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Accurate production forecasting plays a pivotal role in understanding and effectively developing reservoirs. Numerous research shows that machine learning could be used to achieve fast and precise production predictions. In this three-part article, we use long short-term memory (LSTM), a machine learning technique, to predict oil, gas, and water production using real field data. This first part discusses the mathematics behind the LSTM and part two and three focus on its practical implementation. Recurrent neural network (RNN) and its variants, namely LSTM and gated recurrent unit (GRU), are specifically tailored for time-dependent data.
Least-squares reverse-time migration of simultaneous source with deep-learning-based denoising
Wu, Bo (China University of Petroleum (Beijing), China University of Petroleum (Beijing), China University of Petroleum (Beijing)) | Yao, Gang (China University of Petroleum (Beijing), China University of Petroleum (Beijing), China University of Petroleum (Beijing)) | Ma, Xiao (China University of Petroleum (Beijing), China University of Petroleum (Beijing), China University of Petroleum (Beijing)) | Chen, Hanming (China University of Petroleum (Beijing), China University of Petroleum (Beijing), China University of Petroleum (Beijing)) | Wu, Di (China University of Petroleum (Beijing), China University of Petroleum (Beijing), China University of Petroleum (Beijing)) | Cao, Jingjie (Hebei Geo University)
Least-squares reverse-time migration (LSRTM) is currently one of the most advanced migration imaging techniques in the field of geophysics. It utilizes least-squares inversion to fit the observed data, resulting in high-resolution imaging results with more accurate amplitudes and better illumination compensation than conventional reverse-time migration (RTM). However, noise in the observed data and the Born approximation forward operator can result in high-wavenumber artifacts in the final imaging results. Moreover, iteratively solving LSRTM leads to one or two orders of computational cost higher than conventional RTM, making it challenging to apply extensively in industrial applications. Simultaneous source acquisition technology can reduce the computational cost of LSRTM by reducing the number of wavefield simulations. However, this technique can also cause high-wavenumber crosstalk artifacts in the migration results. To effectively remove the high-wavenumber artifacts caused by these mentioned issues, in this paper, we combine simultaneous source and deep-learning to speed up LSRTM, as well as, to suppress high-wavenumber artifacts. A deep-residual neural network (DR-Unet) is trained with synthetic samples, which are generated by adding field noise to synthesized noise-free migration images. Then, the trained DR-Unet is applied on the gradient of LSRTM to remove high-wavenumber artifacts in each iteration. Compared to directly applying DR-Unet denoising to LSRTM results, embedding DR-Unet denoising into the inversion process can better preserve weak reflectors and improve denoising effects. Finally, we tested the proposed LSRTM method on two synthetic datasets and a land dataset. The tests demonstrate that the proposed method can effectively remove high-wavenumber artifacts, improve imaging results, and accelerate convergence speed.
ABSTRACT Prismatic reflections in seismic data carry abundant information about subsurface steeply dipping structures, such as salt flanks or near-vertical faults, playing an important role in delineating these structures when effectively used. Conventional linear least-squares reverse time migration (L-LSRTM) fails to use prismatic waves due to the first-order Born approximation, resulting in a blurry image of steep interfaces. We develop a nonlinear LSRTM (NL-LSRTM) method to take advantage of prismatic waves for the detailed characterization of subsurface steeply dipping structures. Compared with current least-squares migration methods of prismatic waves, our NL-LSRTM is nonlinear and thus avoids the challenging extraction of prismatic waves or the prior knowledge of L-LSRTM results. The gradient of NL-LSRTM consists of the primary and prismatic imaging terms, which can accurately project observed primary and prismatic waves into the image domain for the simultaneous depiction of near-horizontal and near-vertical structures. However, we find that the full Hessian-based Newton normal equation has two similar terms, which prompts us to make further comparison between the Newton normal equation and our NL-LSRTM. We determine that the Newton normal equation is problematic when applied to the migration problem because the primary reflections in the seismic records will be incorrectly projected into the image along the prismatic wavepath, resulting in an artifact-contaminated image. In contrast, the nonlinear data-fitting process included in the NL-LSRTM contributes to balancing the amplitudes of primary and prismatic imaging results, thus making NL-LSRTM produce superior images compared with the Newton normal equation. Several numerical tests validate the applicability and robustness of NL-LSRTM for the delineation of steeply dipping structures and illustrate that the imaging results are much better than the conventional L-LSRTM.
- Geophysics > Seismic Surveying > Seismic Processing > Seismic Migration (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (0.46)
ABSTRACT Prismatic reflections in seismic data carry abundant information about subsurface steeply dipping structures, such as salt flanks or near-vertical faults, playing an important role in delineating these structures when effectively used. Conventional linear least-squares reverse time migration (L-LSRTM) fails to use prismatic waves due to the first-order Born approximation, resulting in a blurry image of steep interfaces. We develop a nonlinear LSRTM (NL-LSRTM) method to take advantage of prismatic waves for the detailed characterization of subsurface steeply dipping structures. Compared with current least-squares migration methods of prismatic waves, our NL-LSRTM is nonlinear and thus avoids the challenging extraction of prismatic waves or the prior knowledge of L-LSRTM results. The gradient of NL-LSRTM consists of the primary and prismatic imaging terms, which can accurately project observed primary and prismatic waves into the image domain for the simultaneous depiction of near-horizontal and near-vertical structures. However, we find that the full Hessian-based Newton normal equation has two similar terms, which prompts us to make further comparison between the Newton normal equation and our NL-LSRTM. We determine that the Newton normal equation is problematic when applied to the migration problem because the primary reflections in the seismic records will be incorrectly projected into the image along the prismatic wavepath, resulting in an artifact-contaminated image. In contrast, the nonlinear data-fitting process included in the NL-LSRTM contributes to balancing the amplitudes of primary and prismatic imaging results, thus making NL-LSRTM produce superior images compared with the Newton normal equation. Several numerical tests validate the applicability and robustness of NL-LSRTM for the delineation of steeply dipping structures and illustrate that the imaging results are much better than the conventional L-LSRTM.
- Geophysics > Seismic Surveying > Seismic Processing > Seismic Migration (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (0.46)
Robust and efficient waveform-based velocity model building by optimal transport in the pseudotime domain: An ocean-bottom cable case study in the North Sea
Provenzano, Giuseppe (Universitรฉ Grenoble Alpes) | Brossier, Romain (Universitรฉ Grenoble Alpes) | Mรฉtivier, Ludovic (Universitรฉ Grenoble Alpes)
ABSTRACT Full-waveform inversion (FWI) in the North Sea has demonstrated its imaging power starting from low-resolution models obtained by traveltime tomography, enriching them with geologically interpretable fine-scale details. However, building a traveltime-based kinematically accurate starting model for FWI is a time-consuming and rather subjective process requiring phase identification and selection. The two main problems faced by FWI starting from noninformative initial models are the susceptibility to cycle skipping and a lack of sensitivity to low wavenumbers in the deep subsurface not sampled by turning waves. On a North Sea ocean-bottom cable 3D data set, a novel building methodology is applied that addresses those issues by jointly inverting reflections and refractions (joint full-waveform inversion [JFWI]) using a robust misfit function in the vertical traveltime domain (pseudotime). Pseudotime addresses reflectivity-velocity coupling and attenuates phase ambiguities at short offsets, whereas a graph-space optimal transport (GSOT) objective function with dedicated data windowing averts cycle skipping at intermediate-to-long offsets. A fast and balanced reflectivity reconstrution is obtained prior to JFWI thanks to an asymptotic-preconditioned impedance waveform inversion (WI). Starting from a linearly increasing one-dimensional model, GSOT-pseudotime JFWI is effective at obtaining a meaningful P-wave velocity macromodel down to depths sampled by reflections only, without phase identification and picking. P-wave FWI, starting from the JFWI-based model, injects the high wavenumbers missing in the JFWI solution, attaining apparent improvements in shallow and deep model reconstruction and imaging compared with the previous studies in the literature, and a satisfactory prediction of the ground-truth logs.
- Europe > Norway > North Sea (0.68)
- Europe > United Kingdom > North Sea (0.54)
- Europe > North Sea (0.45)
- (2 more...)
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (1.00)
- Europe > United Kingdom > North Sea > Central North Sea > Moray Firth > Moray Firth Basin > Moray Firth Basin > Witch Ground Graben > P.213 > Block 16/26a > Brae Field > Alba Field > Caran Sandstone Formation (0.99)
- Europe > United Kingdom > North Sea > Central North Sea > Moray Firth > Moray Firth Basin > Moray Firth Basin > Witch Ground Graben > P.213 > Block 16/26a > Brae Field > Alba Field > Alba Sandstone Formation (0.99)
- Europe > United Kingdom > North Sea > Central North Sea > Moray Firth > Moray Firth Basin > Fladen Ground Spur > Witch Ground Graben > P.213 > Block 16/26a > Brae Field > Alba Field > Caran Sandstone Formation (0.99)
- (5 more...)
ABSTRACT Wave-equation dispersion (WD) inversion techniques for surface waves have proven to be a robust way to invert the S-wave velocity model. Unlike 1D dispersion curve inversion, WD method obviates the need for a layered model assumption and reduces the susceptibility to cycle-skipping issues in surface wave full-waveform inversion. Previous WD inversion experiments conducted on Rayleigh and Love waves have highlighted that inverting Love waves yields better stability due to their independence from the P-wave velocity model. Nevertheless, Rayleigh waves possess the advantage of greater penetration depth compared with Love waves with similar wavelengths. Therefore, combining the two types of surface waves is a feasible way to improve the accuracy of S velocity tomograms. In light of this, we develop a novel approach: a joint WD inversion encompassing Rayleigh and Love waves. This innovative technique adjusts the weighting of individual WD gradients using the sensitivity factor of an equivalent layered model, offering a significant advancement in subsurface characterization. Synthetic model tests demonstrate that the joint WD inversion method can generate a more accurate S-wave velocity model, particularly in the presence of complex low-velocity layers or high-velocity layers, when compared with individual wave WD inversion techniques. Simultaneously, the results of field tests validate the effectiveness of the proposed joint WD inversion strategy in producing a more dependable S-wave velocity distribution that aligns closely with the actual geologic structure.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (1.00)
ABSTRACT Inversion velocity analysis (IVA) is an image-domain method built upon the spatial scale separation of the model. Accordingly, the IVA method is performed with an iterative process composed of two minimization steps consisting of migration (inner loop) and tomography (outer loop), respectively, with each step accounting for its Hessian or not. The migration part provides the common-image gathers (CIGs) with extension in the horizontal subsurface offset. Then, the differential semblance optimization (DSO) misfit measures the focusing of the events in the CIGs, which indicates the quality of the velocity model. Commonly, the velocity updates are obtained from the DSO gradient. IVA is a modified version in which the approximate inverse replaces the adjoint of the inner loop process; in that case, the migration Hessian is approximately diagonal in the high-frequency regime. In this work, we report on implementation of the tomographic Hessian (i.e.,ย the second derivative of the DSO misfit with respect to the background model) for the estimation of the background velocity model. We apply the second-order adjoint-state method to obtain the application of the tomographic Hessian on a vector. Then, we use the truncated-Newton (TN) method to obtain the update directions by computing approximately the application of the inverse of the tomographic Hessian on the descent direction. We also make a theoretical comparison between tomography in the IVA and full-waveform inversion contexts. Two numerical examples are used to compare, in terms of geophysical results and computational costs, the TN method with different gradient-based optimization methods applied to the IVA. A small model allows us to evaluate the eigenvalues of the tomographic Hessian, which explains the large damping needed in the TN case.
In this study, we interpreted a cumulative 600m acoustic image log across the Triassic to Cambro-Ordovician interval in the Berkaoui oil field, Algeria. We interpreted 40 distinct breakout zones which have a combined length of 210m. These breakouts are aligned in the NNE-SSW direction indicating a mean maximum horizontal stress (SHmax) azimuth of 110ยฐN. The observed breakouts are ranked as ยA-Qualityย following the World Stress Map ranking guidelines. The angular width of each breakout has been inferred from the image log analysis and the same has been utilized to infer the SHmax gradient by stress polygon approach following the frictional faulting mechanism. The stress polygon across all the breakout intervals provides a practical Shmax range between 24.7-31.1 MPa/km, with an average gradient of ~ 27 MPa/km. Considering the Shmin range across the studied intervals, we infer a SHmax/Shmin ratio dominantly between 1.40-1.65, which is a much narrower and better-constrained range when compared to the previously published ranges from nearby fields with the same stratigraphy. The relative magnitudes of the in-situ stresses indicate a strike-slip faulting regime in the Berkaoui field. This study presents the utility of image log analysis and integration of breakout interpretation to obtain a more robust geomechanical model with reduced SHmax uncertainty.
- North America > United States (1.00)
- Asia (1.00)
- Africa > Middle East > Algeria > Illizi Province (0.28)
- Africa > Middle East > Algeria > Ouargla Province > Hassi Messaoud (0.28)
- Phanerozoic > Paleozoic > Ordovician (1.00)
- Phanerozoic > Mesozoic > Cretaceous > Upper Cretaceous (0.46)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Geological Subdiscipline > Economic Geology > Petroleum Geology (0.75)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock (0.47)
- Geology > Structural Geology > Tectonics > Plate Tectonics (0.46)
- Geophysics > Borehole Geophysics (1.00)
- Geophysics > Seismic Surveying > Borehole Seismic Surveying (0.72)
- Asia > Middle East > Iraq > Basra Governorate > Arabian Basin > Widyan Basin > Mesopotamian Basin > Zubair Field > Zubair Formation (0.99)
- Asia > Middle East > Iraq > Basra Governorate > Arabian Basin > Widyan Basin > Mesopotamian Basin > Zubair Field > Mishrif Formation (0.99)
- Africa > Middle East > Egypt > Western Desert > Greater Western Dester Basin > Abu Gharadig Basin > Abu Gharadig Field (0.99)
- (10 more...)
Abstract This paper documents the results of diagnostic tests in a well that was equipped with measuring devices for analyzing pressure and acoustic behavior during multistage fracturing treatments. This well was also surveyed by an ultrasonic device for measuring the entry hole sizes of treated and untreated perforations. Well and treatment design parameters selected for scrutiny included cluster perforation density and the circumferential phase angle of entry holes with respect to elevation. Perforation erosional analysis was performed on each frac stage of the diagnostic wells by comparing perforation sizes of treated perforations with intentionally untreated perforations to estimate the eroded area for each perforation, then applying a two-component erosion model to allocate proppant among all the clusters for that frac stage. The allocated proppant was then used to compute treatment uniformity and compared with allocation and uniformity values determined by the DAS provider. This unique dataset was used to perform five categories of analyses: pipe/casing friction pressure, step down testing, perforation entry hole erosion, treating pressure, and inter-cluster proppant allocation and uniformity. Determination of perforation entry-hole erosion parameters are shown to have diagnostic value in assessing treatment confinement and identifying deviations from standard erosion theory. The impact of variable and uncertain initial (untreated) entry hole sizes is shown to adversely impact the accuracy of both DAS and erosion-based proppant allocation routines. Evidence is provided quantifying the negative effect of proppant separating from the fluid stream due to inertia on the accuracy of treatment distribution provided by DAS interpretation.
Joint Inversion of Potential Field Data with Adaptive Unstructured Tetrahedral Mesh
Cai, Hongzhu (China University of Geosciences, Hubei Subsurface Multi-scale Imaging Key Laboratory, State Key Laboratory of Geological Processes and Mineral Resources) | Kong, Ruijin (China University of Geosciences) | He, Ziang (China University of Geosciences) | Wang, Xinyu (China University of Geosciences) | Liu, Shuang (China University of Geosciences) | Huang, Sining (China University of Geosciences) | Kass, M. Andy (Aarhus University) | Hu, Xiangyun (China University of Geosciences, Hubei Subsurface Multi-scale Imaging Key Laboratory, State Key Laboratory of Geological Processes and Mineral Resources)
Inverting potential field data presents a significant challenge due to its ill-posed nature, often leading to non-unique model solutions. Addressing this, our work focuses on developing a robust joint inversion method for potential field data, aiming to achieve more accurate density and magnetic susceptibility distributions. Unlike most previous work that utilizes regular meshes, our approach adopts an adaptive unstructured tetrahedral mesh, offering enhanced capabilities in handling the inverse problem of potential field methods. During inversion, the tetrahedral mesh is refined in response to the model update rate. We integrate a Gramian constraint into the objective function, allowing enforcement of model similarity in terms of either model parameters or their spatial gradients on an unstructured mesh. Additionally, we employ the moving least-squares method for gradient operator computation, essential for model regularization. Our model studies indicate that this method effectively inverts potential field data, yielding reliable subsurface density and magnetic susceptibility distributions. The joint inversion approach, compared to individual dataset inversion, produces coherent geophysical models with enhanced correlations. Notably, it significantly mitigates the non-uniqueness problem, with the recovered anomaly locations aligning more closely with actual ground truths. Applying our methodology and algorithm to field data from the Ring of Fire area in Canada, the joint inversion process has generated comprehensive geophysical models with robust correlations, offering potential benefits for mineral exploration in the region.
- Geophysics > Magnetic Surveying (1.00)
- Geophysics > Gravity Surveying > Gravity Acquisition (1.00)
- Geophysics > Electromagnetic Surveying (1.00)
- (2 more...)
- Materials > Metals & Mining (1.00)
- Energy > Oil & Gas > Upstream (1.00)