Spectral Whitening Research Articles

A method to identify aperiodic disturbances in the ionosphere

Abstract. In this paper, variations in the ionospheric F2 layer's critical frequency are decomposed into their periodic and aperiodic components. The latter include disturbances caused both by geophysical impacts on the ionosphere and random noise. The spectral whitening method (SWM), a signal-processing technique used in statistical estimation and/or detection, was used to identify aperiodic components in the ionosphere. The whitening algorithm adopted herein is used to divide the Fourier transform of the observed data series by a real envelope function. As a result, periodic components are suppressed and aperiodic components emerge as the dominant contributors. Application to a synthetic data set based on significant simulated periodic features of ionospheric observations containing artificial (and, hence, controllable) disturbances was used to validate the SWM for identification of aperiodic components. Although the random noise was somewhat enhanced by post-processing, the artificial disturbances could still be clearly identified. The SWM was then applied to real ionospheric observations. It was found to be more sensitive than the often-used monthly median method to identify geomagnetic effects. In addition, disturbances detected by the SWM were characterized by a Gaussian-type probability density function over all timescales, which further simplifies statistical analysis and suggests that the disturbances thus identified can be compared regardless of timescale.

On estimating attenuation from the amplitude of the spectrally whitened ambient seismic field

SUMMARY Measuring attenuation on the basis of interferometric, receiver–receiver surface waves is a non-trivial task: the amplitude, more than the phase, of ensemble-averaged cross-correlations is strongly affected by non-uniformities in the ambient wavefield. In addition, ambient noise data are typically pre-processed in ways that affect the amplitude itself. Some authors have recently attempted to measure attenuation in receiver–receiver cross-correlations obtained after the usual pre-processing of seismic ambient-noise records, including, most notably, spectral whitening. Spectral whitening replaces the cross-spectrum with a unit amplitude spectrum. It is generally assumed that cross-terms have cancelled each other prior to spectral whitening. Cross-terms are peaks in the cross-correlation due to simultaneously acting noise sources, that is, spurious traveltime delays due to constructive interference of signal coming from different sources. Cancellation of these cross-terms is a requirement for the successful retrieval of interferometric receiver–receiver signal and results from ensemble averaging. In practice, ensemble averaging is replaced by integrating over sufficiently long time or averaging over several cross-correlation windows. Contrary to the general assumption, we show in this study that cross-terms are not required to cancel each other prior to spectral whitening, but may also cancel each other after the whitening procedure. Specifically, we derive an analytic approximation for the amplitude difference associated with the reversed order of cancellation and normalization. Our approximation shows that an amplitude decrease results from the reversed order. This decrease is predominantly non-linear at small receiver– receiver distances: at distances smaller than approximately two wavelengths, whitening prior to ensemble averaging causes a significantly stronger decay of the cross-spectrum.

Predicting the distribution of reservoirs by combining variable wavelet model of seismograms with wavelet edge analysis and modeling

Abstract Reservoir prediction with its unique role in oil and gas fields is constantly facing new challenges, such as high-resolution seismic data and fast-accurate impedance inversion are needed. Generally, conventional methods used to enhance the resolution of seismic data, for example the spectral whitening, sometimes called balancing or broadening, is hard to yield valuable results as the seismic wavelets change during traveling subsurface. Besides, impedance inversion used in reservoir such as acoustic impedance inversion (AII) also confronts problem—low computational efficiency when more geological and geophysical parameters are taken into consideration in the modeling inversion. Based on these questions, in this study, a joint approach is presented. The first approach is the variable wavelet model of seismograms (VWMS), which is carried out by a series of processes such as time partition and frequency domain processing, to enhance the resolution of the seismic traces. Another approach that can improve the computational efficiency of the AII is the acoustic impedance inversion based wavelet edge analysis and modeling (AII-WEAM). In this approach, the algorithms of the AII were replaced by the modified very fast simulated annealing (MVFSA), to improve the inversed speed. By using a gas reservoir predicting example, we show that the joint approaches produce results that are feasible and reliable after comparing with the well data. Hence, these joint approaches have great potential to be the next-generation tools for reservoir description and prediction.

Seismic characterization of a Mississippi Lime resource play in Osage County, Oklahoma, USA

With the advent of horizontal drilling and hydraulic fracturing in the Midcontinent, USA, fields once thought to be exhausted are now experiencing renewed exploitation. However, traditional Midcontinent seismic analysis techniques no longer provide satisfactory reservoir characterization for these unconventional plays; new seismic analysis methods are needed to properly characterize these radically innovative play concepts. Time processing and filtering is applied to a raw 3D seismic data set from Osage County, Oklahoma, paying careful attention to velocity analysis, residual statics, and coherent noise filtering. The use of a robust prestack structure-oriented filter and spectral whitening greatly enhances the results. After prestack time migrating the data using a Kirchhoff algorithm, new velocities are picked. A final normal moveout correction is applied using the new velocities, followed by a final prestack structure-oriented filter and spectral whitening. Simultaneous prestack inversion uses the reprocessed and time-migrated seismic data as input, along with a well from within the bounds of the survey. With offsets out to 3048 m and a target depth of approximately 880 m, we can invert for density in addition to P- and S-impedance. Prestack inversion attributes are sensitive to lithology and porosity while surface seismic attributes such as coherence and curvature are sensitive to lateral changes in waveform and structure. We use these attributes in conjunction with interpreted horizontal image logs to identify zones of high porosity and high fracture density.

Interpreting cross-correlations of one-bit filtered seismic noise

Seismic noise, generated by oceanic microseisms and other sources, illuminates the crust in a manner different from tectonic sources, and therefore provides independent information. The primary measurable is the two-point cross-correlation, evaluated using traces recorded at a pair of seismometers over a finite-time interval. However, raw seismic traces contain intermittent large-amplitude perturbations arising from tectonic activity and instrumental errors, which may corrupt the estimated cross-correlations of microseismic fluctuations. In order to diminish the impact of these perturbations, the recorded traces are filtered using the nonlinear one-bit digitizer, which replaces the measurement by its sign. Previous theory shows that for stationary Gaussian-distributed seismic noise fluctuations one-bit and raw correlation functions are related by a simple invertible transformation. Here we extend this to show that the simple correspondence between these two correlation techniques remains valid for {\it non-stationary} Gaussian and a very broad range of {\it non-Gaussian} processes as well. For a limited range of stationary and non-stationary Gaussian fluctuations, we find that one-bit filtering performs at least as well as spectral whitening. We therefore recommend using one-bit filtering when processing terrestrial seismic noise, with the substantial benefit that the measurements are fully compatible with current theoretical interpretation (e.g., adjoint theory). Given that seismic records are non-stationary and comprise small-amplitude fluctuations and intermittent, large-amplitude tectonic/other perturbations, we outline an algorithm to accurately retrieve the correlation function of the small-amplitude signals.

Vibroseis deconvolution: A comparison of pre and post correlation vibroseis deconvolution data in real noisy data

Vibroseis is a source used commonly for inland seismic exploration . This non-destructive source is often used in urban areas with strong environmental noise. The main goal of seismic data processing is to increase the signal/noise ratio where a determinant step is deconvolution . Vibroseis seismic data do not meet the basic minimum-phase assumption for the application of spiking and predictive deconvolution, therefore various techniques, such as phase shift, are applied to the data, to be able to successfully perform deconvolution of vibroseis data. This work analyzes the application of deconvolution techniques before and after cross-correlation on a real data set acquired for high resolution prospection of deep aquifers. In particular, we compare pre-correlation spiking and predictive deconvolution with Wiener filtering and with post-correlation time variant spectral whitening deconvolution. The main result is that at small offsets, post cross-correlation spectral whitening deconvolution and pre-correlation spiking deconvolution yield comparable results, while for large offsets the best result is obtained by applying a pre-cross-correlation predictive deconvolution. ► Deconvolution of noisy seismic vibroseis data ► Comparison of deconvolution application before and after correlation ► Predictive deconvolution before correlation gives better results.

Performance of different processing schemes in seismic noise cross-correlations

SUMMARY The estimation of the Green's function between two points on the Earth's surface by the cross-correlation of seismic noise time-series became a widely used method in seismology. In general, very long time-series (months to years) as well as massive normalization and/or data selection are necessary to obtain useful cross-correlation functions. One task of this study is to evaluate the influence of different established normalization methods on the obtained cross-correlation functions. Furthermore, we evaluate two waveform preserving time domain normalizations as well as a new fully automated data selection approach. The cross-correlation functions analysed in this study are obtained from 12 months of seismic noise recorded in 2004 at five seismic stations in the United States with station distances on a continental scale. For practical reasons, the cross-correlation functions of such long time-series are calculated by stacking the cross-correlation functions obtained from shorter time windows. We use this stacking process for the implementation of the waveform preserving time domain normalizations. The time window length is in general an important parameter of the cross-correlation processing, as it influences the normalization and data selection. Therefore, we evaluate the cross-correlation functions obtained with 47 different time window lengths between one hr and 24 hr. The time domain normalizations intend to suppress the influence of transient signals like earthquake waves as well as long-term (e.g. seasonal) amplitude variations. We compare the proposed waveform preserving time domain normalizations with the established running absolute mean normalization and the one-bit normalization. We demonstrate that a waveform preserving time domain normalization can replace a non-linear time domain normalization, if a time window length similar to the duration of the typically occurring transient signals is used. Next to the time domain normalizations also the spectral whitening in the frequency domain is evaluated. Spectral whitening is a powerful normalization to improve the emergence of broad-band signals in seismic noise cross-correlations. Nevertheless, we observe spectral whitening to depend strongly on the time window length. An unwanted amplification of a persistent microseism signal is observed on the continental scale with time windows shorter than 12 hr. Our approach of automated data selection is based on a statistical time-series classification and reliably excludes time windows with transient signals occurring contemporaneously at both sites (e.g. earthquake waves). This data selection approach is capable to replace a non-linear time domain normalization, but no improvement of the waveform symmetry or the signal-to-noise ratio of the cross-correlation functions is observed in general.

On the reliability of attenuation measurements from ambient noise cross-correlations

[1] We compare spatially averaged Rayleigh wave attenuation between 10 and 18 sec period observed on the symmetric component of ambient noise cross-correlations with regional seismic event measurements observed by the USArray Transportable Array across the western US. The ambient noise attenuation measurements are shown to be consistent with attenuation observed following an earthquake in Nevada and a mining blast in Wyoming. We demonstrate that common ambient noise data processing procedures such as temporal normalization and spectral whitening can be retained as long as the amplitudes of the cross-correlations are corrected for (1) the duration of the ambient noise cross-correlation, (2) geometrical spreading, and (3) the azimuthal variation in the strength of ambient noise sources. Correction for time-series length can be achieved accurately by dividing the empirical Green's function by the squared root-mean-squared (rms) amplitude of the trailing noise. These results provide strong justification for the ability to constrain seismic attenuation using ambient noise. However, further study of the expected asymmetry in attenuation for waves approaching (incoming) or receding from (outgoing) a central station is needed to understand the effect of uneven noise source distribution prior to estimation of local variations in attenuation.

Statistical Model-Based Noise Reduction Approach for Car Interior Applications to Speech Recognition

This paper presents a statistical model-based noise suppression approach for voice recognition in a car environment. In order to alleviate the spectral whitening and signal distortion problem in the traditional decisiondirected Wiener filter, we combine a decision-directed method with an original spectrum reconstruction method and develop a new two-stage noise reduction filter estimation scheme. When a tradeoff between the performance and computational efficiency under resource-constrained automotive devices is considered, ETSI standard advance distributed speech recognition font-end (ETSI-AFE) can be an effective solution, and ETSI-AFE is also based on the decision-directed Wiener filter. Thus, a series of voice recognition and computational complexity tests are conducted by comparing the proposed approach with ETSI-AFE. The experimental results show that the proposed approach is superior to the conventional method in terms of speech recognition accuracy, while the computational cost and frame latency are significantly reduced.

On the amplitude of surface waves obtained by noise correlation and the capability to recover the attenuation: a numerical approach

Cross-correlation of ambient seismic noise recorded by a pair of stations is now commonly recognized to contain the Green's function between the stations. Although traveltimes extracted from such data have been extensively used to get images of the Earth interior, very few studies have attempted to exploit the amplitudes. In this work, we investigate the information contained in the amplitudes and we probe the capability of noise correlations to recover anelastic attenuation. To do so, we carry out numerical experiments in which we generate seismic noise at the surface of a 1-D Earth model. One of the advantages of our approach is that both uniform and non-uniform distributions of noise sources can be taken into account. In the case of a uniform distribution, we find that geometrical spreading as well as intrinsic attenuation are retrieved, even after strong non-linear operations such as one-bit normalization and spectral whitening applied to the noise recordings. In the case of a non-uniform distribution of sources, the geometrical spreading of the raw noise correlations depends on the distribution, but intrinsic attenuation is preserved. For the one-bit noise and whitened noise correlations, the interpretation of observed amplitude decays requires further study.

Enhancing the vertical resolution of surface georadar data

There are far-reaching conceptual similarities between bi-static surface georadar and post-stack, “zero-offset” seismic reflection data, which is expressed in largely identical processing flows. One important difference is, however, that standard deconvolution algorithms routinely used to enhance the vertical resolution of seismic data are notoriously problematic or even detrimental to the overall signal quality when applied to surface georadar data. We have explored various options for alleviating this problem and have tested them on a geologically well-constrained surface georadar dataset. Standard stochastic and direct deterministic deconvolution approaches proved to be largely unsatisfactory. While least-squares-type deterministic deconvolution showed some promise, the inherent uncertainties involved in estimating the source wavelet introduced some artificial “ringiness”. In contrast, we found spectral balancing approaches to be effective, practical and robust means for enhancing the vertical resolution of surface georadar data, particularly, but not exclusively, in the uppermost part of the georadar section, which is notoriously plagued by the interference of the direct air- and groundwaves. For the data considered in this study, it can be argued that band-limited spectral blueing may provide somewhat better results than standard band-limited spectral whitening, particularly in the uppermost part of the section affected by the interference of the air- and groundwaves. Interestingly, this finding is consistent with the fact that the amplitude spectrum resulting from least-squares-type deterministic deconvolution is characterized by a systematic enhancement of higher frequencies at the expense of lower frequencies and hence is blue rather than white. It is also consistent with increasing evidence that spectral “blueness” is a seemingly universal, albeit enigmatic, property of the distribution of reflection coefficients in the Earth. Our results therefore indicate that spectral balancing techniques in general and spectral blueing in particular represent simple, yet effective means of enhancing the vertical resolution of surface georadar data and, in many cases, could turn out to be a preferable alternative to standard deconvolution approaches.

Detecção de camadas delgadas usando sísmica de reflexão

Improvement of vertical resolution in seismic data is one of the major challenges for the seismic reflection method. The main problem is related to the larger loss of high frequencies relative to the lower ones during seismic wave propagation. As a consequence, the contribution of lower frequencies in the final section is significantly greater than the corresponding one due to higher frequencies. In principle, this situation should not constitute an obstacle to the full recovery of the spectrum, because of the powerful tools available in seismic processing, designed to equalize all frequencies that are present in the data volume. The main reason why these tools in general do not succeed is the presence of noise, for example random noise. Such situation gives rise to a critical frequency, such that all frequencies above it are impossible to recover and, as a consequence, the seismic pulse cannot be made short enough to allow for optimal resolution. Methods to solve the problem by means of random noise attenuation have been extensively investigated and tested without relevant results. The alternative to such techniques is the enhancement of the multiplicity that can be used for stacking. Since the amplitude decays exponentially with frequency, a large multiplicity is necessary in order to attain a significant effective frequency gain. The capability to attain extremely large multiplicity is exactly the main virtue of the Common Reflection Surface (CRS) method. In this paper, we propose the strategy of combining the CRS method with the spectral whitening, a known frequency-recovery technique, so as to optimize vertical resolution in seismic data and, as a consequence, improve the discrimination of thin reservoirs. First tests on synthetic and real data shown in this work are very encouraging and permit to conclude that the proposed approach has a good potential for practical application.

東ベネズエラ堆積盆コパ・マコヤガス田における薄層貯留岩摘出法の検討

It is a key to identify the distribution of multi-reservoir sand layers for exploration and development of Copa Macoya gas field in East Venezuela basin. However, it is difficult to estimate reservoir distribution because the each target sand layer is not thick enough to be detected by the limit of seismic resolution. In addition, synthetic seismograms cannot be tied with surface seismic data because well logs are distorted by borehole washouts, formation damage and other factors.In order to address this problem, damaged data was corrected by applying correlations of highest quality well log data obtained from the surrounding wells, and then pseudo logs were drawn. By using these corrected data the correlation between seismic and synthetic seismograms was improved.These data were used to define lithology index (LI) based on rotation of coordinate axis, using the relation between acoustic impedance (AI) and shear impedance (SI) as an attribute to delineate between sandstone and shale. Next, simultaneous inversion was carried out and LI volume was determined from AI and SI volumes. The LI volume was then processed with spectral whitening in order to improve the resolution of the result of the inversion.In this research, distribution of sand layers was studied by using high resolution LI volume. As a result, distribution showed better correlation with well data than in the past for some of the sand layers. However, the anomalies that indicate the distribution of sand layers in this study area could not always be obtained, because of the limitation of the methodology applied in this study.

A High-Resolution Processing Technique for 3-D Seismic Data Based on Signal Sub-Space Decomposition

We propose a new signal sub-space decomposition (SSD) technique to improve the resolution of 3D seismic data processing. By exploiting the SSD technique, not only we can decompose the signal and noise in 3-D seismic data, but also the composite event into single events according to their different dips. After removal of the noise space, we integrate all the reconstructions corresponding to the signal sub-spaces with improved resolution using the spectral whitening technique. Since we only improve the resolution of the signal and remove the noise at the same time, we can improve the resolution and signal-to-noise ratio (SNR) of the seismic data simultaneously. The application results on the synthetic and real data show that our method has a good perspective of applications.

Use of antenna arrays for GPR surveying in archaeology

ABSTRACTAmong the different geophysical prospecting methods applied in archaeology, ground‐penetrating radar is one that still requires a lot of time to carry out field recordings. A duo‐antenna configuration is proposed that will halve the time needed in the field. Tests have shown that this can be done without any interference between the two antennae. The signals from different antennae do not have the same characteristics and the spectrum and amplitude of the traces are not the same. The use of spectral whitening and energy matching for adjacent traces or samples makes the data sets as similar as possible to allow for unperturbed time‐ or depth‐slices. As a side effect, spectral whitening enhances the vertical resolution and penetration depth of the method.

On the use of complex sar image spectral analysis for target detection: assessment of polarimetry

The objective of this paper is to assess the joint use of the magnitude and the phase of a synthetic aperture radar (SAR) polarimetric image for point target detection and analysis. We first consider a single-look complex (SLC), single polarized radar image including point targets embedded in clutter. A series of sublooks are generated from this SLC image, both in azimuth and in range in order to analyze the inherent speckle effects. The two-looks internal Hermitian product (2L-IHP) is defined and is further shown to qualitatively increase the target/environment contrast. The processing of azimuth and range spectra preliminary to the 2L-IHP derivation (spectral whitening, generation and overlapping of sublooks) is described. A simulation tool is developed to model a point target behavior. Then, the polarimetric extension of the 2L-IHP is proposed, and the optimized polarimetric 2L-IHP is defined. The gain is twofold: in comparison with single polarization, polarimetry is shown to enhance detection capabilities, but also to provide additional information for target analysis.

A noninvasive shallow seismic source comparison on the Oak Ridge Reservation, Tennessee

Nine seismic sources were compared in preparation for production seismic reflection profiling to about 500 m depth at a hazardous waste site on the Oak Ridge Reservation, Tennessee. Test data provided a 125-shotpoint common midpoint profile and a walkaway vertical seismic profile for each source. Sources tested included five swept sources and four impulsive sources. Eight of the sources were “noninvasive,” in that they would not penetrate the ground surface. When spectral whitening methods were applied to the data, the IVI Minivib provided the best image of the subsurface on the basis of continuity and clarity of reflections. Without prewhitening, the performance of the IVI Minivib and the Bison elastic wave generator were similar.

Processing and attenuation of noise in deep seismic-reflection data from the Gulf of Maine

The U.S. Geological Survey deep crustal studies reflection profile across the Gulf of Maine off southeastern New England was affected by three sources of noise: side-scattered noise, multiples, and 20-Hz whale sounds. The special processing most effective in minimizing this noise consisted of a combination of frequency-wavenumber (F-K) filtering, predictive deconvolution, and spectral whitening, each applied in the shot domain (prestack). Application of the F-K filter to remove side-scatter noise in the poststack domain resulted in a much poorer quality profile. The prestack noise suppression processing techniques resulted in a reflection profile with good signal-to-noise ratios and reliable strong reflections, especially at depths equivalent to the lower crust (24–34 km). Certain geologic features, such as a buried rift basin and a crustal fault are resolved much better within the upper crust after this processing. Finite difference migration of these data using realistic velocities produced excellent results. Migration was essential to distinguish between abundant dipping and subhorizontal reflections in the lower crust as well as to show an essentially transparent upper mantle.

A neglected area of Vibroseis development

It should be possible to improve the quality of Vibroseis data through attention to flexible processing ahead of correlation and ahead of summation. These processes include improved noise rejection, spectral whitening and 'beam-steering' techniques. In the past this has been considered impractical due to the difficulty of handling large volumes of raw data and to a lack of integration between field and processing operations. The use of a high-density medium, now available to record raw Vibroseis data without pre-processing in the field, will provide an opportunity for development of improved techniques through the introduction of flexible pre-correlation and pre-summation processing.

3-D Seismic Lithologic Modeling to Delineate Rapidly Changing Reservoir Facies: A Case History from Alberta, Canada: ABSTRACT

The Lower Cretaceous sandstone reservoirs of southern Alberta, Canada, are extremely difficult to develop due to abrupt variations in sandstone and shale distribution. Such reservoirs occur intermittently throughout the study area near Taber, Alberta, where estimated recoverable reserves are approximately 9.75 million bbl. In February 1984, three-dimensional seismic data were recorded for a 4-km/sup 2/ area to delineate one of these reservoirs. Data were collected with a uniform bin size of 20 x 20 m and processed for amplitude and phase compensation, spectral whitening, velocity and static correlations, and poststack three-dimensional migration. The seismic lithologic modeling process (SLIM) was then applied to derive a thin-layer interpretation of the migrated data. The process was loosely constrained by parameters from one of six boreholes located within the survey area. The derived model showed remarkable consistency with the remaining five boreholes and provided a reasonable basis for estimating gross reservoir pore volume, hydrocarbon distribution, and reserves in place. Development drilling based on this model is in progress.