Elastic parameter estimation

This section describes the inversion of a single R_pp and $\theta_{pp}$ offset gather by SVD to produce a single depth trace each of P-impedance (I_p), S-impedance (I_s), and density ($\rho$). Recall that these parameters are of the form $\delta m / \bar{m}$, where $\delta m$ is the change in a given property value, and $\bar{m}$ is the average property value, i.e. -- relative changes in elastic material properties.

Figure shows the three elastic parameter traces I_p(z;x), I_s(z;x) and $\rho(z;x)$ (as a function of depth z, for a fixed surface position x). The first depth trace is the P-impedance trace I_p. The correct model values (in %) from Table are plotted in parentheses, adjacent to the m/i estimated peak values. The I_p estimates are seen to be reasonably accurate. Again the first event at 1960 m is weak due to the mute pattern in the shot records affecting the R_pp estimation, and the events below the gas (2960 m) are weak due to attenuation through the low Q gas layer. The I_s estimates are also seen to be quite reasonable, although perhaps less robust than I_p. Also, although the I_s relative change of 0% has been correctly estimated at the gas sand, there are wavelet sidelobe artifacts which would make it difficult to resolve in field data situations. A similar situation applies to the impedance change at 3100 m where two closely spaced reflections overlap into one apparent reflection. This is analogous to a thin bed resolution problem and linearized amplitude tuning effects. Although the I_s estimate is correct at 3100 m (somewhat fortuitously), the overlap of two distinct wavelets erroneously suggests a single impedance change of a large negative polarity which is clearly incorrect. Lastly, the density variation is completely unreliable, except for perhaps the 1960 m event which has the correct polarity and roughly approximate amplitude due to its large specular angle coverage ($\sim 45^{\circ}$). This will be explained further in the next section under the topic of choice of elastic parameterization for the inversion.

 

impinv
Figure 6 Marine synthetics impedance inversion: I_p, I_s, and $\rho$.

In summary, with accurate synthetic data and a realistic recording geometry and background model, we are able to recover very reasonable I_p estimates, somewhat less robust I_s estimates, and very little (if any) information about density variations.