Estimation of crustal stochastic parameters from seismic exploration data

Abstract

Abstract.Stochastic models for the crystalline crust produce synthetic seismograms that compare well with recorded data for a variety of crustal ages and tectonic environments. In this paper, we explore the parameter space describing such stochastic models as a basis for formulating the inverse problem; that is, we wish to estimate the parameters which define a stochastic model from the recorded backscattered wave field. We base the estimation on approximate relations between the primary reflectivity series, which is the ideal wave field response of a medium, and various seismic gathers. A two-dimensional lateral correlation method is used to investigate the sensitivity of synthetic wave fields to horizontal characteristic length. A derived empirical relationship relates the scale length to the half width of the correlation coefficient. A horizontal wavenumber-time domain spectral analysis successfully estimates the horizontal characteristic length (a•) and the fractal dimension (D) of the stochastic medium from which the wave field was backscattered.

Estimation of the lateral correlation structure of subsurface water content from surface‐based ground‐penetrating radar reflection images

“…[6] To relate the 2-D spatial autocorrelation of a GPR reflection image to that of the underlying water content distribution, we begin with the assumption that the recorded GPR data, after suitable processing, can be approximately modeled by what is known as a primary reflectivity section (PRS) [e.g., Gibson, 1991;Pullammanappallil et al, 1997;Bean et al, 1999]. That is, we assume that the processed and migrated/imaged GPR data can be treated as the convolution product of a reflection coefficient distribution, which is approximately obtained by vertical differentiation of the underlying radar wave velocity distribution, with a source wavelet function.…”

“…In the seismic literature, the current consensus appears to be that, although there clearly exists a relationship between the lateral correlation properties of seismic data and those of the underlying velocity distribution for weakly scattering media, the nature of this relationship is largely unclear. Work by Holliger et al [1994] and Pullammanappallil et al [1997] initially suggested that the average lateral correlation structures of both of these fields should be equivalent. However, the more recent results of Bean et al [1999] and Carpentier and Roy-Chowdhury [2007] have pointed out the fundamental dependence of the lateral correlation properties of a seismic image on bandwidth and on the vertical derivative operator that acts to create reflection coefficients from an impedance field, respectively.…”

“…[3] A number of studies have explored the relationship between the lateral correlation structure of seismic and radar velocity fields and those of the corresponding seismic and GPR reflection data [e.g., Gibson, 1991;Hurich, 1996;Pullammanappallil et al, 1997;Line et al, 1998;Rea and Knight, 1998;Bean et al, 1999;Knight et al, 2004;Oldenborger et al, 2004;Dafflon et al, 2006;Carpentier and Roy-Chowdhury, 2007;Knight et al, 2007]. Although the seismic and GPR communities have to date worked largely independently of one another, it is important to note that the results obtained are mutually transferrable because of the strong mathematical analogies that exist between seismic and electromagnetic wave propagation [e.g., Carcione and Cavallini, 1995;Belina et al, 2009].…”

Geostatistical inversion of seismic and ground‐penetrating radar reflection images: What can we actually resolve?

“…This means that we estimate parameters describing the geostatistical nature of the heterogeneity, rather than a detailed distribution of material properties. To this end, estimation of the geostatistical properties of subsurface velocity heterogeneity from surface-based seismic and ground-penetrating radar (GPR) reflection images has been a long-standing problem of significant interest [e.g., Holliger et al, 1992;Hurich, 1996;Pullammanappallil et al, 1997;Rea and Knight, 1998;Bean et al, 1999;Poppeliers and Levander, 2004;Carpentier and Roy-Chowdhury, 2007;Knight et al, 2007]. Of particular interest has been the estimation of the lateral statistics of a subsurface velocity field from those of the corresponding reflection image, as this information cannot be obtained from borehole log or core analysis.…”

Sub-basalt seismic imaging using optical-to-acoustic model building and wave equation datuming processing

“…This internal heterogeneity and the existence of rough surfaces can severely distort and scatter the seismic wavefield. The role of wave scattering in seismic imagery is well documented in the literature (Gibson and Levander, 1998;Martini et al, 2001;Martini and Bean, 2002a;Pullammanappallil et al, 1997) as well as the effect of irregular interfaces on wave propagation (Hestholm and Ruud, 2000;Bean, 2002a,b, Paul andCampillo, 1988;Purnell et al, 1990). This scattering can be both coherent, where waves reverberate within individual layers, and incoherent, producing 'random noise' through which deeper sub-basalt reflections are difficult to identify (Martini and Bean, 2002a,b).…”