Deconvolution Of Seismic Data Research Articles

Data and model dual-driven seismic deconvolution via error-constrained joint sparse representation

Deconvolution is an essential step in seismic data processing. Sparse-spike deconvolution often is used to enhance the resolution of the seismic image by adding a model-driven regularization term. However, this method does not consider the features of the data, nor does it exactly describe the relationship between seismic data and the desired attribute (such as seismic reflectivity). We have developed a data and model dual-driven seismic deconvolution method based on error-constrained joint sparse representation (SR) using borehole measurement and surface seismic data. The combined features of the borehole reflectivity and the surface seismic data can be obtained through joint dictionary learning. With the help of the joint dictionary, the relationship between seismic waveforms and reflectivity is captured by the sparse coefficients. We construct the regularization term of deconvolution by alternately decomposing the error of the synthesized data via sparse reconstruction and the observed seismic data. Unlike model-driven methods, the constraint term of the new method can be established by the error-constrained SR. Based on this SR, the initial model of reflectivity is obtained to realize the sparse deconvolution of seismic data under the constraint of borehole data features. In general, this method is a data and model dual-driven deconvolution. Synthetic and field data tests demonstrate that this method can effectively improve the resolution and accuracy of deconvolution.

The high‐resolution seismic deconvolution method based on joint sparse representation using logging–seismic data

ABSTRACTSeismic high‐resolution processing is an essential part of seismic processing. Sparse‐spike deconvolution is a widely used method for improving the resolution of seismic data. However, the stratigraphic reflection coefficients do not fully satisfy the hypothesis of sparse‐spike deconvolution, and this method does not make full use of prior information, such as well‐logging data. In this paper, we have developed a high‐resolution processing method based on joint sparse representation using logging and seismic data. This method can extract stratigraphic information from well‐logging reflection coefficients and observational seismic data at the same location by joint dictionary learning. Through joint sparse representation, the relationship between observed seismic data and the reflection coefficient is established. Under the framework of joint sparse representation, the deconvolution of seismic data is realized. The synthetic data and field data tests show that our method can reveal thin layers and can invert reflection coefficients from strongly noisy seismic data accurately. Moreover, the deconvolution results of our method match well with the well‐logging data. The tests demonstrate that the improvement of accuracy of deconvolution results with our method, compared to sparse‐spike deconvolution.

High-Resolution Seismic Data Deconvolution by A0 Algorithm

Sparse spikes deconvolution is one of the oldest inverse problems, which is a stylized version of recovery in seismic imaging. The goal of sparse spike deconvolution is to recover an approximation of a given noisy measurement T = W ∗ r + W 0 . Since the convolution destroys many low and high frequencies, this requires some prior information to regularize the inverse problem. In this paper, the authors continue to study the problem of searching for positions and amplitudes of the reflection coefficients of the medium (SP&ARCM). In previous research, the authors proposed a practical algorithm for solving the inverse problem of obtaining geological information from the seismic trace, which was named A 0 . In the current paper, the authors improved the method of the A 0 algorithm and applied it to the real (non-synthetic) data. Firstly, the authors considered the matrix approach and Differential Evolution approach to the SP&ARCM problem and showed that their efficiency is limited in the case. Secondly, the authors showed that the course to improve the A 0 lays in the direction of optimization with sequential regularization. The authors presented calculations for the accuracy of the A 0 for that case and experimental results of the convergence. The authors also considered different initialization parameters of the optimization process from the point of the acceleration of the convergence. Finally, the authors carried out successful approbation of the algorithm A 0 on synthetic and real data. Further practical development of the algorithm A 0 will be aimed at increasing the robustness of its operation, as well as in application in more complex models of real seismic data. The practical value of the research is to increase the resolving power of the wave field by reducing the contribution of interference, which gives new information for seismic-geological modeling.

Multichannel sparse deconvolution of seismic data with shearlet–Cauchy constrained inversion

Multichannel sparse deconvolution of seismic data with shearlet–Cauchy constrained inversion

Seismic data deconvolution using Kalman filter based on a new system model

Seismic resolution plays an important role in geologic interpretation and reservoir prediction. To improve the vertical resolution of a seismic image, we have developed a new Kalman filter system model for seismic deconvolution. Similar to the conventional Kalman filter model for seismic deconvolution, our new Kalman model is also based on the common viewpoint that a reflected seismic record can be regarded as a convolution of a seismic wavelet with a reflection coefficient series. The new model uses a reversed seismic wavelet to slide across a reflectivity function to achieve the convolution result, instead of using a reversed reflectivity function to slide across a seismic wavelet in the conventional Kalman filter model. A simpler state equation for the new model is achieved, and the number of parameters to select is fewer than the conventional. Furthermore, the number of parameters can be reduced to only one by a theoretical demonstration for stationary noisy signals, which decreases the requirement for multiple parameters selection in the conventional model. The practical selection for this parameter should be a compromise between resolution improvement and noise amplification. Experimental results in the time and frequency domains on synthetic and field seismic records revealed that the Kalman filter based on the new model has the advantages of a higher resolution and peak signal-to-noise ratio (PS/N) than the conventional Kalman filter for stationary and nonstationary signals, and it works similarly to the Wiener filter for stationary signals, and it is superior to the Wiener filter in resolution and PS/N for nonstationary signals. The Kalman filter based on the new model can be applied to seismic resolution improvement.

Dynamic deconvolution of seismic data based on generalized S-transform

Abstract The commonly used methods to improve resolution of seismic data are based on stationary convolution model that is inconsistent with the actual propagation law of seismic wavelet in inhomogeneous media. Therefore, to address this artifact, in this paper authors take seismic scattering and attenuation into integrative consideration, and propose an adaptively dynamic deconvolution method based on generalized S-transform (GST). This method introduces the favorable multi-resolution characteristics of GST into the dynamic deconvolution. Firstly, GST of nonstationary seismic trace can be approximately presented as the product of GST of the dynamic propagating wavelet and the reflectivity in time–frequency domain. We then use polynomial fitting to model the time–frequency spectra of nonstationary seismic trace to obtain the estimation of dynamic propagation wavelet and the reflectivity. This method, without calculating directly the value of Q , is applicable to the case when Q varies, and is robust in the presence of noise. Applications to synthetic and field data validate that this method can effectively enhance seismic data resolution without boosting noise, and restore the attenuated energy of nonstationary seismic signal.

Gabor deconvolution: Estimating reflectivity by nonstationary deconvolution of seismic data

We have extended the method of stationary spiking deconvolution of seismic data to the context of nonstationary signals in which the nonstationarity is due to attenuation processes. As in the stationary case, we have assumed a statistically white reflectivity and a minimum-phase source and attenuation process. This extension is based on a nonstationary convolutional model, which we have developed and related to the stationary convolutional model. To facilitate our method, we have devised a simple numerical approach to calculate the discrete Gabor transform, or complex-valued time-frequency decomposition, of any signal. Although the Fourier transform renders stationary convolution into exact, multiplicative factors, the Gabor transform, or windowed Fourier transform, induces only an approximate factorization of the nonstationary convolutional model. This factorization serves as a guide to develop a smoothing process that, when applied to the Gabor transform of the nonstationary seismic trace, estimates the magnitude of the time-frequency attenuation function and the source wavelet. By assuming that both are minimum-phase processes, their phases can be determined. Gabor deconvolution is accomplished by spectral division in the time-frequency domain. The complex-valued Gabor transform of the seismic trace is divided by the complex-valued estimates of attenuation and source wavelet to estimate the Gabor transform of the reflectivity. An inverse Gabor transform recovers the time-domain reflectivity. The technique has applications to synthetic data and real data.

Phase stability via nonlinear optimization: A case study

Accurate wavelet estimation is crucial in the deconvolution of seismic data. As per the convolution model, the recorded seismic trace is the result of convolution of the Earth's unknown reflectivity series with the propagating seismic source wavelet along with the additive noise. The deconvolution of the source wavelet from the recorded seismic traces provides useful estimates of the Earth's unknown reflectivity and comes in handy as an aid to geological interpretation. This deconvolution process usually involves estimation of a wavelet, before it is removed by digital filtering. Because the Earth's reflectivity and seismic noise are both unknown, the wavelet estimation process is not easy. Statistical methods estimate the wavelet using the statistical properties of the seismic data and are based on certain mathematical assumptions. The most commonly used method assumes that the wavelet is minimum phase and that the amplitude spectrum and the autocorrelation of the wavelet are the same as the amplitude spectrum and the autocorrelation of the seismic traces, within a scale factor, in the time zone from where the wavelet is extracted (stationary assumption).

Blind deconvolution of seismic signals with non-white reflectivities

Seismic deconvolution technology is important in seismic data processing. We propose a new blind deconvolution algorithm for simultaneous wavelet estimation and deconvolution of seismic data. Optimal seismic deconvolution can be achieved by the combined application of a non-white reflectivity model and the blind deconvolution method. We incorporate a scaled Gaussian noise (SGN) model of seismic reflection coefficients into the seismic blind deconvolution method. The SGN model has the property of scale invariance. We present a framework to generalise the conventional deconvolution procedure to handle reflection coefficients that do not follow the white-noise model. Reflection coefficients are assumed to have an autocorrelation function with a power spectrum roughly proportional to some power of frequency.The seismic blind deconvolution method consists of three steps: (1) selection of initial reflectivities, (2) determination of the hyper parameters of the problem, and (3) an iterative procedure to solve the resulting equations until a tolerance criterion is satisfied. The alternative relaxation solution and pre-conditioned conjugate gradient algorithm are employed for practical numerical implementation. Seismic blind deconvolution not only can better realise the simultaneous evaluation of the seismic wavelet and the reflection coefficients, but also has advantages of stable algorithm and fast convergence. The test shows that the method is an effective tool of improving the resolution of seismic data that can effectively broaden the useful band of records.

The deconvolution of seismic data as a fluctuation analysis

The seismic convolutional model states that a seismic record is the convolution of the earth’s reflectivity with the seismic wavelet. In seismic processing the purpose of deconvolution is to remove (or collapse) the seismic wavelet. In this way, the

Enhancement of Deep Seismic Reflections in Pre-stack Data by Adaptive Filtering

—Adaptive filters offer advantages over Wiener filters for time-varying processes. They are used for deconvolution of seismic data which exhibit non-stationary behavior, and seldom for noise reduction. Different algorithms for adaptive filtering exist. The least-mean-squares (LMS) algorithm, because of its simplicity, has been widely applied to data from different fields that fall outside geophysics. The application of the LMS algorithm to improve the signal-to-noise ratio in deep reflection seismic pre-stack data is studied in this paper. Synthetic data models and field data from the DEKORP project are used to this end.¶Three adaptive filter techniques, one-trace technique, two-trace technique and time-slice technique, are examined closely to establish the merits and demerits of each technique. The one-trace technique does not improve the signal-to-noise ratio in deep reflection seismic data where signal and noise cover the same frequency range. With the two-trace technique, the strongest noise reduction is achieved for small noise on the data. The filter efficiency decreases rapidly with increasing noise. Furthermore, the filter performance is poor upon application to common-midpoint (CMP) gathers with no normal-moveout (NMO) corrections. Application of the two-trace method to seismic traces before dynamic correction results in gaps in the signal along the reflection hyperbolas. The time-slice technique, introduced in this paper, offers the best answer. In this case, the one-trace technique is applied to the NMO-corrected gathers across all traces in each gather at each time to separate the low-wavenumber component of the signal in offset direction from the high-wavenumber noise component. The stacking velocities used for the dynamic correction do not need to be known very accurately because in deep reflection seismics, residual moveouts are small and have only a minor influence on the results of the adaptive time-slice technique. Noise reduction is more significant with the time-slice technique than with the two-trace technique. The superiority of the adaptive time-slice technique is demonstrated with the DEKORP data.

Deconvolution of seismic data using adaptive Gaussian mixtures

Based on a Gaussian mixture model for the reflectivity sequence, the authors present a new technique for blind deconvolution of seismic data. The method obtains a deconvolution filter that maximizes at its output a measure of the relative entropy between the proposed Gaussian mixture and a pure Gaussian distribution. A new updating procedure for the mixture parameters is included in the algorithm: it allows one to apply the algorithm without any prior knowledge about the signal and noise. A simulation example illustrates the performance of the proposed method.

Spectral factorization technique for estimation of an ARMA operator for multichannel deconvolution of seismic data

A new spectral factorization method is presented for the estimation of a causal as well as a causally invertible ARMA operator from the correlation sequence of seismic traces. The method has been implemented for multichannel deconvolution of seismic traces with the aim of exploiting the trace‐to‐trace correlation that exists within seismograms. A layered earth model with a small reflectivity sequence has been considered, and the seismic traces have been considered as the output of a linear system driven by white noise reflection coefficient sequences. The present method is the concatenation of three algorithms, namely Kung's method for state variable (F,G,H) realization using a singular value decomposition (SVD) algorithm, Faurre's technique for computation of the strong spectral factor and Leverrier's algorithm for ARMA representation of the spectral factor. The inverted ARMA operator is used as a recursive filter for deconvolution of seismic traces. In the example shown, two traces with a covariance sequence of 160 ms length have been considered for multichannel deconvolution of stacked seismic traces. The results presented, when compared with those obtained from a conventional deconvolution algorithm, have shown encouraging prospects.

The critical reflection theorem

In predictive deconvolution of seismic data, it is assumed that the response of the earth is white. Any nonwhite components are presumed to be caused by the source wavelet or by unwanted multiples. We show that this whiteness assumption is invalid at precritical incidence. We consider plane waves incident on a layered acoustic half‐space. At exactly critical incidence at any interface in the half‐space, the lower layer acts similar to a rigid plate. The response of the half‐space is then all‐pass, or white. This result we call the critical reflection theorem. The response is also white if the waves are postcritically incident on the lower half‐space. In normal data processing these postcritical components are removed by muting. Thus the whiteness assumption is normally applied to exactly that part of the data where it is invalid. The demarcation between precritical and postcritical incidence can be exploited for the purposes of deconvolution, provided the data can be decomposed into plane waves. To develop this application, we consider the response of a point source in the uppermost layer of the layered half‐space, with a free surface above. The response is simply a superposition of the plane‐wave responses already studied, with complications introduced by the source and receiver ghosts and by multiples in the upper layer. At postcritical incidence the earth response is white for all plane‐wave components; the source spectrum may be estimated from the postcritical plane‐wave components after removing the effects of ghosts and multiples in the upper layer. If the source signature is already known, the demarcation criterion can be used to separate intrinsic absorption effects from attenuation effects caused by scattering.

Deconvolution of noisy seismic data—A method for prestack wavelet extraction

The presence of random additive noise is the most important degrading factor in the deconvolution of seismic data. Noise‐induced distortion of signal phase and amplitude produces severe stack attenuation, makes poststack recovery difficult with spectral enhancement techniques, and leaves the stratigraphic imprint unclear. The random noise component in the data is estimated from trace segments before the first arrivals and at the bottom of the record beyond seismic basement. An autocorrelation of this noise is used to adjust the signal autocorrelation prior to Wiener‐Levinson deconvolution filter design. To improve the robustness of the technique, an iterative surface‐consistent wavelet solution (common source, receiver, and offset) is used in preference to a single‐channel operation. Use of this deconvolution technique is shown by synthetic and case examples to result in correct phase alignment, enhanced stacking fidelity, and extended signal bandwidth even on very noisy data. The improvement, coupled with sensible handling of coherent noise energy, is crucial for the interpretation of subtle statigraphic plays in many areas.

Adaptive Least Squares for Parametric Spectral Estimation and Its Application to Pulse Estimation and Deconvolution of Seismic Data

The method of recursive least squares, which has been used extensively in the field of system identification will be developed for adaptive parametric spectral estimation of digital signals. The method will be applied for adaptive pulse estimation and deconvolution of seismic data. Unlike the Levinson-type deconvolution method, the adaptive least-squares method does not need to estimate a priori the autocorrelation function and it avoids the windowing problem of a time-limited signal. Because of the recursive nature of the method, it is suitable for adaptive estimation and removal of time-varying pulses, and it is computationally simple and suitable for implementation on small computers with less memory requirements. The method has been implemented on different simulated examples, and the results are given and discussed.

ESTIMATION OF MARINE SOURCE SIGNATURES FROM DIRECT ARRIVALS TO HYDROPHONE GROUPS*

AbstractDeterministic deconvolution of seismic data recorded with a non‐minimum phase source, such as a sparker, requires an estimate of the source signature. Present methods of deterministic signature estimation and deconvolution require additional field equipment (near‐ or far‐field hydrophones), or else make a deterministic estimate of the effective source signature (the free‐field source signature convolved with source and receiver ghosts). By analyzing the direct arrival signal to normal hydrophone groups it is shown that extraction of the free‐field source signature from this signal is possible for a spherically symmetric source, and it is demonstrated that the use of this signature for a preliminary deterministic deconvolution gives better results on sparker data than minimum‐phase whitening deconvolution applied on its own. The applicability of the method to non‐spherically symmetric sources, such as arrays, is also discussed.This paper is published with the permission of the Director, Bureau of Mineral Resources, Geology and Geophysics, Canberra, Australia.

White-Noise Filter and Smoother with Application to Seismic Data Deconvolution

The problem of estimating white noise is discussed. Using the time series analysis method, based on the vector ARMA innovation model this paper presents the new multiple-channel steady-state optimal white noise filter and smoother applied to seismic data deconvolution, which are different from Mendel's single-channel steady-state white noise estimators that are based on the state-space model and Kalman filtering

SEISMIC LITHOLOGIC MODELLING

Seismic data constitute a noise-contaminated bandlimited representation of lithologic information. Therefore, attempts to recover lithologic information, such as velocity and density of thin layers, from seismic data cannot give a unique or verifiably correct result. Nevertheless, an interpreter must produce detailed geologic models on the basis of such data.Our interactive modelling procedure quantitatively refines the model that the interpreter derives from available geologic, borehole, and seismic data. The procedure starts from the initial model and perturbs its parameters (velocity, density, and layer thickness) to find the least-squares best fit between the stacked field data and the synthetic section derived from the model. The layer parameters are explicitly varied only at selected locations along the profile and are linearly interpolated to intermediate positions. This approach is based on an assumption of smooth lateral change for parameters, and enables the process to see through much of the noise.Synthetic data tests demonstrate that, even for significantly different initial models, the procedure can find solutions that are close to the correct model. Moreover, the procedure is stable in the presence of noise and not severely dependent on the shape of the bandlimited seismic signal or on details of the initial hypothesis.Application of the method to stacked data from the Denver Basin provides evidence that an interpreter's model can be refined so as to better match the seismic data while honouring available non-seismic data as well. A low-velocity anomaly in the final solution is well correlated with a known hydrocarbon play; the anomaly disappears near the dry well. Application of the method to stacked data from widely different data environments further demonstrates the value of the technique for refining thin-layer interpretations, thus providing, in effect, a geology-based deconvolution of seismic data.

On the Application of the Fast Kalman Algorithm to Adaptive Deconvolution of Seismic Data

The application of a recently proposed fast implementation of the recursive least squares algorithm, called the Fast Kalman Algorithm (FKA) to adaptive deconvolution of seismic data is discussed. The newly proposed algorithm does not require the storage and updating of a matrix to calculate the filter gain, and hence is computationally very efficient. Furthermore, it has an interesting structure yielding both the forward and backward prediction residuals of the seismic trace and thus permits the estimation of a ?smoothed residual? without any additional computations. The paper also compares the new algorithm with the conventional Kalman algorithm (CKA) proposed earlier [3] for seismic deconvolution. Results of experiments on simulated as well as real data show that while the FKA is a little more sensitive to the choice of some initial parameters which need to be selected carefully, it can yield comparable performance with greatly reduced computational effort.