Migration of Synthetic Seismograms For Crustal Structures With Random Heterogeneities

SUMMARY Studying seismic wave propagation in non‐deterministic media is interesting as some parts of the Earth (e.g. in the continental lower crust) may be amenable to a stochastic description. In this paper we study the acoustic response of a 1‐D binary stochastic fractal medium and separate the single‐ from the multiple‐scattered wavefield. We show that, for our models with scales that (partly) overlap the seismic bandwidth, amplitude changes occur due to both the presence of multiple scattering and the multiscale nature of the impedance contrasts. We study these changes as functions of σc (a measure of the nominal bimodal reflection coefficient), ka (a measure of the relative length scales of the medium compared to the wavelength of the probing waves) and γ, the scatterer density. As our models are binary (two lithologies), the results should be interpreted as an upper bound for the general class of acoustic 1‐D stochastic fractal model responses. We present a measure to quantify the interference of single‐ and multiple‐scattered wavefields, and use this measure to study the importance of the three aforementioned dependences. Since stochastic fractal media have been proposed for Ivrea‐type lower crust, we relate our results to such a model and find that amplitudes may increase by up to 45±15 per cent. The contribution of multiple scattering to this increase ranges from 1±1 to 20±15 per cent, the main contribution being due to the multiscale nature of the impedance contrasts. We claim that the parameters used to model Ivrea‐type lower crust (σc=5 per cent, γ≈5×10−2, 1≤ka≤24 and μ=9.6×10−1) are robust, although we recognize that the scatterer density γ is determined by the vertical sampling Δz in our models. The heuristic argument that extra geometrical spreading in two/three dimensions will further diminish the importance of multiple‐scattering effects, combined with our results, makes it tempting to claim that multiple scattering is not important for 2/3‐D generalizations of our 1‐D models. However, in the light of indirect evidence for the importance of multiple scattering in Ivrea‐type lower crust reported by other authors, we argue that elasticity (P–S conversions) may be important. Therefore, we believe that it is necessary to study the 2‐D case with a similar direct approach to that presented in this paper before a satisfactory conclusion can be drawn about the validity of the standard processing of deep seismic reflection data and the importance of multiple scattering.

Section: Discussionmentioning

confidence: 65%

Amplitude effects due to multiscale impedance contrasts and multiple scattering: implications for Ivrea-type continental lower crust

Douma

Roy‐Chowdhury

2001

“…Evidence of such behaviour is found in the western Pacific, which contains zones of more intense scattering (Vidale & Hedlin 1998) and ultra‐low‐velocity zones (Wen & Helmberger 1998) in the lowermost 50–100 km of the mantle. The work of Emmerich et al . (1993) suggests that further work may be needed in testing the effects of multiple scattering in regions where isotropic heterogeneity may be mistaken for anisotropic heterogeneity when velocity perturbations approach 5 per cent.…”

Section: Discussionmentioning

confidence: 99%

Anisotropy of heterogeneity scale lengths in the lower mantle from PKIKP precursors

Cormier

1999

The anisotropy of heterogeneity scale lengths in the lower mantle is investigated by modelling its effect on the high‐frequency precursors of PKIKP scattered by the heterogeneities. Although models having either an isotropic or an anisotropic distribution of scale lengths can fit the observed coda shapes of short‐period precursors, the frequency content of broad‐band PKIKP precursors favours a dominantly isotropic distribution of scale lengths. Precursor coda shapes are consistent with 1 per cent fluctuations in P velocity in the wavenumber band 0.05–0.5 km−1 extending to 1000 km above the core–mantle boundary, and with a D″ region open to circulation throughout the lower mantle. The level of excitation of PKIKP precursors observed in the frequency band 0.02–2 Hz requires a power spectrum of heterogeneity that is nearly white or slowly increasing with wavenumber. Anisotropy of scale lengths may exist in a D″ layer having larger horizontal than vertical scale lengths and produce little or no detectable effects on PKIKP precursors for P‐velocity perturbations as high as 3 per cent when averaged over a vertical scale of several kilometres, and much higher when averaged over scales of hundreds of metres or less.

“…Also, a reliable seismic velocity model is crucial for successful imaging of the geological structure which also includes true amplitude recovery, normal moveout corrections, stacking and migration. The above are not always valid/available for wavefields backscattered from strongly scattering stochastic fields (Gibson & Levander 1990; Emmerich et al 1993); alternate seismic processing and imaging strategies may, therefore, also be considered.…”

Section: Introductionmentioning

confidence: 99%

Underestimation of scale lengths in stochastic fields and their seismic response: a quantification exercise

Carpentier¹,

Roy‐Chowdhury²

2007

S U M M A R YThe possibility that parts of the Earth's continental lower crust can be described with stochastic geological models has been suggested for some time. Recent studies of deeper well logs also indicate a possible stochastic structure at mid-crustal levels. This motivates a closer examination of the relation between the statistics of reflection wavefields and that of the lower crust. Such a relation can put important constraints on possible lower crustal models. This study follows up earlier efforts to quantify the statistics of both stochastic lower crustal models and the reflected wavefield. Since modelling of the seismic response of stochastic (von Karman) fields implies the usage of the impedance contrast field of the latter, we wish to compare the second-order statistics of both types of fields (velocity and impedance). This study concludes that the vertical derivative operator on a von Karman velocity field, implicitly present in the impedance contrast field, alters the second-order horizontal von Karman statistics of the velocity fields in a profound way. Wavefield effects, undoubtedly present in observed seismic data, which have earlier been proposed as possible causes for the aforementioned change, seem to play a secondary role. The vertical derivative operation, inherent in the impedance contrast field, reduces the estimated horizontal scale length and Hurst number by a factor of 2-22 and 1-3, respectively. Original vertical scale length and Hurst number of the velocity fields have a (quasi-)linear influence on this underestimation. Horizontal scale lengths and Hurst numbers were also estimated from the seismic response (Primary Reflectivity Section) of the von Karman fields. The values obtained are close to those obtained from the causative impedance contrast fields, and are similarly underestimated. This suggests a dominant role for the vertical derivative operator in the underestimation of horizontal scale length and Hurst number. This attempt to quantify the relation between the horizontal spatial statistics of von Karman fields and the estimates derived from their seismic response, may be useful in upscaling the latter.