Spectral Matrix Filtering Research Articles

Multi-component seismic wavefield separation via spectral matrix filtering

SUMMARY Spectral matrix filtering (SMF) is a vector-processing method that uses frequency, slowness and particlemotion information to distinguish between wave types. The algorithm operates in the f-x domain and exploits the eigenstructure of the frequency-domain covariance matrix of the multi-component seismic signal. SMF has previously been demonstrated on VSP data. A number of practical considerations for the application of SMF to surface-reflection data are considered. Practical application of SMF requires the user to specify a number of data-dependent parameters, including trace-width and time extent of the data-analysis window, and the frequency bandwidth of the filter. Synthetic and realdata examples illustrate that SMF can successfblly extract high-amplitude wavefields while preserving other wave types in a surface-seismic record. Thus, while extensive testing suggests that SMF is not viable for separating P and PS reflection wavefields, SMF has the potential to routinely suppress groundroll energy and other high-amplitude surface-related events that can mask desirable reflection energy.

On the detection and identification of converted and reflected phases from receiver functions

Summary We develop a simple methodology to extract information related to crustal structure such as the mean VP/VS ratio, the magnitude of lateral variations and the presence of discontinuities from a selection of receiver functions. We show that crustal phases can be detected and exploited on individual receiver functions. Two filtering techniques, based on singular value decomposition and spectral matrix filtering, are proposed to enhance the coherent phases in receiver functions. Additionally, the relative traveltimes and slownesses between the different phases are utilized for a more reliable phase identification. We apply these methods to data of station PRU (Czech Republic) and compare the results with a classical time-domain waveform inversion. We find a good qualitative agreement between the simple crustal models inferred from the two approaches. Waveform modelling suggests that the identification of converted phases can still be ambiguous and other geophysical or geological constraints are needed.

Ground-motion amplitude across ridges

AbstractLocal amplification and wave diffraction on an elongated ridge near Sourpi in central Greece were studied by the analysis of seismic records of local and regional earthquakes. Data were obtained during field work especially designed for this purpose. These data were analyzed in the frequency and time domains. In the frequency domain, spectral ratios show amplifications of 1.5 to 3 at the ridge top relative to the base of the ridge. The horizontal components of motion are more amplified than the vertical component and the observed spectral ratios seem stable for different earthquake locations. Theoretical spectral ratios, calculated by the indirect boundary element method, are dependent on earthquake location but are in general agreement with the observed spectral ratios. Another dataset, from Mont St. Eynard in the French Alps, showed similar characteristics with spectral amplitudes on the top of the ridge up to four times those on the flank. These relative amplifications are within the range predicted by numerical simulations. The numerical simulations also show that the topographic effect involves the emission of diffracted waves propagating from the top toward the base of the ridge. The use of a seven-station array on the ridge at Sourpi made it possible to identify such waves. The analysis was performed with wave separation methods using singular value decomposition and spectral matrix filtering. Our results show agreement between experimental data and theoretical results supporting the use of numerical simulations for estimation of purely topography-induced amplification on ridge tops. Our results also show that such amplification is moderate for the ridges under study.

Wave Separation. Part Two: Applications

Identifying waves in seismic sections sometimes requires the waves to be separated. The geophysicist has a variety of complementary filters at his disposal that can be used to perform optimum separations if they are carefully chosen and combined. The first part of this article was devoted to the principle and methods of wave separation. Wave separation methods can be divided up into three categories : acceptance region methods, inversion methods and matrix methods. The tau-p method and f-k filtering belong to the first category while the parametric method belongs to the second one. Matrix filtering by means of the cross-spectral matrix (SMF : Spectral Matrix Filtering), the singular value decomposition (SVD) and the Karhunen-Loeve method (KLT-Karhunen-Loeve Transform) belong to the third group. Matrix methods are used both to separate waves and to break data down into a signal space and a noise space. Here in the second part, we use synthetic data to compare how well the SVD and SMF methods perform in separating waves with only one eigenvector. We show that SMF filtering can be made much more effective by introducing models and present the SMF method with adapted or constrained models. We also introduce a field example of wave separation by conventional SMF filtering, then a synthetic example and two field examples of wave separation by SMF filtering with models. We demonstrate the advantages of using different wave separation methods together (f-k, KLT and SMF) to achieve optimum separation. The data that serve to illustrate this are full waveform acoustic data acquired in a horizontal drain hole. A VSP-type well survey is used to compare the different methods : f-k, SVD, SMF and the parametric method. The last example shows how SMF processing can be used for anisotropy measurement. The f-k filter requires a large number of traces that have been distance sampled at short intervals. The more stable the wave that is being extracted and the more clearly located it is in the f-k domain, the more efficient the filter is. The method is very cost-effective in CPU time. The KLT or SVD filter requires flattening the wave that is to be extracted, which must additionally be of greater amplitude. Filtering is carried out without any edge effect and the wave amplitude variations are preserved. It serves to separate the normal incidence wave from the other waves and the noise. The SMF filter (spectral matrix) is expensive in CPU time It makes the hypothesis that the wave is locally stable and does not require the data to be flattened. It can be used to separate very close neighboring waves without resorting to restrictive a priori hypotheses. It gives a measurement of time delays and also provides a measurement of variations in amplitude and phase spectra during propagation. This measurement is much better than the one supplied by the Wiener method, since it operates on all the traces. Additionally, it is used to separate data into a signal space and a noise space. The parametric method is the most expensive as regards time. It is simple to implement and requires no flattening or preparation of data. It extracts the waves according to chosen parameters, especially time delays. It is particularly recommended in offset vertical seismic profiling where the slowness of upgoing waves is unknown. It is robust with respect to some input parameters if the noise is low in comparison to the signal that is to be extracted. Many applications to field data have illustrated the effectiveness of these wave separation techniques. However, application to a new type of data often requires performance to be monitored to choose the best method.

Wave Separation. Part One: Principle and Methods

This article is a practical review of the different wave separation methods used in seismic. A wave is described by its propagation vector and its wavelet. The first part of the article shows how the propagation vector can be used to define both the type of propagation (plane or nonplane wave) and the characteristics of the medium (dispersive or faulted medium). Wave separation and wave-type identification can then be dealt with by studying the scalar product between two waves or between a wave and a reference model. The main filtering methods are described, in particular : f-k filtering, tau-p filtering, Karhunen-Loeve filtering and spectral matrix filtering. The efficiency of the different methods is assessed with synthetic data. The problem of extracting a wave from noise is also discussed and illustrated with a field example. The second part will be devoted to wave separation per se. The different methods described in the first part are applied to real data, in particular borehole survey seismic data. Special attention is given to the use of specific, less well-known methods such as spectral matrix filtering with adapted or constrained models.

Wavefield Decomposition using Spectral Matrix Techniques

A spectral matrix technique described by Mari and Gavin has been developed and extended for analysing interfering seismic events. It may be used with both single and multi-component data. Spectral matrix filtering removes random noise and may be used to enhance picked coherent events. This leads to a possible wave-field decomposition procedure for use in separating interfering coherent events. Conventional event-separation procedures require large geophone arrays to avoid spatial aliasing. Spectral matrix filtering does not require such dense coverage and so may be used in areas where conventional surveys may not be possible. The technique is illustrated using synthetic and physical scale-model data.

Vertical Seismic Profile in Horizontal Wells

Summary. An offset vertical-seismic-profile (VSP) survey was performed on Lacq 91, a horizontal well drilled in a reservoir layer about 50 m thick. This paper describes the field acquisition and the specific data-processing sequence that led to a usable seismic section. The paper also demonstrates the usefulness of horizontal well seismic surveys for reservoir studies. Introduction Horizontal wells have proved to be an efficient way to produce hydrocarbon reservoirs, leading to substantial gains in productivity and recovery. Many horizontal productivity and recovery. Many horizontal wells have been drilled throughout the world and many more are expected. It is therefore time to develop techniques to optimize production through the few hundred meters of production through the few hundred meters of drainhole offered by a horizontal well. From this point of view, one of the more important needs is to evaluate the reservoir in the horizontal well area. Moreover, because the oil industry currently is concerned with reservoir characterization, we should acknowledge the potential horizontal wells have for providing better reservoir appraisal. Among possible reservoir characterization techniques, seismic surveys used in horizontal wells seem to be very promising in giving an image of the reservoir and the surrounding layers over a large area. But the implementation of VSP's in horizontal wells encounters two main difficulties: the ability to run the seismic tool into the horizontal well without damaging the quality of the recordings and the ability to process the seismic data in the case where reflectors are almost parallel with the borehole axis. In June 1988, a borehole seismic survey consisting of a set of three offset VSP's was performed in a horizontal well to prove the performed in a horizontal well to prove the feasibility of and the usefulness in horizontal well seismic. With these objectives, an experiment was performed in Lacq 91, a horizontal well drilled in a 50-m-thick layer of a reservoir in France. At the time of the experiment, Lacq 91 was not producing. Data acquisition used three vibroseis trucks and a three-component downhole tool, including a hydrophone and an inclinometer. Offset VSP's were recorded on 69 different downhole tool positions spaced irregularly at vertical depths (between 352 and 665 m) associated with horizontal departures that varied between 84 and 575 m from the wellhead. Drillpipes pushed the downhole tool in the horizontal section of the well. The processing sequence included data editing, tool-rotation correction, wave separation, deconvolution, and migration. In horizontal wells, ascending and descending events with close apparent velocities cannot be separated by conventional apparent-velocity filters. In this experiment, the ascending waves were very weak compared with the descending waves, so they were separated by spectral matrix filtering. After wave separation, the deconvolved migrated data represented a VSP/common-depth-point (CDP) stacked section with a lateral investigation of about 500 m. Results obtained with geophone recordings are compared with those obtained from the hydrophone recordings, which exhibits a strong level of tube waves. The comparison correlates with information from cemented and perforated zones. To the best of our knowledge, the Lacq 91 experiment was the first VSP operation done in a horizontal well. This paper further describes the field acquisition and the specific data-processing sequence used in the Lacq 91 experiment. It also demonstrates that use of a borehole seismic profile in a horizontal well confirms information available from geological and reservoir engineering studies. VSP Data Acquisition In Horizontal Wells Data acquisition in Lacq 91 involved running a borehole geophone through a wireline into the most vertical part of the well and through a specific downhole system (HORSEIS) in the most horizontal part. Fig. 1a shows the HORSEIS downhole system, which is used to run a seismic sonde into a highly deviated or horizontal borehole to make VSP'S. It can be used on- or offshore with conventional VSP equipment (i.e., vibrators or air guns, a seismic sonde, and a data-acquisition system). Equipment Description. A seismic sonde is linked by a logging wireline several meters long to the sonde support of the HORSEIS system (Fig. 1b). The borehole sonde preferably should include a seismic cartridge containing three geophones. In this experiment, three ungimbaled geophones were mounted in a trirectangular pattern. JPT P. 1486

Spectral Matrix Filtering Applied to Vsp Processing

The spectral matrix computed from VSP-traces transfer functions contains information about each wave making up the VSP data set. Using a filter based on the eigenvectors of the spectral matrix leads to a decomposition of input traces in eigensections. The eigensections associated with the largest eigenvalues contain the contribution of the correlated seismic events. Signal space is denoted as the sum of these eigensections. Other eigensections represent noise. When the different waves making up the VSP have very different amplitudes, decomposition of input traces into eigensections leads to wave separation without any required knowledge about the apparent velocities of the waves. Limitations of wave separation by the multichannel filtering are a function of the scalar product values of the waves (in frequency domain) and of the relative wave amplitudes. The spectral matrix filtering can always be used to enhance signal-to-noise ratio on VSP data. The eigenvalues of the spectral matrix can be used to estimate the signal-to-noise ratio as a function of frequency. It is possible to qualify the behavior of a VSP tool in a well and to detect some resonant frequencies probably generated by poor coupling. Field data examples are shown. The first example shows data recorded in a vertical well whose converted shear waves are separated from upgoing and downgoing compressional waves using a spectral matrix filter. This field case shows the efficiency of the spectral matrix filter in extracting weak events. The second example shows data recorded in a highly deviated well, where very close apparent velocity events are successfully separated by use of spectral matrix filtering.