What you can get from reflection seismology

Luckily, it has been discovered that certain functions of $\rho$ and K can be reliably determined and mapped. The velocity v and the acoustic impedance R are given by the equations

$$\begin{eqnarray} v \ \ \ &=&\ \ \ \sqrt { K / \rho } \\ R \ \ \ &=&\ \ \ \sqrt { K \rho }\end{eqnarray}$$ (24) (25)

Mathematically, it is a simple job to back-solve equations (24) and (25), which gives

$$\begin{eqnarray} K \ \ \ &=&\ \ \ v\,R \\ \rho \ \ \ &=&\ \ \ {R \over v }\end{eqnarray}$$ (26) (27)

In practice, the solutions (26) and (27) have little value because the two parameters v and R are seen through nonoverlapping spectral windows. The acoustic impedance R is seen through the typical 10 to 100 Hz spectral window of good quality reflection data. Since the low frequency part of the spectrum is missing, it is common to say that it is not the impedance which is seen, but the gradient $\ \it\hbox{reflectivity} \ =$$c(x,z) \ =$$d\ln R/ dz=$R^-1dR/dz which is more familiar at a layer boundary where it has the form (R₁-R₂) / (R₁+R₂).

The velocity v is seen through a much smaller window. Observation of it involves studying travel time as shot-to-geophone offset varies and will be described in chapter . With this second window it is hard to discern sixteen independent velocity measurements on a 4-second reflection time axis. So this window goes from zero to about 2 Hz, as depicted in Figure 13.

 

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Figure 13 Reliability of information obtained from surface seismic measurements.

Note that there is an information gap from 2-10 Hz. Even presuming that rock physics can supply us with a relationship between $\rho$ and K, the gap seriously interferes with the ability of a seismologist to predict a well log before the well is drilled. What seismologists can do somewhat reliably is predict a filtered log.

The observational situation described above has led reflection seismologists to a specialized use of the word velocity. To a reflection seismologist, velocity means the low spatial frequency part of ``real velocity.'' The high-frequency part of the ``real velocity'' isn't called velocity: it is called reflectivity. Density is generally disregarded as being almost unmeasurable by surface reflection seismology.