Henri-Pierre Valero

Broadband Dispersion Extraction Using Simultaneous Sparse Penalization

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 l1 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.

Spectral-method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures

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 calcu-late 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...

Automatic dispersion extraction using continuous wavelet transform

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 Pronys 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 wavenumber-frequency 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.

Monopole radial profiling of compressional slowness

Estimation of near-borehole formation compressional slowness is of significant value for petrophysical and geomechanical applications. Probing the near-borehole (shallow) formation and measuring the radial variation of slowness near-borehole can help identify damaged or altered zones, which is valuable information for wellbore stability and optimal well completion. To obtain the properties of the nonaltered zone, it is necessary to probe the formation as deeply as possible, which requires using an acoustic tool with a sufficiently long source-to-receiver (TR) spacing and a large array aperture. A recently developed sonic tool implements these characteristics and hence meets these objectives (i.e., probing shallow and deep). In addition to these hardware enhancements, a robust and automatic inversion scheme that provides a twodimensional (2D) image of the formation compressional slowness near-borehole has been developed. This technique is based on the inversion of transit times estimated from the waveform recorded by the tool. This inversion scheme is based on an analytical approach, making the implementation of the algorithm fast, robust, and suitable for the wellsite environment. In this paper, we demonstrate how the theoretical improvements, summarized here, enable presentation of a robust and reliable 2D image of the formation compressional slowness variation in the nearborehole in real time and with minimal user interaction. A real field data example will be presented and discussed to illustrate this new profiling technique.

An Automatic Procedure to Detect Microseismic Events Embedded in High Noise

SUMMARY Automatic detection of the presence of microseismic events in noisy recorded hydraulic fracture montoring (HFM) data is not an easy task. The main reasons are first that most of the processing has to be done in an unsupervised manner and next that the signal to noise ratio can vary enormously from one experiment to another and indeed can be quite low; making it difficult to detect the signal embedded in the noise. Moreover the noise often includes spatially correlated components such as borehole modes from pump noise which could look like propagating events making it difficult to identify which are the true desired events. Therefore, in order to solve this detection problem, a statistical procedure combining both the signal and noise information is developed to properly and automatically detect weak events embedded in high noise. This approach based on a new statistical test is applied to detect which time windows contain coherent arrivals across components and sensors in the multi-component array and to indicate the confidence in this detection. Examples on real field data are presented indicating the effectiveness of this method.

Robust Detection and Estimation for Logging While Drilling Monopole Acoustic Data

In this paper, we present methods and strategies for robust detection and slowness estimation of weak compressional (P) and shear (S) waves in borehole sonic logging in noisy environments such as while logging while drilling, by proposing methods for enhancing the semblance used in the slowness time coherence method used in the logging. In this direction our contributions are two fold. First, we propose a novel class of shrinkage estimators in the discrete Radon transform domain derived from data semblance, for waveform de-noising to combat random additive noise and reflections. In this context we also identify necessary and sufficient conditions for the optimality of the proposed estimator. Our second contribution lies in developing a novel method to cancel energy propagating at the slowness of borehole modes, chiefly Stoneley, and to a lesser extent, shear, that significantly lowers the semblance of the weaker head wave arrivals. This approach is based on representing the data using time-frequency compact space-time propagators. Finally, we present an algorithm that combines the space time shrinkage in the discrete Radon transform domain and the proposed interference cancelation strategies for enhanced compressional and shear detection via semblance processing. The algorithm is validated on synthetic data and demonstrated to enhance performance on real logging while drilling field data sets.

Space-time methods for robust slowness estimation for monopole logging while drilling

In this paper we present methods for interference cancelation for robust slowness estimation from noisy Monopole Logging While Drilling (LWD) data. The main contributions are two fold. First, we show via tests on real data sets presence of systematic propagative interferences in Monopole LWD data, which is the primary reason for loss of compression and shear semblance in the Slowness Time Coherence (STC) processing of the LWD data. This interference in turn is mostly dominated by Stoneley type propagative component, which, unlike the main Stoneley mode, is time persistent over the entire acquisition interval. In addition, we also show that in fast formations the shear wave can significantly interfere with the compressional wave making the compressional slowness estimates quite bad. Second, based on these observations we propose a Successive Interference Cancellation (SIC) algorithm to estimate and cancel these interferences leading to STC enhancement and improved slowness estimation of the head waves. The...

Borehole flexural waves in formations with radially varying properties

Elastic wave propagation in a fluid-filled borehole is affected by near-wellbore alteration of formation properties. Near-wellbore alteration can be caused by several sources, such as overbalance drilling, borehole stress concentrations, shale swelling, near- wellbore mechanical damage and supercharging of permeable formations. Optimal completions of a well for production require both identification and estimation of the radial extent of alteration in reservoir intervals. Measured borehole flexural dispersions in the presence of radial gradients in formation properties can be inverted to estimate the radial extent of mechanical alteration. However, the presence of a tool structure that carries the acoustic transmitters and hydrophone receivers also introduces certain amount of bias on the measured borehole flexural dispersions. This paper describes the Backus-Gilbert inversion of synthetic borehole flexural data for radial variation in formation shear slowness (slowness is inverse of velocity). The inversion algorithm accounts for the tool bias on the measured data by introducing an equivalent structure of a heavy-fluid column placed concentrically with the borehole axis. This simple structure enables computation of the eigensolution for a reference homogeneous and isotropic formation that are used for calculating the data kernel in the perturbation integral equation. The solution of this integral equation yields the radial variation in the formation shear modulus in terms of fractional differences in the measured and reference dispersion at various wavenumbers. Results are presented for both radially increasing and decreasing shear slownesses away from the borehole.

Joint Multi-Mode Dispersion Extraction in Frequency-Wavenumber and Space-Time Domains

In this paper, we present a novel broadband approach for the extraction of dispersion curves of multiple time frequency overlapped dispersive modes from borehole acoustic data. The new approach works jointly in the frequency-wavenumber and space-time domains and, in contrast to existing methods it efficiently handles multiple signals with significant time frequency overlap. The proposed method begins by exploiting the slowness (phase and group) and time location estimates obtained by a broadband dispersion extraction method based on frequency-wavenumber ( f-k) domain sparsity penalization proposed in [A. Aeron, S. Bose, H.-P. Valero, and V. Saligrama, “Broadband dispersion extraction using simultaneous sparse penalization,” IEEE Trans. Signal Process., vol. 50, no. 10, pp. 4821-4837, 2011]. In this context, we first present a Cramér-Rao Bound (CRB) analysis for slowness estimation and show that for the f-k domain broadband processing, group slowness estimates have more variance than the phase slowness and time location estimates. In order to improve the group slowness estimates, we exploit the time compactness property of the modes to effectively represent the data as a linear superposition of time compact space-time propagators parameterized by the phase and group slowness. A linear least squares estimation algorithm in the space-time domain is then used to obtain improved group slowness estimates. The performance of the method is demonstrated on real borehole acoustic data sets.

An ultrasonic echo characterization approach based on particle swarm optimization

Presented is a hands-free approach for the extraction and characterization of ultrasonic echoes embedded in noise. By means of model-based nondestructive evaluation approaches, echoes can be represented parametrically by arrival time, amplitude, frequency, etc. Inverting for such parameters is a non-linear task, usually employing gradient-based, least-squared minimization such as Gauss-Newton (GN). To improve inversion stability, suitable initial echo parameter guesses are required which may not be possible under the presence of noise. To mitigate this requirement, particle swarm optimization (PSO) is employed in lieu of GN. PSO is a population-based optimization technique wherein a swarm of particles explores a multidimensional search space of candidate solutions. Particles seek out the global optimum by iteratively moving to improve their position by evaluating their individual performance as well as that of the collective. Since the inversion problem is non-linear, multiple suboptimal solutions exist, and in this regard PSO has a much lower propensity of becoming trapped in a local minima compared to gradient-based approaches. Due to this, it is possible to omit initial guesses and utilize a broad search range instead, which becomes far more trivial. Real pulse-echoes were used to evaluate the efficacy of the PSO approach under varying noise severity. In all cases, PSO characterized the echo correctly while GN required an initial guess within 30% of the true value to converge.