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- Volume 57, Issue 1, 2009
Geophysical Prospecting - Volume 57, Issue 1, 2009
Volume 57, Issue 1, 2009
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Slowness surface approximations for qSV‐waves in transversely isotropic media
Authors Alexey Stovas and Yuriy RoganovABSTRACTThe vertical slowness approximations are widely used in phase‐shift migration methods for quasi P‐ and quasi SV‐waves in transversely isotropic medium. The description of the vertical slowness needed for the migration application for shear waves in transverse isotrophy media is generally complicated. The reason is that this type of approximations results in much simpler expressions for the vertical slowness and, which is most important, they contain fewer parameters than exact expressions.
We derive slowness surface approximations valid for qSV‐wave propagation in transversely isotropic and tilted transversely isotropic media by applying an approximation extracted from acoustic approximation for qP‐wave propagation. One approximation has the same accuracy as a qP‐wave acoustic approximation for the same range of horizontal slowness, the other approximations are wide‐angle ones.
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Migration velocity analysis for tilted transversely isotropic media
Authors Laxmidhar Behera and Ilya TsvankinABSTRACTTilted transversely isotropic formations cause serious imaging distortions in active tectonic areas (e.g., fold‐and‐thrust belts) and in subsalt exploration. Here, we introduce a methodology for P‐wave prestack depth imaging in tilted transversely isotropic media that properly accounts for the tilt of the symmetry axis as well as for spatial velocity variations.
For purposes of migration velocity analysis, the model is divided into blocks with constant values of the anisotropy parameters ε and δ and linearly varying symmetry‐direction velocity VP0 controlled by the vertical (kz) and lateral (kx) gradients. Since determination of tilt from P‐wave data is generally unstable, the symmetry axis is kept orthogonal to the reflectors in all trial velocity models. It is also assumed that the velocity VP0 is either known at the top of each block or remains continuous in the vertical direction. The velocity analysis algorithm estimates the velocity gradients kz and kx and the anisotropy parameters ε and δ in the layer‐stripping mode using a generalized version of the method introduced by Sarkar and Tsvankin for factorized transverse isotropy with a vertical symmetry axis.
Synthetic tests for several models typical in exploration (a syncline, uptilted shale layers near a salt dome and a bending shale layer) confirm that if the symmetry‐axis direction is fixed and VP0 is known, the parameters kz, kx, ε and δ can be resolved from reflection data. It should be emphasized that estimation of ε in tilted transversely isotropic media requires using nonhyperbolic moveout for long offsets reaching at least twice the reflector depth. We also demonstrate that application of processing algorithms designed for a vertical symmetry axis to data from tilted transversely isotropic media may lead to significant misfocusing of reflectors and errors in parameter estimation, even when the tilt is moderate (30°). The ability of our velocity analysis algorithm to separate the anisotropy parameters from the velocity gradients can be also used in lithology discrimination and geologic interpretation of seismic data in complex areas.
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Addressing non‐uniqueness in linearized multichannel surface wave inversion
More LessABSTRACTThe multichannel analysis of the surface waves method is based on the inversion of observed Rayleigh‐wave phase‐velocity dispersion curves to estimate the shear‐wave velocity profile of the site under investigation. This inverse problem is nonlinear and it is often solved using ‘local’ or linearized inversion strategies. Among linearized inversion algorithms, least‐squares methods are widely used in research and prevailing in commercial software; the main drawback of this class of methods is their limited capability to explore the model parameter space. The possibility for the estimated solution to be trapped in local minima of the objective function strongly depends on the degree of nonuniqueness of the problem, which can be reduced by an adequate model parameterization and/or imposing constraints on the solution.
In this article, a linearized algorithm based on inequality constraints is introduced for the inversion of observed dispersion curves; this provides a flexible way to insert a priori information as well as physical constraints into the inversion process. As linearized inversion methods are strongly dependent on the choice of the initial model and on the accuracy of partial derivative calculations, these factors are carefully reviewed. Attention is also focused on the appraisal of the inverted solution, using resolution analysis and uncertainty estimation together with a posteriori effective‐velocity modelling. Efficiency and stability of the proposed approach are demonstrated using both synthetic and real data; in the latter case, cross‐hole S‐wave velocity measurements are blind‐compared with the results of the inversion process.
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Comparison of scaling methods for waveform inversion
Authors Ugeun Jang, Dong‐Joo Min and Changsoo ShinABSTRACTWaveform inversion can lead to faint images for later times due to geometrical spreading. The proper scaling of the steepest‐descent direction can enhance faint images in waveform inversion results. We compare the effects of different scaling techniques in waveform inversion algorithms using the steepest‐descent method. For the scaling method we use the diagonal of the pseudo‐Hessian matrix, which can be applied in two different ways. One is to scale the steepest‐descent direction at each frequency independently. The other is to scale the steepest‐descent direction summed over the entire frequency band. The first method equalizes the steepest‐descent directions at different frequencies and minimizes the effects of the band‐limited source spectrum in waveform inversion. In the second method, since the steepest‐descent direction summed over the entire frequency band is divided by the diagonal of the pseudo‐Hessian matrix summed over the entire frequency band, the band‐limited property of the source wavelet spectrum still remains in the scaled steepest‐descent directions. The two scaling methods were applied to both standard and logarithmic waveform inversion. For standard waveform inversion, the method that scales the steepest‐descent direction at every frequency step gives better results than the second method. On the other hand, logarithmic waveform inversion is not sensitive to the scaling method, because taking the logarithm of wavefields automatically means that results for the steepest‐descent direction at each frequency are commensurate with each other. If once the steepest‐descent directions are equalized by taking the logarithm of wavefields in logarithmic waveform inversion, the additional equalizing effects by the scaling method are not as great as in conventional waveform inversion.
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Effects of uncertainty in rock‐physics models on reservoir parameter estimation using seismic amplitude variation with angle and controlled‐source electromagnetics data
Authors Jinsong Chen and Thomas A. DickensABSTRACTThis paper investigates the effects of uncertainty in rock‐physics models on reservoir parameter estimation using seismic amplitude variation with angle and controlled‐source electromagnetics data. The reservoir parameters are related to electrical resistivity by the Poupon model and to elastic moduli and density by the Xu‐White model. To handle uncertainty in the rock‐physics models, we consider their outputs to be random functions with modes or means given by the predictions of those rock‐physics models and we consider the parameters of the rock‐physics models to be random variables defined by specified probability distributions. Using a Bayesian framework and Markov Chain Monte Carlo sampling methods, we are able to obtain estimates of reservoir parameters and information on the uncertainty in the estimation. The developed method is applied to a synthetic case study based on a layered reservoir model and the results show that uncertainty in both rock‐physics models and in their parameters may have significant effects on reservoir parameter estimation. When the biases in rock‐physics models and in their associated parameters are unknown, conventional joint inversion approaches, which consider rock‐physics models as deterministic functions and the model parameters as fixed values, may produce misleading results. The developed stochastic method in this study provides an integrated approach for quantifying how uncertainty and biases in rock‐physics models and in their associated parameters affect the estimates of reservoir parameters and therefore is a more robust method for reservoir parameter estimation.
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Testing Gassmann fluid substitution: sonic logs versus ultrasonic core measurements
Authors Marcos Grochau and Boris GurevichABSTRACTAlthough Gassmann fluid substitution is standard practice for time‐lapse studies, its validity in the field environment rests upon a number of underlying assumptions. The impact of violation on the predictions of Gassmann equations can only ultimately be validated by in situ testing in real geological environments. In this paper we show a workflow that we developed to test Gassmann fluid substitution by comparing saturated P‐wave moduli computed from dry core measurements against those obtained from sonic and density logs. The workflow has been tested on 43 samples taken from a 45 m turbidite reservoir from the Campos Basin, offshore Brazil. The results show good statistical agreement between the P‐wave elastic moduli computed from cores using the Gassmann equation with the corresponding moduli computed from log data. This confirms that all the assumptions of the Gassmann are adequate within the measurement error and natural variability of elastic properties. These results provide further justification for using the Gassmann theory to interpret time‐lapse effects in this sandstone reservoir and in similar geological formations.
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Velocity variations in carbonate rocks due to dual porosity and wave‐induced fluid flow
Authors Remy Agersborg, Tor Arne Johansen and Morten JakobsenABSTRACTStiffness variations in carbonates may be described as resulting from different concentrations of flat compliant pores or cracks, which can have a significant effect on the effective stiffness and acoustic properties (e.g., velocities and attenuations) of dry as well as saturated carbonates, although they carry extremely little porosity. As shown in this paper, the effects of dual porosity and wave‐induced fluid flow or pore pressure communication may also play a significant role. On the basis of a previously published T‐matrix approach to model the effective viscoelastic properties of cracked porous media, we illustrate the (frequency‐dependent) effects of wave‐induced fluid flow (mainly squirt flow) or pore pressure communication for a model structure consisting of a mixture of fluid‐saturated porous grains and fluid‐saturated cavities (vugs, etc.) that are embedded in a solid matrix associated with carbonates. We assume that the pores within the porous grains are decoupled from the pores in the solid matrix (and possibly saturated with different fluids) but that each pore system at the micro and/or mesoscale may or may not be connected. For each of four different connectivity models, we present numerical results for four different cases of microstructure (that emphasize the importance of cracks and flat compliant pores). Our numerical results indicate that the velocity and attenuation spectra of carbonates vary significantly, even when the crack density and all other volume concentrations are constant.
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Forward modelling and inverse problem in the comprehensive interpretation of well logs
Authors U. Woznicka, J. Jarzyna and A. CichyABSTRACTComprehensive interpretation of well logs often consists in solving a set of equations with complex boundary conditions. For each log, the equation combines geological parameters and a response by the device. Minimization is a way of obtaining the best solution that involves finding the minimum of the defined error function. In the case discussed here, an error is a measure of the difference between recorded and theoretical logs.
The simplest and quickest way to determine a solution to the presented problem is to apply the conjugate gradient descent method to minimize the error function. This approach is not efficient in some cases when logging in regions with complex geology.
We prove that a special algorithm using the Monte Carlo method combined with the conjugate gradient descent method gives considerably better results in comprehensive interpretation. A measure of the quality of the proposed method is the discrepancy between the standard solution obtained from commercial software used in the petroleum industry and the new algorithm result.
We present examples of the application of the proposed algorithm for comprehensive interpretation in typical Zechstein dolomite beds and the Carboniferous sandstone layer in the Polish Lowland.
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Application of the continuous wavelet transform on seismic data for mapping of channel deposits and gas detection at the CO2SINK site, Ketzin, Germany
More LessABSTRACTConventional seismic data are band limited and therefore, provide limited geological information. Every method that can push the limits is desirable for seismic data analysis. Recently, time‐frequency decomposition methods are being used to quickly extract geological information from seismic data and, especially, for revealing frequency‐dependent amplitude anomalies. Higher frequency resolution at lower frequencies and higher temporal resolution at higher frequencies are the objectives for different time‐frequency decomposition methods. Continuous wavelet transform techniques, which are the same as narrow‐band spectral analysis methods, provide frequency spectra with high temporal resolution without the windowing process associated with other techniques. Therefore, this technique can be used for analysing geological information associated with low and high frequencies that normally cannot be observed in conventional seismic data. In particular, the continuous wavelet transform is being used to detect thin sand bodies and also as a direct hydrocarbon indicator. This paper presents an application of the continuous wavelet transform method for the mapping of potential channel deposits, as well as remnant natural gas detection by mapping low‐frequency anomalies associated with the gas. The study was carried out at the experimental CO2 storage site at Ketzin, Germany (CO2SINK). Given that reservoir heterogeneity and faulting will have significant impact on the movement and storage of the injected CO2, our results are encouraging for monitoring the migration of CO2 at the site. Our study confirms the efficiency of the continuous wavelet transform decomposition method for the detection of frequency‐dependent anomalies that may be due to gas migration during and after the injection phase and in this way, it can be used for real‐time monitoring of the injected CO2 from both surface and borehole seismics.
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Comparison of surface seismic sources at the CO2SINK site, Ketzin, Germany
More LessABSTRACTIn 2004 three seismic surface sources (VIBSIST, accelerated weight drop and MiniVib) were tested in a pilot study at the Ketzin test site, Germany, a study site for geological storage of CO2 (EU project CO2SINK). The main objectives of this pilot study were to 1) evaluate the response of the Ketzin site to reflection seismics, especially at the planned injection depth, 2) test different acquisition parameters and 3) use the results to guide the planning of the 3D survey. As part of these objectives, we emphasize the source performance comparison in this study. The sources were tested along two perpendicular lines of 2.4 km length each. Data were acquired by shooting at all stations (source and receiver spacing of 20 m) on both lines, allowing common‐midpoint stacked sections to be produced. The sources' signal characteristics based on signal‐to‐noise ratio, signal penetration and frequency content of raw shot records were analysed and stacked sections were compared. The results show that all three surface sources are suitable for reflection seismic studies down to a depth of about 1 km and provide enough bandwidth for resolving the geological targets at the site, i.e., the Weser and Stuttgart Formations. Near surface conditions, especially a thick weathering layer present in this particular area, strongly influence the data quality, as indicated by the difference in reflectivity and signal‐to‐noise ratio of the two common‐midpoint lines. The stacked sections of the MiniVib source show the highest frequency signals down to about 500 ms traveltime (approximately 500 m depth) but also the shallowest signal penetration depth. The VIBSIST source generates signals with the highest signal‐to‐noise ratio and greatest signal penetration depth of the tested sources. In particular, reflections below 900 ms (approximately 1 km depth) are best imaged by the VIBSIST source. The weight drop performance lies in between these two sources and might be recommended as an appropriate source for a 3D survey at this site because of the shorter production time compared to the VIBSIST and MiniVib sources.
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Thermal effect of magma intrusion on the electrical properties of magnetic rocks from Hammamat sediments, Cairo, Egypt
Authors Mohamed M. Gomaa and Ragaa ElsayedABSTRACTThe thermal effects of magmatic intrusion on the conductivity and dielectric constant of magnetic rocks from Hammamat sediments, NE desert, Cairo, Egypt (latitude ∼27° and longitude ∼33°) were investigated experimentally in the laboratory using nonpolarizing electrodes. Granitic magma was intruded into the Hammamat sediments, which are a mixture of mainly magnetite with sandstone and due to the thermal effect the area around was extensively heated and altered to different degrees. Due to this magma intrusion, magnetite was transformed (by heating) to hematite to different degrees according to its location from the intrusion. Complex impedance measurements were performed in the frequency range of 10 Hz to 100 KHz at normal temperature (∼20°C) and at a relative humidity of ∼50% RH. Samples were collected at different locations perpendicular to the core of the magma intrusion. Experimental data indicate that the electrical properties vary strongly as we move away (with distance) from the magma intrusion. The conductivity of hematite is ∼10−2 S/m and that of magnetite is ∼104 S/m. As we move from magnetite to hematite (to the core of the magma intrusion) it is supposed that the conductivity will decrease but it was found that the conductivity increases (which is supposed to be abnormal). The conductivity increases with increasing frequency from ∼10−8 S/m to ∼10−5 S/m with almost power‐law dependence on frequency. The conductivity increases in the order of one decade due to the variation from magnetite to hematite. The increase of conductivity, as we move from magnetite to hematite, was argued to be due to the heating that partially or completely melts the samples, thus the porosity of the samples was decreased and accordingly the conductivity and dielectric constant increased. It was also supposed that the grains of the conductor in the samples are coated or isolated with insulator material. A percolation behaviour for the conductivity and dielectric constant, characteristic of random conductor‐insulator mixtures, was found with distance, where continuous paths of the conductive material occur accompanied by peaking of the dielectric constant.
Complex impedance plots show that as we move in the direction of altered samples (towards hematite) the relation between real and imaginary impedance changes from a linear form to an arc of a depressed semicircle and increases in depression as we move in the direction of the altered samples, which is consistent with the above interpretation.
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Pushing the vibrator ground‐force envelope towards low frequencies
By Zhouhong WeiABSTRACTSeveral mechanical and hydraulic limitations hinder the ground‐force energy output of a seismic vibrator at low frequencies. The hydraulic pump flow, pump response time, reaction mass stroke, servo valve stroke, engine horsepower, accumulator size, harmonic distortion and vehicle chassis isolation each play a role in limiting the ground‐force energy output of vibrators. In addition, the peak‐decoupling force – which is defined as the smaller value of either the maximum peak force or the hold‐down weight – also plays a role in limiting ground‐force energy production. A model useful for simulating seismic vibrator dynamics is developed to evaluate the impact of these parameters on the vibrator fundamental force envelope at low frequencies. Model data show that among these factors the reaction mass stroke and the peak‐decoupling force are key parameters for setting the target fundamental force that can be achieved at low frequencies. Formulas are derived to estimate fundamental force, peak force and the reaction mass displacement. These formulas can serve as guidelines for sweep designers who plan to design low frequency sweeps with considerable dwell time in the lower frequency ranges. Test data show that formulas can be used to profile the vibrator envelope at low frequencies.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 69 (2021)
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Volume 57 (2009)
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Volume 53 (2005)
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