculate weights for each incident angle Weights for each incident angle = Calculated based on known sin and cosine values at a given time t and angle θ Simplified calculation at zero incidence = When theta is zero, sin theta is zero and cos theta is one</p> Signup and view all the answers

<p>Effectiveness of modeling reflectivity = Useful for interpreting amplitude variations with offset based on relevant quantities to exploration seismic. Practicality of deriving information from reflectivity = Not useful when trying to derive information from reflectivity despite being able to model it using parameters. Usefulness of assumptions in Aki-Richards equation = Helps simplify calculations but may not always accurately represent real geological scenarios. Role of approximations in industry = Key methods developed based on these approximations have significantly impacted prestack seismic data interpretation.</p> Signup and view all the answers