Reconstructing the adhesion stiffness distribution in a laminated elastic plate: Exact and approximate inverse scattering solutions

SUMMARYWe explore the potential of multi-angle AVO inversion of P-P and P-S reflections from a fracture to estimate fracture properties. Although AVO analysis of welded interface like geological layer boundaries is common, the use of AVO variations for nonwelded boundaries like fractures is yet to be investigated. We conduct laboratory experiments to measure reflection responses of dry and wet fractures. The observed P-P reflections of the fracture and the fracture aperture are very well predicted by the nonwelded interface model. We invert the angledependent P-P reflectivity of the fracture to estimate both normal and tangential fracture compliances. The estimated value of the normal compliance is accurate, and it is also possible to obtain the value of the non-zero tangential compliance. We find that supplementing the information of converted P-S reflections in the AVO inversion greatly improves the estimate of the tangential compliance. The calculated compliance ratio clearly shows the existence of fluid in the fracture. This finding can be crucial for new applications in a wide range of scale -from earthquake seismology, deep and shallow seismic exploration, to nondestructive material testing.

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“…tered elastic waves have been used to characterize heterogeneous fracture compliances (e.g., Leiderman et al, 2007;Minato andGhose, 2013, 2014).…”

Section: P-p and P-s Joint Avo Inversionmentioning

confidence: 99%

Laboratory estimation of fracture compliance of a fluid-filled fracture using AVO response of a nonwelded interface

Minato

Ghose

2016

SEG Technical Program Expanded Abstracts 2016

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“…Following Leiderman et al (2007), we estimate the compliance distribution from seismic scattering response. Given the incident stress fieldτ τ τ inc , elastic medium parameters and the background compliance Z 0 , we calculate the perturbed compliance distribution εZ 1 from the upgoing stress field at the fracturê τ τ τ − .…”

Section: (C) Inverse Scattering Solution To Estimate the Compliance Dmentioning

confidence: 99%

“…Extending further the work of Nakagawa et al (2004) and Leiderman et al (2007), we employ the perturbation theory to obtain the dominant information and the power spectral density (PSD) of the heterogeneous fracture compliance. We illustrate this using numerical examples of the modeled scattering response and the estimated compliance distribution and its PSD through fitting the power spectrum of the scattered wavefield.…”

Section: Introductionmentioning

confidence: 99%

Extracting Heterogeneous Compliance of a Single Fracture from Seismic Scattering Coupled with Perturbation Theory

Minato¹,

Ghose²

2013

London 2013, 75th Eage Conference en Exhibition Incorporating SPE Europec

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SUMMARYWe have presented a new methodology to model the scattered wavefield due to a heterogeneous distribution of compliance along a single fracture and then to invert this compliance distribution or its power spectral density (PSD) from the scattered seismic response. We illustrate the validity through numerical examples using Gaussian PSD. First, we show that the perturbation theory offers very close result to that obtained from exact relation (wdSDD approach), by considering only the first 3 orders of perturbation. By solving the inverse scattering problem we can estimate the heterogeneous compliance distribution quite accurately. Next, in order to estimate the PSD of the heterogeneous compliance distribution, the normalized power of the stress field is used. We use the result from the wdSDD approach to represent the observed data. We show the possibility of successful extraction of the correct PSD by curve-fitting. The techniques presented here can lead to a conceptually new and accurate approach for estimating heterogeneous compliance distribution and the corresponding spatial variation in roughness and aperture along the fracture plane. This may, in turn, be related to the crucial fluid flow properties in the fractured subsurface.

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“…If the heterogeneity further away from the fracture is taken into consideration, additional steps of processing are needed to calculate correctly the stress field from the scattered wavefield. Leiderman et al (2007) have developed a method to directly estimate the heterogeneous compliance distribution from the scattered wavefield. Their method assumes a multilayered background medium.…”

Section: Introductionmentioning

confidence: 99%

Power spectral density of the heterogeneous fracture compliance from scattered elastic wavefields

Minato

Ghose

2014

GEOPHYSICS

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Using the scattered elastic wavefield, a method to derive the power spectral density (PSD) of the heterogeneous compliance distribution, along the plane of a single fracture, is formulated. The method involves estimation of the stress field at the fracture depth from the scattered wavefield followed by least-squares optimization of the PSD of the stress field. We consider a 2D geometry and incident plane waves. The derivations are made in the frequency-wavenumber domain. To derive the relationship between the scattered wavefield and the PSD of the heterogeneous compliance, perturbation theory is used. In the forward modeling, the scattering response of the heterogeneous compliance is estimated, assuming a stationary random process. Numerical tests of the proposed method of PSD estimation offer important insights. The estimated PSD of the compliance (given by the standard deviation δ and the correlation length l c , assuming a Gaussian distribution) as a statistical measure of the heterogeneous fracture compliance is robust against fracture depth uncertainties. Furthermore, the sparse spatial sampling of the wavefield is not problematic as long as the data contain those wavenumber components which represent the slope of the PSD of the stress field. However, when the sampling interval is too large compared to the correlation length of the heterogeneous compliance distribution, it is difficult to estimate accurately the PSD of the compliance due to spatial aliasing and small amplitude variation within the available wavenumber. For a given spatial sampling, the use of higher frequencies results in a stronger amplitude variation in the scattered wavefield. This leads to better estimates of the PSD of the compliance via a least-squares optimization. In the presence of white noise, a change in the PSD of the stress field at the fracture depth significantly affects the PSD estimates. In this case, a data-driven amplitude correction improves the estimates of δ and l c .

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Reconstructing the adhesion stiffness distribution in a laminated elastic plate: Exact and approximate inverse scattering solutions

Cited by 24 publications

References 12 publications

Laboratory estimation of fracture compliance of a fluid-filled fracture using AVO response of a nonwelded interface

Laboratory estimation of fracture compliance of a fluid-filled fracture using AVO response of a nonwelded interface

Extracting Heterogeneous Compliance of a Single Fracture from Seismic Scattering Coupled with Perturbation Theory

Power spectral density of the heterogeneous fracture compliance from scattered elastic wavefields

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