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- Volume 60, Issue 3, 2012
Geophysical Prospecting - Volume 60, Issue 3, 2012
Volume 60, Issue 3, 2012
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Shifted hyperbola moveout approximation revisited
Authors Alexey Stovas and Sergey FomelABSTRACTThe shifted hyperbola approximation is widely used in seismic applications. Mostly, this approximation is applied to reflection moveout in multilayered media. The traditional domain for this application is the t ‐ x domain. In this paper, we discuss the use of this approximation in the τ ‐ p and t ‐ p domains. The accuracy of the shifted hyperbola approximation defined in different domains is illustrated by analytical and numerical examples.
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A practical review of geostatistical processing applied to geophysical data: methods and applications
Authors Matthieu Bourges, Jean‐Luc Mari and Nicolas JeannéeABSTRACTNowadays, geostatistics is commonly applied for numerous gridding or modelling tasks. However, it is still under used and unknown for classical geophysical applications. This paper highlights the main geostatistical methods relevant for geophysical issues, for instance to improve the quality of seismic data such as velocity cubes or interpreted horizons. These methods are then illustrated through four examples. The first example, based on a gravity survey presents how a geostatistical interpolation can be used to filter out a global trend, in order to better define real anomalies. In the second case study, dedicated to refraction surveying, geostatistical filtering is used to filter out acquisition artefacts and identify the main geological structures. The third one is an example of porosity being integrated geostatistically with a seismic acoustic impedance map. The last example deals with geostatistical time to depth conversion; the interest of performing geostatistical simulations is finally discussed.
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Frequency‐domain acoustic‐elastic coupled waveform inversion using the Gauss‐Newton conjugate gradient method
Authors Ho Seuk Bae, Sukjoon Pyun, Wookeen Chung, Seung‐Goo Kang and Changsoo ShinABSTRACTWe developed a frequency‐domain acoustic‐elastic coupled waveform inversion based on the Gauss‐Newton conjugate gradient method. Despite the use of a high‐performance computer system and a state‐of‐the‐art parallel computation algorithm, it remained computationally prohibitive to calculate the approximate Hessian explicitly for a large‐scale inverse problem. Therefore, we adopted the conjugate gradient least‐squares algorithm, which is frequently used for geophysical inverse problems, to implement the Gauss‐Newton method so that the approximate Hessian is calculated implicitly. Thus, there was no need to store the Hessian matrix. By simultaneously back‐propagating multi‐components consisting of the pressure and displacements, we could efficiently extract information on the subsurface structures. To verify our algorithm, we applied it to synthetic data sets generated from the Marmousi‐2 model and the modified SEG/EAGE salt model. We also extended our algorithm to the ocean‐bottom cable environment and verified it using ocean‐bottom cable data generated from the Marmousi‐2 model. With the assumption of a hard seafloor, we recovered both the P‐wave velocity of complicated subsurface structures as well as the S‐wave velocity. Although the inversion of the S‐wave velocity is not feasible for the high Poisson's ratios used to simulate a soft seafloor, several strategies exist to treat this problem. Our example using multi‐component data showed some promise in mitigating the soft seafloor effect. However, this issue still remains open.
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Traveltime parameters in a tilted elliptical anisotropic medium‡
Authors Pavel Golikov and Alexey StovasABSTRACTIn this paper, we derive analytical expressions for one‐way and two‐way kinematical parameters in elliptical tilted transverse isotropy media. We show that the homogeneous elliptical tilted transverse isotropy models result in hyperbolic moveout with a reflection point sideslip x0, which can be considered as an additional traveltime parameter for one‐way wave propagation. For homogeneous elliptical tilted transverse isotropy models we show that the inversion of one‐way traveltime parameters suffers from the ambiguity for large tilts. It is shown that the accuracy of the inversion is sensitive to the error in x0. We also derive and invert the traveltime parameters for a vertically heterogeneous elliptical tilted transverse isotropy model with a tilt gradually changing with depth. The a priori knowledge of parameter δ is very important for inversion. The wrong choise of this parameter results in significant errors in inverted model parameters.
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Wave‐equation migration with dithered plane waves
Authors Francesco Perrone and Paul SavaABSTRACTWave‐equation based shot‐record migration provides accurate images but is computationally expensive because every shot must be migrated separately. Shot‐encoding migration, such as random shot‐encoding or plane‐wave migration, aims to reduce the computational cost of the imaging process by combining the original data into synthesized common‐source gathers. Random shot‐encoding migration and plane‐wave migration have different and complementary features: the first recovers the full spatial bandwidth of the image but introduces strong artefacts, which are due to the interference between the different shot wavefields; the second provides an image with limited spatial detail but is free of crosstalk noise. We design a hybrid scheme that combines linear and random shot‐encoding in order to limit the drawbacks and merge the advantages of these two techniques. We advocate mixed shot‐encoding migration through dithering of plane waves. This approach reduces the crosstalk noise relative to random shot‐encoding migration and increases the spatial bandwidth relative to conventional plane‐wave migration when the take‐off angle is limited to reduce the duration of the plane‐wave gather. In turn, this decreases the migration cost. Migration with dithered plane waves operates as a hybrid encoding scheme in‐between the end members represented by plane‐wave migration and random shot‐encoding. Migration with dithered plane waves has several advantages: every synthesized common‐source gather images in a larger aperture, the crosstalk noise is limited and higher spatial resolution is achievable compared to shot‐record migration, random shot‐encoding and linear shot‐encoding, respectively. Computational cost is also reduced relative to both random and linear shot‐encoding migration since fewer synthesized common‐source gathers are necessary to obtain a high signal‐to‐noise ratio and high spatial resolution in the final image.
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Geophysical benefits from an improved seismic vibrator
Authors Zhouhong Wei, Michael A. Hall and Thomas F. PhillipsABSTRACTThe seismic vibrator has become a very important source for land data acquisition and there have been dramatic improvements in recent times in the application of the vibroseis technique. These improvements have led to much increased productivity and in many cases much denser source sampling. At the same time, the vibrator itself has seen little improvement over the last couple of decades. There are needs in a few areas where an improvement in the vibrator itself can bring benefits to the quality of the seismic data acquired. This paper describes progress in four such areas, low‐frequency performance, high‐frequency performance, an improved estimate of the vibrator groundforce and source signature consistency over variable ground conditions. Each of these vibrator characteristics will be discussed in turn. Meanwhile, two field test results in which the performance of two different vibrators in these four areas are compared.
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Controlled source strength variation by changing the firing pressure ‐ a sensitivity study for 4D calibration
Authors Daniel Barker and Martin LandrøABSTRACTFor a 4D seismic operation to be successful, it is important to know what kind of 4D signal we expect to observe, as well as its magnitude. Normally, in a 4D feasibility study, we use rock physics models to quantify the effect of fluid or pressure changes within the reservoir and calculate the corresponding effects to the seismogram. However, to find if the predicted changes are actually observable at a given field, a dedicated calibration procedure might give valuable insight. One such procedure for marine seismics is to gradually change the source strength by varying the firing pressure in order to detect the sensitivity threshold for a given subsurface reflection. This procedure would be practical and feasible if the change of the source signature changes linearly with the source pressure. However, non‐linear effects will lead to minor changes in the later arrivals of the source signature, the so‐called bubble. By investigating these introduced errors for a reasonable air‐gun array we conclude that the method is still feasible since we find it possible to control and diminish the impact of the introduced errors.
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Field measurements of normal and shear fracture compliance
Authors C. Hobday and M.H. WorthingtonABSTRACTField estimates of the normal and shear compliance of water saturated fractures were obtained from a seismic experiment carried out on a wave‐cut platform of Upper Caithness Flagstone on the North coast of Scotland. The rocks are cut by two orthogonal sets of vertical fractures. Vertical geophones were glued to the rock surface and seismic waves were generated by striking the surface with a sledge hammer. First arrival traveltimes were obtained for source‐receiver distances up to 30 m. Differences of compressional velocity with direction across the platform were interpreted as resulting from the compliance of the fractures intersected by the transmitted waves. The average normal compliance for fractures at this site is 4.0 × 10−12± 1.0 × 10−12 m/Pa. There is much less certainty about the precise value of shear compliance. However, the normal/shear compliance ratio is determined to be ≤0.1.
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Lithology and fluid prediction from prestack seismic data using a Bayesian model with Markov process prior
Authors Hugo Hammer, Odd Kolbjørnsen, Håkon Tjelmeland and Arild BulandABSTRACTWe invert prestack seismic amplitude data to find rock properties of a vertical profile of the earth. In particular we focus on lithology, porosity and fluid. Our model includes vertical dependencies of the rock properties. This allows us to compute quantities valid for the full profile such as the probability that the vertical profile contains hydrocarbons and volume distributions of hydrocarbons. In a standard point wise approach, these quantities can not be assessed. We formulate the problem in a Bayesian framework, and model the vertical dependency using spatial statistics. The relation between rock properties and elastic parameters is established through a stochastic rock model, and a convolutional model links the reflectivity to the seismic. A Markov chain Monte Carlo (MCMC) algorithm is used to generate multiple realizations that honours both the seismic data and the prior beliefs and respects the additional constraints imposed by the vertical dependencies. Convergence plots are used to provide quality check of the algorithm and to compare it with a similar method. The implementation has been tested on three different data sets offshore Norway, among these one profile has well control. For all test cases the MCMC algorithm provides reliable estimates with uncertainty quantification within three hours. The inversion result is consistent with the observed well data. In the case example we show that the seismic amplitudes make a significant impact on the inversion result even if the data have a moderate well tie, and that this is due to the vertical dependency imposed on the lithology fluid classes in our model. The vertical correlation in elastic parameters mainly influences the upside potential of the volume distribution.
The approach is best suited to evaluate a few selected vertical profiles since the MCMC algorithm is computer demanding.
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Experimental verification of the fracture density and shear‐wave splitting relationship using synthetic silica cemented sandstones with a controlled fracture geometry
Authors Philip Tillotson, Jeremy Sothcott, Angus Ian Best, Mark Chapman and Xiang‐Yang LiABSTRACTWe present laboratory ultrasonic measurements of shear‐wave splitting from two synthetic silica cemented sandstones. The manufacturing process, which enabled silica cementation of quartz sand grains, was found to produce realistic sandstones of average porosity 29.7 ± 0.5% and average permeability 29.4 ± 11.3 mD. One sample was made with a regular distribution of aligned, penny‐shaped voids to simulate meso‐scale fractures in reservoir rocks, while the other was left blank. Ultrasonic shear waves were measured with a propagation direction of 90° to the coincident bedding plane and fracture normal. In the water saturated blank sample, shear‐wave splitting, the percentage velocity difference between the fast and slow shear waves, of <0.5% was measured due to the bedding planes (or layering) introduced during sample preparation. In the fractured sample, shear‐wave splitting (corrected for layering anisotropy) of 2.72 ± 0.58% for water, 2.80 ± 0.58% for air and 3.21 ± 0.58% for glycerin saturation at a net pressure of 40 MPa was measured. Analysis of X‐ray CT scan images was used to determine a fracture density of 0.0298 ± 0.077 in the fractured sample. This supports theoretical predictions that shear‐wave splitting (SWS) can be used as a good estimate for fracture density in porous rocks (i.e., SWS = 100εf, where εf is fracture density) regardless of pore fluid type, for wave propagation at 90° to the fracture normal.
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Estimating magnetic dike parameters using a non‐linear constrained inversion technique: an example from the Särna area, west central Sweden
Authors Majid Beiki and Laust B. PedersenABSTRACTIn this paper, we describe a non‐linear constrained inversion technique for 2D interpretation of high resolution magnetic field data along flight lines using a simple dike model. We first estimate the strike direction of a quasi 2D structure based on the eigenvector corresponding to the minimum eigenvalue of the pseudogravity gradient tensor derived from gridded, low‐pass filtered magnetic field anomalies, assuming that the magnetization direction is known. Then the measured magnetic field can be transformed into the strike coordinate system and all magnetic dike parameters – horizontal position, depth to the top, dip angle, width and susceptibility contrast – can be estimated by non‐linear least squares inversion of the high resolution magnetic field data along the flight lines.
We use the Levenberg‐Marquardt algorithm together with the trust‐region‐reflective method enabling users to define inequality constraints on model parameters such that the estimated parameters are always in a trust region. Assuming that the maximum of the calculated gzz (vertical gradient of the pseudogravity field) is approximately located above the causative body, data points enclosed by a window, along the profile, centred at the maximum of gzz are used in the inversion scheme for estimating the dike parameters. The size of the window is increased until it exceeds a predefined limit. Then the solution corresponding to the minimum data fit error is chosen as the most reliable one.
Using synthetic data we study the effect of random noise and interfering sources on the estimated models and we apply our method to a new aeromagnetic data set from the Särna area, west central Sweden including constraints from laboratory measurements on rock samples from the area.
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Gravity and magnetic investigation on the distribution of volcanic rocks in the Qinggelidi area, north‐eastern Junggar Basin (north‐west China)
Authors Yang Yushan, Li Yuanyuan and Liu TianyouABSTRACTA detailed investigation on the location of magmatic intrusions in the Carboniferous strata of the Qinggelidi area, north‐eastern Junggar Basin, is presented based on the interpretation of gravity and magnetic data constrained by petrophysical data, seismics and surface geology. The wavelet multi‐resolution analysis based on the discrete wavelet transform is adopted to the regional‐residual separation of gravity and magnetic anomalies. A power spectrum analysis is applied to estimate the source depths corresponding to different scales. A comparative analysis on the characteristics of local gravity and magnetic anomalies improved our understanding of volcanic rock distribution in the Carboniferous strata. Generally speaking, in total 75 anomalies are recognized, among which 23 are inferred to be the responses of basalts, diabases and andesites with high density and strong magnetization. Twelve anomalies are assumed to be caused by andesites, rhyolites and volcanic breccias with medium‐low density and high magnetization. There are still five anomalies that are believed to be generated by volcanic tuffs with low density and weak magnetization. Lastly, four cross‐sections in 3D gravity and magnetic modelling are displayed to provide a more thorough image of volcanic rocks in our study area.
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Update of the precision geoid determination in Korea
Authors Tae‐Suk Bae, Jisun Lee, Jay Hyoun Kwon and Chang‐Ki HongABSTRACTFrom the late 1990s, many studies on local geoid construction have been made in South Korea. However, the precision of the previous geoid has remained about 15 cm due to distribution and quality problems of gravity and GPS/levelling data. Since 2007, new land gravity data and GPS/levelling data have been obtained through many projects such as the Korean Land Spatilaization, Unified Control Point and Gravity survey on the Benchmark. The newly obtained data are regularly distributed to a certain degree and show much better improvement in their quality. In addition, an airborne gravity survey was conducted in 2008 to cover the Korean peninsula (South Korea only). Therefore, it is expected that the precision of the geoid could be improved. In this study, the new South Korean gravimetric geoid and hybrid geoid are presented based on land, airborne, ship‐borne, altimeter gravity data, geopotential model and topographic data. As for the methodology, the general remove‐restore approach was applied with the best chosen parameters in order to produce a precise local geoid. The global geopotential model EGM08 was used to remove the low‐frequency components using degree and order up to 360 and the short wavelength part of the gravity signal was dealt with by using the Shuttle Radar Topography Mission data. The parameters determined empirically in this study include for Stokes’ integral 0.5° and for Wong‐Gore kernel 110–120°, respectively and 10 km for both the Bjerhammar sphere depth and attenuation factor. The final gravimetric geoid in South Korea ranges from 20–31 m with a precision of 5.45 cm overall compared to 1096 GPS/levelling data. In addition, the South Korean hybrid geoid produces 3.46 cm and 3.92 cm for degrees of fitness and precision, respectively and a better statistic of 2.37 cm for plain and urban areas was achieved. The gravimetric and hybrid geoids are expected to improve further when the refined land gravity data are included in the near future.
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Research note: Laboratory study of the influence of changing the injection rate on the geometry of the fluid front and on P‐wave ultrasonic velocities in sandstone
Authors Sofia Lopes and Maxim LebedevABSTRACTForced imbibition was performed in reservoir sandstone by injecting water into a dry sample. The injection was monitored with X‐ray computed tomography and acoustic acquisition to simultaneously visualize the displacement of the fluid and quantify its presence by calculating saturation and P‐wave velocities.
We observed a strong influence when changing the injection rates on the acoustic response. Upon decreasing the injection rate from 5 mL/h to 0.1 mL/h, P‐wave velocities decreased sharply: 100 m/s in 1 h. This behaviour is related to the partially saturated conditions of the sample (76% of saturation) before decreasing the injection rate. The air that is still trapped is free to move due to a decrease of pore pressure that is no longer forced by the higher injection rate. After 1 hour, P‐wave velocities started increasing with small changes in saturation. Stopping injection for 16 hrs decreased saturation by 8% and P‐wave velocities by 100 m/s. Restarting injection at 5 mL/h increased saturation to 76% while P‐wave velocities fluctuated considerably for 2 hrs until they stabilized at 2253 m/s. Through the computed tomography scans we observed a water front advancing through the sample and how its shape changed from a plane to a curve after decreasing the injection rate.
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Research Note: Internal/external seismic source wavefield separation and cancellation
By C.J. ThomsonABSTRACTA compact representation is obtained for the separation of a scalar wavefield on a closed surface into parts due to internal and external sources. The formula assumes that the total field and its gradients are known on the surface, as is the exact Green function of the medium. The derivation involves four rather straightforward applications of Green’s theorem or the representation theorem, though it is a remarkable result in that waves from either source that traverse the boundary many times are appropriately separated. The intermediate results at the four steps of the derivation also shed light on the possibility of acoustic shielding from unwanted sources without knowledge of the Green function for the medium.
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Volume 72 (2023 - 2024)
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