The effect of random velocity functions on the travel times and amplitudes of seismic waves

Abstract

Comparisons of the results of the numerical experiments were made with a record section from a long-range refraction profile recorded in Saskatchewan in 1979 by the Canadian COCRUST group. A non-layered interpretation of the observations indicated that an rms velocity deviation of only 1 per cent at any depth and a correlation distance of 5 km were sufficient to explain the irregularities in the observations.

Quantitative determination of uncertainties in seismic refraction prospecting

“…We have chosen to examine the resultant velocity profiles at two locations: 25 percent along the profile, or 24 km from each shot point. For each location, the uncertainties allow the velocity structure above 3 km depth to be fit equally well by a simple velocity increase with depth; this result is quite consistent with that of Ojo and Mereu (1986) who showed that apparently linear segments on traveltime curves might result from small random heterogeneities superposed on a linear velocity increase, particularly in the upper few km where crack closure might lead to a large velocity gradient. For the profile 24 km from SP 12 (Figure 4a), a layer of fairly constant velocity (4.31 km/s), which could have a slight velocity gradient, occurs from 3-6 km depth.…”

“…Furthermore, a simple but realistic assumption about the distributions of the above errors is that these errors are normally distributed; the argument for this assumption is from the central limit theorem in probability theory (see the deterministic and indeterministic decomposition of Ojo and Mereu, 1986). Finally, we assume that the three different types of errors are independent; this is obviously an acceptable assumption.…”

“…Cerveny and Firbas (1984) discussed these methods and provided a method of numerical modeling and inversion of traveltimes of seismic body waves in inhomogeneous anisotropic media. Ojo and Mereu (1986) discussed the magnitude of small-scale velocity inhomogeneities that could account for apparent linearity of segments of first-arrival traveltime curves from refraction data. However, as far as we know, the quantitative measurements of the inhomogeneities (or the estimation of the magnitude of the uncertainties) have not, as yet, been addressed.…”

“…We treat these three types of errors as "random" errors, following Ojo and Mereu's (1986) arguments. The key point is that any "local fixed" effect on the traveltime ofrefracted waves in a relatively large formation can be viewed as a random effect on the total traveltime.…”

Quantitative determination of uncertainties in seismic refraction prospecting

“…On the contrary, trying to investigate the properties, such as velocities, of the Earth's interior under the simplified assumption that the real medium is homogeneous may lead to serious errors (Cerveny and Firbas, 1984;Ojo and Mereu, 1986). To obtain uncertainties in the results of seismic refraction prospecting, the principal errors (or uncertainties) need to be classified.…”