- #Kennett elastic wave avo modelling hampson russell full
- #Kennett elastic wave avo modelling hampson russell series
#Kennett elastic wave avo modelling hampson russell series
In structured areas, a series of shot gathers are generated based on a geological model and these shot gathers are the input for further processing. In AVO modeling, a single shot gather with a flat-layered model can be generated for the cases where the structural effect is not the major concern. It calculates particle motion for a space location at an advanced time exclusively from the motion that is already determined for previous time. In finite difference calculation, explicit scheme approach is often used. For 3-D case, one may refer to the finite difference equations given by Jastram and Tessmer (1994). (1976) gave a detailed description of 2-D finite difference equations. To numerically stimulate wave propagation in subsurface, the equations of motion are often transformed into finite difference equations with given boundary conditions. In Table 2, Sx and Sz are source components.
The form expressed by displacements, ux and uz is derived through using strain-displacement relations and stress-strain relations. The equations of motion are derived first based on Newton’s law and expressed by stress components σ x, σ z and τ zx. Table 2 lists 2-D elastic wave equations. For example, Shuey’s equation yields estimates of zero-offset reflectivity and gradient and Fatti’s equation gives estimates of P- and S-reflectivities. In AVO attribute inversion, least squares method (L2) or absolute deviation minimization (L1) methods that fits the observed amplitudes to a linear equation are often used.
AVO attributes are then calculated based on the simplified Zoeppritz equations that have been discussed in Part 1 of this paper (Li et al., 2003). In AVO modeling, Zoeppritz equations are used to generate exact solutions. Zoeppritz equations for reflected P-wave and converted S-wave. It can be seen that they have complex forms. Where a1, b1 and r1 are P- and S-wave velocities and density for the layer above and a2, b2 and r2 are for the layer below i1 and i2 are reflected and transmitted angles for P-wave and j1 and j2 are the reflected and transmitted angles for S-waves. The commonly used equations are: an incident P-wave is reflected as a P-wave (P-P) or a converted S-wave (P-SV). Zoeppritz equations and elastic wave equationsįor a two-layer interface, in total sixteen Zoeppritz equations describe the energy partitioning of reflected and transmitted waves (Aki and Richards, 1980). This paper, Part 2 of AVO Modeling in Seismic Processing and Interpretation, reviews Zoeppritz equations and elastic wave equations and discusses pros and cons of the methodologies in AVO modeling. For structured plays, elastic wave equation modeling is especially useful in both imaging and AVO analysis.īased on Zoeppritz modeling and elastic wave equation modeling, different methodologies in AVO modeling are developed to take into account of the issues in association with data acquisition, processing and interpretation. Baker (1989) summarized the advantages using wave equation modeling in the cases of complex geology or complex wave phenomena as: a) automatic generation of diffractions, critical refraction and multiples b) more accurate amplitudes and waveforms, especially in the presence of small structures and thin beds and c) no missing of seismic events regardless of complexity. It overcomes the shortcomings of the ray tracing approach that breaks down in many cases such as at the edges where the calculated amplitude is infinite or in the shadow zones where the amplitude is zero. Elastic wave equation modeling, however, accounts for direct waves, primary and multiple-reflection waves, converted waves, head waves, as well as diffraction waves. Zoeppritz modeling has the advantages of being fast and easy for identifying primary reflections. The main difference between these two techniques is the former calculates the primary-only reflectivities and the latter calculates particle displacements in subsurface.
#Kennett elastic wave avo modelling hampson russell full
Zoeppritz’s equations with ray tracing and full elastic wave equation with finite difference method (FDM) are two most commonly used techniques in AVO modeling.