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- Volume 66, Issue 8, 2018
Geophysical Prospecting - Volume 66, Issue 8, 2018
Volume 66, Issue 8, 2018
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Inverse problem for Goupillaud‐layered earth model and dynamic deconvolution
Authors Virgil Bardan and Enders A. RobinsonABSTRACTThis paper presents, in a tutorial form, some analytical inversion techniques for the Goupillaud‐layered earth model. Finding the reflection coefficients from the reflection seismogram is the inverse problem for the model. For this reason we present a thorough description of the inverse problem for the Goupillaud model, two solutions to solve the inverse scattering problem using linear discrete equations and the solution obtained using the classic dynamic deconvolution method. The inversion is achieved using Robinson's polynomials Pk(z), Qk(z), Ak(z) and their reverse polynomials, as well as some properties of the model (the Lorentz transformation and the Einstein subtraction formula). The method of dynamic deconvolution, which makes the inversion of the model very simple computationally, is based on the physical structure of the reflection seismogram. We present the classic dynamic deconvolution algorithm for the non‐free‐surface Goupillaud model to show that the dynamic deconvolution method can provide efficient discrete procedures for the inversion. For this reason, though the inverse dynamic deconvolution procedures are old algorithms, they could be useful today for solving inverse scattering problems arising in exploration geophysics and various fields.
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Seismic time‐lapse imaging using interferometric least‐squares migration: Case study
Authors Mrinal Sinha and Gerard T. SchusterABSTRACTSeismic time‐lapse surveys are susceptible to repeatability errors due to varying environmental conditions. To mitigate this problem, we propose the use of interferometric least‐squares migration to estimate the migration images for the baseline and monitor surveys. Here, a known reflector is used as the reference reflector for interferometric least‐squares migration, and the data are approximately redatumed to this reference reflector before imaging. This virtual redatuming mitigates the repeatability errors in the time‐lapse migration image. Results with synthetic and field data show that interferometric least‐squares migration can sometimes reduce or eliminate artifacts caused by non‐repeatability in time‐lapse surveys and provide a high‐resolution estimate of the time‐lapse change in the reservoir.
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Travel time computations using a compact eikonal equation for vertical transverse isotropic media
Authors Peyman Moghaddam, Reza Khajavi and Henk KeersABSTRACTEikonal solvers often have stability problems if the velocity model is mildly heterogeneous. We derive a stable and compact form of the eikonal equation for P‐wave propagation in vertical transverse isotropic media. The obtained formulation is more compact than other formulations and therefore computationally attractive. We implemented ray shooting for this new equation through a Hamiltonian formalism. Ray tracing based on this new equation is tested on both simple as well as more realistic mildly heterogeneous velocity models. We show through examples that the new equation gives travel times that coincide with the travel time picks from wave equation modelling for anisotropic wave propagation.
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Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid‐characteristic method
More LessABSTRACTThis paper introduces a novel method of modelling acoustic and elastic wave propagation in inhomogeneous media with sharp variations of physical properties based on the recently developed grid‐characteristic method which considers different types of waves generated in inhomogeneous linear‐elastic media (e.g., longitudinal, transverse, Stoneley, Rayleigh, scattered PP‐, SS‐waves, and converted PS‐ and SP‐waves). In the framework of this method, the problem of solving acoustic or elastic wave equations is reduced to the interpolation of the solutions, determined at earlier time, thus avoiding a direct solution of the large systems of linear equations required by the FD or FE methods. We apply the grid‐characteristic method to compare wave phenomena computed using the acoustic and elastic wave equations in geological medium containing a hydrocarbon reservoir or a fracture zone. The results of this study demonstrate that the developed algorithm can be used as an effective technique for modelling wave phenomena in the models containing hydrocarbon reservoir and/or the fracture zones, which are important targets of seismic exploration.
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Correlation‐based reflection waveform inversion by one‐way wave equations
Authors Liangguo Dong, Zhongyi Fan, Hongzhi Wang, Benxin Chi and Yuzhu LiuABSTRACTReflection full waveform inversion can update subsurface velocity structure of the deeper part, but tends to get stuck in the local minima associated with the waveform misfit function. These local minima cause cycle skipping if the initial background velocity model is far from the true model. Since conventional reflection full waveform inversion using two‐way wave equation in time domain is computationally expensive and consumes a large amount of memory, we implement a correlation‐based reflection waveform inversion using one‐way wave equations to retrieve the background velocity. In this method, one‐way wave equations are used for the seismic wave forward modelling, migration/de‐migration and the gradient computation of objective function in frequency domain. Compared with the method using two‐way wave equation, the proposed method benefits from the lower computational cost of one‐way wave equations without significant accuracy reduction in the cases without steep dips. It also largely reduces the memory requirement by an order of magnitude than implementation using two‐way wave equation both for two‐ and three‐dimensional situations. Through numerical analysis, we also find that one‐way wave equations can better construct the low wavenumber reflection wavepath without producing high‐amplitude short‐wavelength components near the image points in the reflection full waveform inversion gradient. Synthetic test and real data application show that the proposed method efficiently updates the background velocity model.
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An automated cross‐validation method to assess seismic time‐to‐depth conversion accuracy: a case study on the Cooper and Eromanga basins, Australia
Authors David Kulikowski, Catherine Hochwald and Khalid AmrouchABSTRACTSelecting a seismic time‐to‐depth conversion method can be a subjective choice that is made by geophysicists, and is particularly difficult if the accuracy of these methods is unknown. This study presents an automated statistical approach for assessing seismic time‐to‐depth conversion accuracy by integrating the cross‐validation method with four commonly used seismic time‐to‐depth conversion methods. To showcase this automated approach, we use a regional dataset from the Cooper and Eromanga basins, Australia, consisting of 13 three‐dimensional (3D) seismic surveys, 73 two‐way‐time surface grids and 729 wells. Approximately 10,000 error values (predicted depth vs. measured well depth) and associated variables were calculated. The average velocity method was the most accurate overall (7.6 m mean error); however, the most accurate method and the expected error changed by several metres depending on the combination and value of the most significant variables. Cluster analysis tested the significance of the associated variables to find that the seismic survey location (potentially related to local geology (i.e. sedimentology, structural geology, cementation, pore pressure, etc.), processing workflow, or seismic vintage), formation (potentially associated with reduced signal‐to‐noise with increasing depth or the changes in lithology), distance to the nearest well control, and the spatial location of the predicted well relative to the existing well data envelope had the largest impact on accuracy. Importantly, the effect of these significant variables on accuracy were found to be more important than choosing between the four methods, highlighting the importance of better understanding seismic time‐to‐depth conversions, which can be achieved by applying this automated cross‐validation method.
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Design, modelling and imaging of marine seismic swarm surveys
More LessABSTRACTAutonomous marine vehicles instrumented with seismic sensors allow for new efficient seismic survey designs. One such design is the swarm survey, where a group, or swarm, of slow moving autonomous marine vehicles record seismic data from shots fired by a source vessel sailing around circles within the swarm. The size of the swarm is dictated by the maximum offset requirement of the survey, and it can be shaped to acquire wide‐ and full‐azimuth data. The swarm survey design equation describes the relationship between the source and receiver positions of the survey and the subsurface coverage or fold. It is used to adapt the swarm to the seismic survey requirements and to calculate survey duration time estimates as function of available equipment. It is shown that a survey conducted by a slowly moving swarm requires six times fewer shots than an equivalent seabed node survey conducted over 85.5 km2. Swarm surveys can also be adapted to efficiently conduct infill surveys and replace multi‐vessel undershoots. The efficiency of the survey can further be increased when the autonomous marine vehicles are towing short streamers with multiple receivers. Synthetic tests show that the seismic images for swarm surveys are comparable to those from streamer surveys, while little variation in image quality is found when reducing the number of autonomous marine vehicles but equipping them with a short streamer with multiple receivers.
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A compound method for random noise attenuation
Authors Diriba Gemechu, Jianwei Ma and Xueshan YongABSTRACTRandom noise attenuation, preserving the events and weak features by improving signal‐to‐noise ratio and resolution of seismic data are the most important issues in geophysics. To achieve this objective, we proposed a novel seismic random noise attenuation method by building a compound algorithm. The proposed method combines sparsity prior regularization based on shearlet transform and anisotropic variational regularization. The anisotropic variational regularization which is based on the linear combination of weighted anisotropic total variation and anisotropic second‐order total variation attenuates noises while preserving the events of seismic data and it effectively avoids the fine‐scale artefacts due to shearlets from the restored seismic data. The proposed method is formulated as a convex optimization problem and the split Bregman iteration is applied to solve the optimization problem. To verify the effectiveness of the proposed method, we test it on several synthetic seismic datasets and real datasets. Compared with three methods (the linear combination of weighted anisotropic total variation and anisotropic second‐order total variation, shearlets and shearlet‐based weighted anisotropic total variation), the numerical experiments indicate that the proposed method attenuates random noises while alleviating artefact and preserving events and features of seismic data. The obtained result also confirms that the proposed method improves the signal‐to‐noise ratio.
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Monitoring CO2 saturation using time‐lapse amplitude versus offset analysis of 3D seismic data from the Ketzin CO2 storage pilot site, Germany
Authors Monika Ivandic, Peter Bergmann, Juliane Kummerow, Fei Huang, Christopher Juhlin and Stefan LuethABSTRACTThe injection of CO2 at the Ketzin pilot site commenced in June 2008 and was terminated in August 2013 after 67 kT had been injected into a saline formation at a depth of 630–650 m. As part of the site monitoring program, four 3D surface seismic surveys have been acquired to date, one baseline and three repeats, of which two were conducted during the injection period, and one during the post‐injection phase. The surveys have provided the most comprehensive images of the spreading CO2 plume within the reservoir layer. Both petrophysical experiments on core samples from the Ketzin reservoir and spectral decomposition of the 3D time‐lapse seismic data show that the reservoir pore pressure change due to CO2 injection has a rather minor impact on the seismic amplitudes. Therefore, the observed amplitude anomaly is interpreted to be mainly due to CO2 saturation. In this study, amplitude versus offset analysis has been applied to investigate the amplitude versus offset response from the top of the sandstone reservoir during the injection and post‐injection phases, and utilize it to obtain a more quantitative assessment of the CO2 gaseous saturation changes. Based on the amplitude versus offset modelling, a prominent decrease in the intercept values imaged at the top of the reservoir around the injection well is indeed associated solely with the CO2 saturation increase. Any change in the gradient values, which would, in case it was positive, be the only signature induced by the reservoir pressure variations, has not been observed. The amplitude versus offset intercept change is, therefore, entirely ascribed to CO2 saturation and used for its quantitative assessment. The estimated CO2 saturation values around the injection area in the range of 40%–60% are similar to those obtained earlier from pulsed neutron‐gamma logging. The highest values of 80% are found in the second seismic repeat in close vicinity to the injection and observation wells.
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Gravity and magnetic field characteristics and hydrocarbon prospects of the Tobago Basin
Authors Bingqiang Yuan, Lijun Song, Li Han, Shaole An and Chunguan ZhangABSTRACTThe Tobago Basin, which is located offshore northern Venezuela with a southern margin close to Trinidad and Tobago, has an area of approximately 59,600 km2. The Tobago Basin has relatively favourable hydrocarbon prospects, and to date, exploration work has mainly concentrated on small areas of the southwestern portion of the basin. To conduct a comprehensive study of the structural framework of the basin and the characteristics of the basement in order to identify prospective zones for hydrocarbon exploration, shipborne‐measured and satellite‐measured gravity data, shipborne‐measured magnetic data, and aeromagnetic survey data were analysed. A regularisation filtering method was used to separate and obtain regional and residual gravity and magnetic anomalies. Directional gradients of gravity and magnetic anomalies and the total horizontal gradient and vertical second derivative of gravity anomalies were employed to extract information about fault structures. Regression analysis methods were used to determine the basement depth. The geological significance of the gravity and magnetic fields was examined, the structural framework of the basin was assessed, the basement depth was estimated, and favourable hydrocarbon exploration prospects within the basin were identified. The results show that the Tobago Basin contains complex structures consisting mainly of two groups of faults trending in northeasterly and northwesterly directions and that the major northeasterly trending faults control the main structural configuration and depositional system within the basin. The basement of the Tobago Basin has deep rises and falls. It can be divided into the following four secondary tectonic units: the western sub‐basin, the central uplift area, the southern sub‐basin, and the northeastern sub‐basin. The central uplift area and northeastern sub‐basin are most likely to have developed hydrocarbon accumulations and should be targeted for further exploration.
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Effects of the sea floor topography on the 1D inversion of time‐domain marine controlled source electromagnetic data
Authors Ji Cai, Bülent Tezkan and Yuguo LiABSTRACTTime‐domain marine controlled source electromagnetic methods have been used successfully for the detection of resistive targets such as hydrocarbons, gas hydrate, or marine groundwater aquifers. As the application of time‐domain marine controlled source electromagnetic methods increases, surveys in areas with a strong seabed topography are inevitable. In these cases, an important question is whether bathymetry information should be included in the interpretation of the measured electromagnetic field or not. Since multi‐dimensional inversion is still not common in time‐domain marine controlled source electromagnetic methods, bathymetry effects on the 1D inversion of single‐offset and multi‐offset joint inversions of time‐domain controlled source electromagnetic methods data are investigated. We firstly used an adaptive finite element algorithm to calculate the time‐domain controlled source electromagnetic methods responses of 2D resistivity models with seafloor topography. Then, 1D inversions are applied on the synthetic data derived from marine resistivity models, including the topography in order to study the possible topography effects on the 1D interpretation. To evaluate the effects of topography with various steepness, the slope angle of the seabed topography is varied in the synthetic modelling studies for deep water (air interaction is absent or very weak) and shallow water (air interaction is dominant), respectively. Several different patterns of measuring configurations are considered, such as the systems adopting nodal receivers and the bottom‐towed system. According to the modelling results for deep water when air interaction is absent, the 2D topography can distort the measured electric field. The distortion of the data increases gradually with the enlarging of the topography's slope angle. In our test, depending on the configuration, the seabed topography does not affect the 1D interpretation significantly if the slope angle is less or around 10°. However, if the slope angle increases to 30° or more, it is possible that significant artificial layers occur in inversion results and lead to a wrong interpretation. In a shallow water environment with seabed topography, where the air interaction dominates, it is possible to uncover the true subsurface resistivity structure if the water depth for the 1D inversion is properly chosen. In our synthetic modelling, this scheme can always present a satisfactory data fit in the 1D inversion if only one offset is used in the inversion process. However, the determination of the optimal water depth for a multi‐offset joint inversion is challenging due to the various air interaction for different offsets.
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3D upper crustal density structure of the Deccan Syneclise, Central India
Authors K.N.D. Prasad, A.P. Singh and V.M. TiwariABSTRACTA constrained 3D density model of the upper crust along a part of the Deccan Syneclise is carried out based on the complete Bouguer anomaly data. Spectral analysis of the complete Bouguer gravity anomaly map of the study region suggests two major sources: short wavelength anomalies (<100 km) caused primarily due to the density inhomogeneities at shallow crustal level and long wavelength anomalies (>100 km) produced due to the sources deeper than the upper crust. A residual map of the short wavelength anomalies is prepared from the complete Bouguer anomaly using Butterworth high‐pass filter (100 km cut‐off wavelength). Utilizing the constraints from deep resistivity sounding, magnetotellurics and deep seismic sounding studies, 2.5D density models have been generated along 39 profiles of this region. The mismatch between the calculated response of the a priori 2.5D model with the residual (short wavelength) gravity anomalies is minimized by introducing high‐density intrusive bodies (≥2.81 g/cm3) in the basement. With these 2.5D density models, the initial geometry of our 3D density model, which includes alluvium, Deccan trap, Mesozoic sediment and high‐density intrusive bodies in the basement up to a depth of 7 km (upper crust), is generated. In the final 3D model, Deccan trap extends from 200 m to nearly 1700 m below the 90–150 m thick Quaternary sediment. Further down, the sub‐trappean Mesozoic sediment is present at a depth range of 600–3000 m followed by the basement. The derived 3D density model also indicates six intrusive bodies of density 2.83 g/cm3 in the basement at an average depth of about 4–7 km that best fits the residual gravity anomaly of the study area.
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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 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 57 (2009)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 54 (2006)
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Volume 52 (2004)
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Volume 49 (2001)
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Volume 1 (1953)