S U M M A RYThis paper presents an application of 2.5-D asymptotic viscoacoustic di¡raction tomography to ultrasonic data recorded during a physically scaled laboratory experiment. This scaled experiment was used to test the reliability of our method when applied to a real data set to estimate the attenuation factor Q.Di¡raction tomography relies on ray theory to compute the Green functions in a smooth background medium and on the Born approximation to linearize the relation between the scattered wave¢eld and the velocity and Q perturbations. The perturbations are inferred from the data by an iterative (linear) quasi-Newtonian algorithm.The inversion formula was speci¢cally developed to account for the acquisition geometry designed in this study. The derivation of the Hessian operator shows that, for this acquisition, the velocity and Q perturbations are theoretically decoupled.The processing of the data was split into two steps: ¢rst, we applied the tomography to the data without deconvolving them. Second, we designed a post-processing procedure for the tomographic images to remove the source signature and to estimate the absolute values of the velocity and the attenuation factor Q. At the conclusion of the ¢rst step, both the velocity and the Q tomographic images allowed one to delineate the gross contour of the target. We obtained an excellent match between the observed data and the viscoacoustic ray^Born synthetics. The match obtained with the viscoacoustic rheology was signi¢cantly better than for a purely acoustic one.In the second step, the post-processing allowed us to recover the shape of the target. We estimated the absolute values of the velocity and Q, although we had no quality control with regard to these results (the rheological properties of the material used in this study were unknown). The results suggest that the uncertainty of the velocity measurement is lower than that for Q.The application presented in this study suggests that the procedure that we designed (experimental set-up, tomography, post-processing) can be useful for estimating rock properties in the framework of a laboratory experiment. Generalization of the method to other acquisition con¢gurations such as surface seismic data requires further work.
In this paper, we propose a broadband method to extract the dispersion curves for multiple overlapping dispersive modes from borehole acoustic data under limited spatial sampling. The proposed approach exploits a first order Taylor series approximation of the dispersion curve in a band around a given (center) frequency in terms of the phase and group slowness at that frequency. Under this approximation, the acoustic signal in a given band can be represented as a superposition of broadband propagators each of which is parameterized by the slowness pair above. We then formulate a sparsity penalized reconstruction framework as follows. These broadband propagators are viewed as elements from an overcomplete dictionary representation and under the assumption that the number of modes is small compared to the size of the dictionary, it turns out that an appropriately reshaped support image of the coefficient vector synthesizing the signal (using the given dictionary representation) exhibits column sparsity. Our main contribution lies in identifying this feature and proposing a complexity regularized algorithm for support recovery with an 1 type simultaneous sparse penalization. Note that support recovery in this context amounts to recovery of the broadband propagators comprising the signal and hence extracting the dispersion, namely, the group and phase slownesses of the modes. In this direction we present a novel method to select the regularization parameter based on Kolmogorov-Smirnov (KS) tests on the distribution of residuals for varying values of the regularization parameter. We evaluate the performance of the proposed method on synthetic as well as real data and show its performance in dispersion extraction under presence of heavy noise and strong interference from time overlapped modes.
A method, called "seismic endoscopy," able to perform three-dimensional (3-D) acoustical imaging in a cylindrical volume around shallow-depth boreholes is described. The main characteristics of borehole tools designed and constructed in our laboratory are presented. Several tests performed in an acoustical water tank are used to illustrate the basic imaging algorithms adapted to the particular acquisition geometry of the probes. In particular, both the filtering of borehole waves and azimutal refocusing are discussed. Index Terms-Azimuthal move out (AMO), borehole waves, continuous wavelet transform, three-dimensional (3-D) geophysical imaging, tube waves, vertical seismic profile.
In this paper we present a novel framework for automatic extraction of dispersion characteristics from acoustic array data. Traditionally high resolution narrow-band array processing techniques such as Prony's polynomial method and forward backward matrix pencil method have been applied to this problem. Fundamentally these techniques extract the dispersion components frequency by frequency in the wavenumberfrequency transform domain of the array data. The dispersion curves are subsequently extracted by a supervised post processing and labelling of the extracted wavenumber estimates, making such an approach unsuitable for automated processing. Moreover, this frequency domain processing fails to exploit useful time information. In this paper we present a method that addresses both these issues. It consists in taking the continuous wavelet transform (CWT) of the array data and then applying a wide-band array processing technique based on a modified Radon transform on the resulting coefficients to extract the dispersion curve(s). The time information retained in the CWT domain is useful not only for separating the components present but also for extracting group slowness estimates. The latter help in the automated extraction of smooth dispersion curves. In this paper we will introduce this new method referred to as the Exponential Projected Radon Transform (EPRT) in the CWT domain and limit ourselves to the analysis for the case of one dispersive mode. We will apply the method to synthetic and real data sets and compare the performance with existing methods.
A new spectral-method algorithm can be used to study wave propagation in cylindrically layered fluid and elastic structures. The cylindrical structure is discretized with Chebyshev points in the radial direction, whereas differentiation matrices are used to approximate the differential operators. We express the problem of determining modal dispersions as a generalized eigenvalue problem that can be solved readily for all eigenvalues corresponding to various axial wavenumbers. Modal dispersions of guided modes can then be expressed in terms of axial wavenumbers as a function of frequency. The associated eigenvectors are related to the displacement potentials that can be used to calculate radial distributions of modal amplitudes as well as stress components at a given frequency. The workflow includes input parameters and the construction of differentiation matrices and boundary conditions that yield the generalized eigenvalue problem. Results from this algorithm for a fluid-filled borehole surrounded by an elastic formation agree very well with those from a root-finding search routine. Computational efficiency of the algorithm has been demonstrated on a four-layer completion model used in a hydrocarbon-producing well. Even though the algorithm is numerically unstable at very low frequencies, it produces reliable and accurate results for multilayered cylindrical structures at moderate frequencies that are of interest in estimating formation properties using modal dispersions.
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