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A comparison of shot‐encoding schemes for wave‐equation migration
Authors Jeff Godwin and Paul SavaAvailable online: 03 May 2013More LessABSTRACTIn the last decade the seismic imaging industry has begun collecting data volumes with a substantial amount of data redundancy through new acquisition geometries including: wide‐azimuth, rich‐azimuth and full‐azimuth geometries. The increased redundancy significantly improves image quality in areas with complex geology, but requires considerably greater computational power to construct an image because of the additional data and the need to use advanced imaging algorithms. One way to reduce the computational cost of processing such datasets is to blend shot‐records, using shot‐encoding, together prior to imaging which reduces the number of migrations necessary for imaging. The downside to doing so is that blending introduces strong, non‐physical, cross‐talk noise into the final image. By carefully choosing the shot‐encoding scheme, we can reduce the additional noise inserted into the image and maximally reduce the number of migrations necessary. We describe a theory of blended imaging that explains all shot‐encoding schemes, and use the theory to design a new class of encodings that use amplitude weights instead of phase‐shifts or time‐delays. We are able to use amplitude encoding to produce blended images of the same quality as previous encoding schemes at a similiar computational cost. Furthermore, we compare the results of amplitude encoding with the results from well‐known shot‐encoding schemes from previous work including: plane‐wave migration, random‐time delay, modulated‐shot migration, and decimated shot‐record migration. In our comparison, we find that plane‐wave migration is in many ways an optimal shot‐encoding scheme. However, we find that plane‐wave migration produces results that are comparable to decimated shot‐record migration when the total cost of imaging is taken into account, thereby calling into question the utility of shot‐encoding in general. Overall, this work questions the potential for shot‐encoding in standard (shot‐record) seismic imaging because blended imaging does not appear to sufficiently reduce the cost of imaging given the quality of the blended image compared to decimated shot‐record migration.
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Elastic moduli and the aspect ratio spectrum of rock using simulated annealing
Authors Satoshi Izumotani and Shigenobu OnozukaAvailable online: 17 April 2013More LessABSTRACTWe propose a new method for estimating pore volume concentrations associated with inclusions with different aspect ratios and also the rock matrix and pore fluid moduli using very fast simulated annealing. We use the Kuster and Toksöz effective modulus formulations as a forward model that takes the pore shapes into consideration.
In order to provide this method, we first estimated the model parameters, then calculated the P‐ and S‐wave velocities as a function of pressure in dry and saturated conditions and finally compared the calculated velocities with the measured ultrasonic velocities of sandstone, limestone and granite. The calculated velocity fitted well with the measured velocity. Furthermore, we verified the calculated bulk modulus and shear modulus of the rock matrix. As these moduli were consistent with the results from other experiments and were almost the same as those by the inversion method, we believe that this method can satisfactorily calculate the moduli.
Next, we conducted optimization under several cases of moduli setting. We obtained the best results using the independent shear modulus under saturated conditions. The result indicates that the shear modulus varies according to the fluid in the pores in sandstone.
Finally, we optimized the average aspect ratio of rock and found that the average aspect ratio may depend on the type of rock. The velocity calculated by the single aspect ratio is similar to the velocity calculated by using a spectrum of aspect ratios for the same rock.
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Decomposition of a compliance tensor for fractures and transversely isotropic medium
By Çağrı DinerAvailable online: 17 April 2013More LessABSTRACTThe purpose of this paper is to develop an analytical method to decompose an observed anisotropic compliance tensor into two transversely isotropic (TI) tensors that are associated with layers and fractures. Specifically, the fracture parameters and the TI background medium parameters are obtained from a given monoclinic compliance tensor. Here the set of parallel fractures and TI medium can be arbitrarily oriented in ; they are not constrained to vertical and horizontal directions respectively. First the summation of the two TI tensors, which represent fractures and layerings, is obtained in order to have the form of the resultant monoclinic medium. The orientation of each TI medium is represented by one Euler angle once the mirror plane normal of the monoclinic tensor is determined. This is because the mirror plane normal of the monoclinic medium is perpendicular to the rotation axes of the two TI tensors. Thus a layered medium with one set of parallel fractures is represented by nine parameters; two for rotationally symmetric fractures, five for a generic background TI medium and two Euler angles for the orientations of the structures. The decomposition problem, which is to find these nine parameters from a given monoclinic compliance tensor with thirteen parameters, is solved in the paper. Finally, the decomposition method is extended to media with three structures, namely two sets of fractures and layerings whose rotation axes lie in the same plane.
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Controlled laboratory experiments to assess the geomechanical influence of subsurface injection and depletion processes on 4D seismic responses
Authors Rune M. Holt and Jørn F. StenebråtenAvailable online: 08 April 2013More LessABSTRACTLaboratory experiments are performed with soft synthetic reservoir sandstone cemented under stress and with synthetic overburden (caprock) material consisting of compacted clay (kaolinite) in brine. The rock‐like materials are loaded mechanically under stress paths representative of stress changes occurring in the subsurface as a result of injection (increasing pore pressure) or depletion followed by injection into a storage reservoir. Static stress‐strain behaviour and multidirectional P‐ and S‐wave velocities are monitored during the tests. The tests with sandstone are performed on dry material and simple poroelastic modelling is performed to relate these data to the behaviour of fluid (water / CO2) saturated samples under the same stress paths. The focus is on identifying 4D seismic attributes that may be used in the field to interpret monitoring measurements. This could help diagnose stress changes in the overburden, signalling the risk of CO2 leakage from a reservoir if the compressive or tensile strength limit of the overburden is reached and of course to help quantify amounts of CO2 stored.
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2D tomographic inversion of complex resistivity data on cylindrical models
Available online: 06 March 2013More LessABSTRACTThe resistive and capacitive response of a multiphase subsoil can be analysed by amplitude and phase models of the electrical complex resistivity. The main goal of this work is to extend the 2D transformed formulation used for electrical site investigations for cylindrical laboratory models, solving the complex resistivity forward problem starting from the Complete Electrode Model approach. This formulation is tested by a comparison with the full 3D solution and is proven to be stable and accurate. Inversion of complex resistivity data is achieved through a Matlab interface included in the EIDORS environment, with the addition of numerous new functions. Three synthetic examples are discussed, to understand the potential and limits of this approach in comparison with the 3D inversion. Laboratory experiments on a cylindrical laboratory model with a horizontal cross‐section of 10 electrodes validated synthetic results. The model having a height of 1 m and a diameter of 500 mm is made by sand contaminated from the top by an engineered fluid with electrical properties similar to chlorinated solvents.
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Measurement of the normal/tangential fracture compliance ratio (ZN/ZT) during hydraulic fracture stimulation using S‐wave splitting data
Authors James P. Verdon and Andreas WüstefeldAvailable online: 28 February 2013More LessABSTRACTWe develop a method to invert S‐wave splitting (SWS) observations, measured on microseismic event data, for the ratio of normal to tangential compliance (ZN/ZT) of sets of aligned fractures. We demonstrate this method by inverting for ZN/ZT using SWS measurements made during hydraulic fracture stimulation of the Cotton Valley tight gas reservoir, Texas. When the full SWS data set is inverted, we find that ZN/ZT= 0.74 ± 0.04. Windowing the data by time, we were able to observe variations in ZN/ZT as the fracture stimulation progresses. Most notably, we observe an increase in ZN/ZT contemporaneous with proppant injection. Rock physics models and laboratory observations have shown that ZN/ZT can be sensitive to (1) the stiffness of the fluid filling the fracture, (2) the extent to which this fluid can flow in and out of the fracture during the passage of a seismic wave and (3) the internal architecture of the fracture, including the roughness of the fracture surfaces, the number and size of any asperities and the presence of material filling the fracture. These factors have direct implications for modelling the fluid‐flow properties of fractures. Consequently, the ability to image ZN/ZT using SWS will provide useful information about fractured rocks and allow additional constraints to be placed on reservoir behaviour.
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Adaptive scaling for an enhanced dynamic interpretation of 4D seismic data
Authors Reza Falahat, Asghar Shams and Colin MacBethAvailable online: 27 February 2013More LessABSTRACTIn this study, importance is drawn to the role of engineering principles when interpreting dynamic reservoir changes from 4D seismic data. In particular, it is found that in clastic reservoirs the principal parameters controlling mapped 4D signatures are not the pressure and saturation changes per se but these changes scaled by the corresponding thickness (or pore volume) of the reservoir volume that these effects occupy. For this reason, pressure and saturation changes cannot strictly be recovered by themselves, this being true for all data interpretation. This understanding is validated both with numerical modelling and analytic calculation. Interestingly, the study also indicates that the impact of gas saturation on the seismic can be written using a linear term but that inversion for gas saturation can yield at best only the total thickness/pore volume of the distribution. The above provides a basis for a linear equation that can readily and accurately be used to estimate pressure and saturation changes. Quantitative updates of the static and dynamic components of the simulation model can be achieved by comparing thickness or pore volume‐scaled changes from the simulator with the corresponding quantities on the inverted observations.
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Imaging by forward propagating the data: theory and application
Authors Akbar Zuberi and Tariq AlkhalifahAvailable online: 27 February 2013More LessABSTRACTThe forward (modelled) wavefield for conventional reverse time migration (RTM) is computed by extrapolating the wavefield from an estimated source wavelet. In the typical case of a smooth subsurface velocity, this wavefield lacks the components, including surface reflections, necessary to image multiples in the observed data. We, instead, introduce the concept of forward propagating the recorded data, including direct arrivals, as part of RTM. We analyse the influence of the main components of the data on the imaging process, which include direct arrivals, primaries and surface‐related multiples. In our RTM methodology, this implies correlating the forward extrapolated recorded data wavefield with its reversely extrapolated version prior to applying the zero‐lag cross‐correlation imaging condition. The interaction of the data components with each other in the cross‐correlation process will image primaries and multiples, as well as introduce cross‐talk artefact terms. However, some of these artefacts are present in conventional RTM implementation and they tend to be relatively weak. In fact, for the surface seismic experiment, forward propagating the direct arrivals is almost equivalent to forward propagating a source and it tends to contribute the majority of the data imaging energy. In addition, primaries and multiples recorded in the data become multiples of one higher order. Forward propagating the recorded data to recreate the source will relieve us from the requirement of estimating the source function. It will also include near‐surface information necessary to improve the image in areas with near‐surface complexity. Data from a simple synthetic layered model, as well as the Marmousi model, are used to demonstrate some of these features.
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Pseudo‐remote reference processing of magnetotelluric data: a fast and efficient data acquisition scheme for local arrays
Available online: 27 February 2013More LessABSTRACTThe basic physical properties of the magnetic source field, namely its homogeneity and spatial coherence, have been used for a variety of magnetotelluric processing techniques including remote reference processing. In the present work we propose a data acquisition and processing technique for a large number of stations distributed over a localized area ideally on a grid. For pseudo‐remote reference processing it is necessary to use the following station setup: five‐component MT data are only measured at some sites (base stations) while at the majority of sites (local stations) only the electric and vertical magnetic fields are recorded. The impedance tensor and vertical magnetic transfer functions at each local station are computed by assigning the magnetic fields of a base station to the local station as if they had been measured there. This approach can lead to biased or erroneous estimates of local transfer functions at stations in the vicinity of strong conductivity contrasts that can be corrected using the interstation transfer functions between the horizontal magnetic fields measured at the base station(s).
We test this approach with a data set collected in the vicinity of the Groß Schönebeck geothermal test site. Magnetotelluric data were collected at 146 local and 5 base stations distributed over an approximately 5 km × 25 km wide grid with site spacing ranging from 500 m × 500 m to 1000 m × 1000 m in the frequency range 128–0.001Hz. The obtained pseudo‐remote reference transfer functions are generally smooth and consistent and conductivity models obtained from 2D inversion of the data are in agreement with previous conductivity models from the study area.
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Applicability of 1D and 2.5D marine controlled source electromagnetic modelling
Authors Ali Moradi Tehrani and Evert SlobAvailable online: 27 February 2013More LessABSTRACTWe present two‐and‐a‐half dimensional (2.5D) and three‐dimensional (3D) integral equation modelling of the marine controlled source electromagnetic method. We implement 2.5D modelling using a point source and a two‐dimensional reservoir and compare the results with point source responses from one‐dimensional and three‐dimensional reservoir models. These methods are based on an electric field domain integral equation formulation. We show how the 2.5D method performs in terms of both accuracy and computing speed with different configurations. We compare the results from 1D, 2.5D and 3D modelling, for a symmetrically placed reservoir and the in‐line acquisition configuration, as a function of different reservoir sizes in the cross‐line direction, thickness and for different frequencies and depths. Depending on the model’s parameters 2.5D modelling can be considered as an accurate and fast method for marine controlled source electromagnetic acquisition optimization and interpretation. If the thickness of the reservoir is less than one fifth of the skin depth of the embedding and if the depth of the reservoir is two or more times the skin depth of the embedding, the largest amplitude difference between two‐dimensional and three‐dimensional reservoirs is less than 10% when the source is above the centre of the reservoir. In this paper we discuss supporting examples with different configurations, where the 2.5D results lead to an optimistic detection estimate. Phase differences between 2.5D and 3D modelling are even smaller and the 2.5D solution can be used to assess the ability to detect the reservoir with a given acquisition configuration.
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Spectral decomposition with f−x−y preconditioning
Authors David Bonar and Mauricio SacchiAvailable online: 27 February 2013More LessABSTRACTSpectral decomposition, or local time‐frequency analysis, tries to enhance the amount of information one can obtain from a seismic volume by finding the frequency content of the seismic data at each time sample. However, if a small amount of noise is present within the seismic amplitude volume, it has the potential to become more prominent in the spectrally decomposed data especially if high‐resolution or sparsity promoting methods are utilized. To combat this problem post‐processing noise removal has commonly been employed, but these techniques can potentially degrade the resolution of small‐scale geological structures in their attempt to remove this noise. Rather than de‐noising the spectrally decomposed data after they are generated, we propose to incorporate the ideas of f−x−y deconvolution within the spectral decomposition process to create an algorithm that has the ability to de‐noise the time‐frequency representation of the data as they are being generated. By incorporating the spatial prediction error filters that are utilized for f−x−y deconvolution with the spectral decomposition problem, a spatially smooth time‐frequency representation that maintains its sparsity, or high‐resolution characteristics, can be obtained. This spatially smooth high‐resolution time‐frequency representation is less likely to exhibit the random noise that was present in the more conventionally obtained time‐frequency representation. Tests on a real data set demonstrate that by de‐noising while the time‐frequency representation is being constructed, small‐scale geological structures are more likely to maintain their resolution since the de‐noised time‐frequency representation is specifically built to reconstruct the data.
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Influence of borehole‐eccentred tools on wireline and logging‐while‐drilling sonic logging measurements
Authors David Pardo, Pawel J. Matuszyk, Carlos Torres‐Verdin, Angel Mora, Ignacio Muga and Victor M. CaloAvailable online: 13 February 2013More LessABSTRACTWe describe a numerical study to quantify the influence of tool‐eccentricity on wireline (WL) and logging‐while‐drilling (LWD) sonic logging measurements. Simulations are performed with a height‐polynomial‐adaptive (hp) Fourier finite‐element method that delivers highly accurate solutions of linear visco‐elasto‐acoustic problems in the frequency domain. The analysis focuses on WL instruments equipped with monopole or dipole sources and LWD instruments with monopole excitation. Analysis of the main propagation modes obtained from frequency dispersion curves indicates that the additional high‐order modes arising as a result of borehole‐eccentricity interfere with the main modes (i.e., Stoneley, pseudo‐Rayleigh and flexural). This often modifies (decreases) the estimation of shear and compressional formation velocities, which should be corrected (increased) to account for borehole‐eccentricity effects. Undesired interferences between different modes can occur at different frequencies depending upon the properties of the formation and fluid annulus size, which may difficult the estimation of the formation velocities.
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Application of seismic full waveform inversion to monitor CO2 injection: modelling and a real data example from the Ketzin site, Germany
Authors Fengjiao Zhang, Christopher Juhlin, Monika Ivandic and Stefan LüthAvailable online: 29 January 2013More LessABSTRACTSeismic monitoring of an injected carbon dioxide (CO2) distribution at depth is an important issue in the geological storage of CO2. To help monitor changes in the subsurface during CO2 injection a series of 2D seismic surveys were acquired within the framework of the CO2SINK and CO2MAN projects at Ketzin, Germany at different stages of the injection process. Here we investigate using seismic full waveform inversion as a qualitative tool for time‐lapse seismic monitoring given the constraints of the limited maximum offsets of the 2D seismic data. Prior to applying the inversion to the real data we first made a number of benchmark tests on synthetic data using a similar geometry as in the real data. Results from the synthetic benchmark tests show that it is difficult to recover the true value of the velocity anomaly due to the injection but that it is possible to qualitatively locate the distribution of the injected CO2. After the synthetic studies, we applied seismic full waveform inversion on the real time‐lapse data from the Ketzin site along with conventional time‐lapse processing. Both methods show a similar qualitative distribution of the injected CO2 and agree well with expectations based upon more extensive 3D time‐lapse monitoring in the area.
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Review paper: Instrumentation for marine magnetotelluric and controlled source electromagnetic sounding
Available online: 29 January 2013More LessABSTRACTWe review and describe the electromagnetic transmitters and receivers used to carry out magnetotelluric and controlled source soundings in the marine environment. Academic studies using marine electromagnetic methods started in the 1970s but during the last decade these methods have been used extensively by the offshore hydrocarbon exploration industry. The principal sensors (magnetometers and non‐polarizing electrodes) are similar to those used on land but magnetotelluric field strengths are not only much smaller on the deep sea‐floor but also fall off more rapidly with increasing frequency. As a result, magnetotelluric signals approach the noise floor of electric field and induction coil sensors (0.1 nV/m and 0.1 pT) at around 1 Hz in typical continental shelf environments. Fluxgate magnetometers have higher noise than induction coils at periods shorter than 500 s but can still be used to collect sea‐floor magnetotelluric data down to 40–100 s. Controlled source transmitters using electric dipoles can be towed continuously through the seawater or on the sea‐bed, achieving output currents of 1000 A or more, limited by the conductivity of seawater and the power that can be transmitted down the cables used to tow the devices behind a ship. The maximum source‐receiver separation achieved in controlled source soundings depends on both the transmitter dipole moment and on the receiver noise floor and is typically around 10 km in continental shelf exploration environments. The position of both receivers and transmitters needs to be navigated using either long baseline or short baseline acoustic ranging, while sea‐floor receivers need additional measurements of orientations from compasses and tiltmeters. All equipment has to be packaged to accommodate the high pressure (up to 40 MPa) and corrosive properties of seawater. Usually receiver instruments are self‐contained, battery powered and have highly accurate clocks for timekeeping, even when towed on the sea‐floor or in the water column behind a transmitter.
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3D pseudo‐seismic imaging of transient electromagnetic data – a feasibility study
Authors G.Q. Xue, L.‐J. Gelius, L. Xiu, Z.P. Qi and W.Y. ChenAvailable online: 15 January 2013More LessABSTRACTWe investigate a pseudo‐seismic approach based on the so‐called inverse Q‐transform as an alternative way of processing transient electromagnetic (TEM) data. This technique transforms the diffusive TEM response into that of propagating waves obeying the standard wave‐equation. These transformed data can be input into standard seismic migration schemes with the potential of giving higher resolution subsurface images. Such images contain geometrical and qualitative information about the medium but no quantitative results are obtained as in model‐based inversion techniques. These reconstructed images can be used directly for geological interpretation or in further constraining possible inversions. We extend the original Q‐transform based on an electrical‐source formulation to the case of a large‐loop TEM source. Moreover, an efficient discrete version of the inverse of this modified Q‐transform is presented using a regularization method. Application of this inverse transform to the measured TEM responses gives the corresponding pseudo‐seismic data, which are input into a 3D migration scheme. We then use a 3D boundary element type of Kirchhoff migration to ensure high computational efficiency. This proposed method was applied to both synthetic data as well as field measurements taken from an engineering geology survey. The results indicate that the resolution of the TEM data is significantly improved when compared with standard apparent‐resistivity plots, demonstrating that higher resolution 3D transient electromagnetic imaging is feasible using this method.
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Estimated source wavelet‐incorporated reverse‐time migration with a virtual source imaging condition
Authors Youngseo Kim, Yongchae Cho and Changsoo ShinAvailable online: 15 January 2013More LessABSTRACTMany geophysicists perform reverse‐time migration using a variety of artificial sources to obtain the source wavefield. Upon processing the seismic data, however, it is difficult to recover the original phase and amplitude of the source wavelet used for seismic exploration, regardless of the source. We have therefore used several artificial source wavelets such as Ricker or the first derivative Gauss wavelets expressed by well‐known functions. There are some differences between these artificial source wavelets and the original source wavelets, resulting in imperfect migration images. Artificial source wavelets tend to distort the exact location of subsurface reflectors and they create noise around the boundary of the stratum. To solve this problem, we applied the source estimation technique to the reverse‐time migration algorithm. The source estimation technique approximates the source wavelet to the original exploration source wavelet by a deconvolution method. This technique is used in full waveform inversion and provides better inversion results as demonstrated by other studies. To prove the effect of reverse‐time migration with source estimation, we tested this algorithm on the Sigsbee2a model, SEG/EAGE 3D salt model and 3D real field land data. Using the resulting images of these three models, we found that the source estimation technique can yield better migration images. To suppress the artefacts produced in the migration image, we used a wavenumber filter and Laplacian filter on 2D and 3D examples, respectively. Furthermore, we used the pseudo‐Hessian similar to the source illumination to scale the migration image because the virtual source imaging condition was used for reverse‐time migration.
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Robust error on magnetotelluric impedance estimates
Authors Pierre Wawrzyniak, Pascal Sailhac and Guy MarquisAvailable online: 07 January 2013More LessABSTRACTWe propose here a new, robust, methodology to estimate the errors on a magnetotelluric (MT) impedance tensor. This method is developed with the bounded influence remote‐reference processing (BIRRP) code in a single site configuration. The error is estimated by reinjecting an electric field residual obtained after the calculation of an impedance tensor into a tensor function calculation procedure. We show using synthetic examples that the error tensor calculated with our method yields a more reliable error estimate than the one calculated from Jackknife statistics. The modulus of realistic error estimates can be used as a quality control and an accurate inversion constraint of MT surveys. Moreover, reliable error estimates are necessary for new applications of MT to dynamic subsurface processes such as reservoir monitoring.
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Influence of a velocity model and source frequency on microseismic waveforms: some implications for microseismic locations
Authors P.J. Usher, D.A. Angus and J.P. VerdonAvailable online: 10 December 2012More LessABSTRACTIn this paper, we examine the influence of a velocity model and microseismic source frequency on microseismic waveforms and event locations. Finite‐difference waveform synthetics are generated based on the Cotton Valley hydraulic fracture experiment, where we vary the vertical heterogeneity of the velocity models as well as the microseismic source frequencies. We find that differences between plausible velocity models lead to changes in arrival times of approximately 0.0035 seconds for P‐waves and 0.0085 seconds for S‐waves. Based on the average P‐ and S‐wave velocities, the difference in the P‐ and S‐wave traveltimes is equivalent to approximately 20 m in location difference. Significant increases in the waveform coda develop with increasing model heterogeneity and increasing source frequency. The presence of signal noise as well as other sources of error (e.g., uncertainty in geophone location) will likely lead to further increase in uncertainty in location error estimates. Thus we note that location error due to incorrect velocity models cannot be ignored.
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Statics‐preserving projection filtering
Authors Yann Traonmilin and Necati GulunayAvailable online: 10 December 2012More LessABSTRACTProjection filtering has been used for many years in seismic processing as a tool to extract a signal out of noisy data. The effectiveness of projection filtering reaches a limit when seismic events are affected by static shifts. Such shifts degrade the lateral coherency of the data, which is the strongest assumption made by projection filtering. We propose an algorithm to estimate projection filters and static shifts simultaneously in order to perform noise attenuation in the presence of static shifts in the data. We then show results on synthetic and real data to demonstrate the denoising capabilities of our algorithm.
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