Quantitative determination of uncertainties in seismic refraction prospecting

Abstract

We present a model of the propagation of refracted seismic waves in planar (horizontal or dipping) layered structures in which we quantify the errors from various sources. The model, called the (mixed) variance component model, separates the errors originating on the surface from those due to inhomogeneities of subsurface layers. The model starts with the assumption of homogeneous (constant-velocity) layers, but by taking the principal errors into account, variations from this model (including degree of velocity inhomogeneity, vertical velocity gradients, and gradational interfaces) can be identified.A complete solution to the variance component model by Bayesian methods relies on the Gibbs sampler, a recently well-developed statistical technique. Using the Gibbs sampler and Monte Carlo methods, we can estimate the posterior distributions of any parameter of interest. Thus, in addition to estimating the various errors, we can obtain the velocity-versus-

The sensitivity of seismic refraction velocity models to survey geometry errors, assessed using Monte Carlo analysis

“…Here, t e is defined as the uncertainty in each individual first-break pick introduced by human error and the limited resolution of the data, and as such these errors are independently distributed from geophone to geophone (Liu and Stock, 1993). The correct determination of firstbreak times is also affected by the distortion of waveforms due to filtering effects (Geldart and Sheriff, 2004;Northwood, 1967) and cycle skipping, where first-breaks are picked a cycle or half cycle too early or, more commonly, late.…”

“…as Palmer's (1980) Generalised Reciprocal Method, Visual Interactive Raytracing (Whiteley, 2004), Full Waveform Inversion (Tarantola, 1986), and Wavepath Eikonal Traveltime Tomography (Schuster and Quintus-Bosz, 1993), but these are computationally expensive compared to PM. The simplicity of PM has led to its continued use in near-surface investigations (e.g., Hausmann et al, 2007;Ross et al, 2019), to determine static corrections for seismic reflection investigations (e.g., Bridle, 2007;Opara et al, 2018) and to constrain starting models in seismic inversions (e.g., MASW) (Liu and Stock, 1993). Furthermore, it provides a simple analytic framework for establishing and appreciating the sensitivity of errors to subsurface parameters and survey design.…”

“…The target refractor depth (z D ) is the sum of the unit thicknesses at geophone D. The calculation of unit thicknesses and velocities with PM assumes i) homogeneous and isotropic velocities in overburden layers, ii) that the target refractor has a dip angle <10 o , and iii) first arrivals are the direct wave or critical refractions (Hagedoorn, 1959;Reynolds, 2011). The issues arising when these assumptions are violated have been investigated by Dampney and Whiteley (1980) and Liu and Stock (1993): deviations from assumption (i) can be detected by repeating refraction calculations for adjacent, overlapping seismic spreads, and the contribution of these deviations to the total result uncertainty can be quantified using MC and the Gibbs sampler (Casella and George, 1992). Assumption (ii) is an improvement on the delay-time method's…”

Seismic inversion and uncertainty analysis using a transdimensional Markov chain Monte Carlo method

“…The uncertainty in geophysical inverse problems was estimated by various stochastic inversion algorithms, such as MCMC (Liu and Stock, 1993;Malinverno and Briggs, 2004;Chen and Dickens, 2009;Gunning et al, 2010;Kwon and Snieder, 2011), SA (Dosso, 2002;Dosso and Nielsen, 2002;Bhattacharya et al, 2003;Roy et al, 2005;Varela et al, 2006), PSO (Fernández-Martínez et al, 2012;Rumpf and Tronicke, 2015), and rjMCMC Reading and Gallagher, 2013;Dadi, 2014;Galetti et al, 2015;Dadi et al, 2015).…”