Access the full text.
Sign up today, get DeepDyve free for 14 days.
G. Fehmers, C. Höcker (2003)
Fast structural interpretation with structure-oriented filteringStructure-Oriented FilteringGeophysics, 68
(2006)
Image estimation by example: Geophysical soundings image construction
J. Claerbout (1985)
Imaging the Earth's Interior
M. Giboli, R. Baina, L. Nicoletis, B. Duquet (2012)
Reverse Time Migration surface offset gathers part 1: a new method to produce ‘classical’ common image gathersSeg Technical Program Expanded Abstracts
Sergey Fomel, A. Guitton (2006)
Regularizing seismic inverse problems by model reparameterization using plane-wave constructionGeophysics, 71
S. Spitz (1991)
Seismic trace interpolation in the F-X domainGeophysics, 56
Yang Zhao, H. Zhang, Jidong Yang, T. Fei (2018)
Reducing artifacts of elastic reverse time migration by the deprimary techniqueGEOPHYSICS
J. Ronen (1987)
Wave‐equation trace interpolationGeophysics, 52
Yang Zhao, F. Niu, Zhishuai Zhang, Xiang Li, Jinhong Chen, Jidong Yang (2020)
Signal Detection and Enhancement for Seismic Crosscorrelation Using the Wavelet-Domain Kalman FilterSurveys in Geophysics, 42
Yang Zhao, F. Niu, Hongwei Liu, Xueyi Jia, Jidong Yang, S. Huo (2020)
Source‐Receiver Interferometric Redatuming Using Sparse Buried Receivers to Address Complex Near‐Surface Environments: A Case Study of Seismic Imaging Quality and Time‐Lapse RepeatabilityJournal of Geophysical Research: Solid Earth, 125
J. Etgen (2012)
3D Wave Equation Kirchhoff MigrationSeg Technical Program Expanded Abstracts
S. Doherty, O. Yilmaz (2000)
Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data
Sergey Fomel (2010)
Predictive painting of 3D seismic volumesGeophysics, 75
H. Chauris, M. Noble, G. Lambaré, P. Podvin (2002)
Migration velocity analysis from locally coherent events in 2‐D laterally heterogeneous media, Part I: Theoretical aspectsGeophysics, 67
G. Fehmers, C. Höcker (2002)
Fast structural interpretation with structure-oriented filteringGeophysics, 68
B. Duquet, P. Lailly (2006)
Efficient 3D wave-equation migration using virtual planar sourcesGeophysics, 71
Jin-Hai Zhang, T. Zheng (2015)
Receiver Function Imaging with Reconstructed Wavefields from Sparsely Scattered StationsSeismological Research Letters, 86
J Zhang (2014)
10.1785/0220140028%JSeismologicalResearchLettersSeismol Res Lett, 86
Yang Zhao, Tao Liu, Xueyi Jia, Hongwei Liu, Z. Xue, H. Zhang, Hejun Zhu, Hong Liang (2020)
Surface-offset gathers from elastic reverse time migration and velocity analysisGeophysics, 85
C. Stork (1992)
REFLECTION TOMOGRAPHY IN THE POSTMIGRATED DOMAINGeophysics, 57
K. Marfurt (2006)
Robust estimates of 3D reflector dip and azimuthGeophysics, 71
Zhiping Yang, Shouting Huang, Rui Yan (2015)
Improved Subsalt Tomography using RTM Surface Offset GathersSeg Technical Program Expanded Abstracts
Z. Xue, H. Zhang, Yang Zhao, Sergey Fomel (2019)
Pattern‐guided dip estimation with plane‐wave destruction filtersGeophysical Prospecting, 67
A. Ehinger, P. Lailly, K. Marfurt (1996)
Green's function implementation of common-offset, wave-equation migrationGeophysics, 61
(2020)
https:// doi
Sergey Fomel (2002)
Applications of plane-wave destruction filtersGeophysics, 67
Reverse Time Migration (RTM) Surface Offset Gathers (SOGs) are demonstrated to deliver more superior residual dip information than ray-based approaches. It appears more powerful in complex geological settings, such as salt areas. Still, the computational cost of constructing RTM SOGs is a big challenge in applying it to 3D field data. To tackle this challenge, we propose a novel method using dips of local events as a guide for RTM gather interpolation. The residual-dip information of the SOGs is created by connecting local events from depth-domain to time-domain via ray tracing. The proposed method is validated by a synthetic experiment and a field example. It mitigates the computational cost by an order of magnitude while producing comparable results as fully computed RTM SOGs. Keywords Surface-offset gathers · Reverse-time migration · Dip-guided interpolation · Reduced costs · Local-event raytracing 1 Introduction gathers. In contrast, reverse time migration, a method based on the two-way wave equation, can handle complex veloc- Classic ray-based migration velocity analysis (MVA) mainly ity overhang, has no dip limitations, thus can provide high- involves three major steps: (1) constructing offset or angle quality gathers for accurate estimation of residual moveout. domain gathers from Kirchhoff migration, (2) picking resid- Ehinger et al. (1996) initially performed the common-offset ual moveouts from these migrated gathers, and (3) inverting wave-equation migration by generating Green’s functions the updated velocity model using ray tracing. In compli- from the surface and then used them in a frequency-depend- cated geological regions, ray-based imaging methods such ent one-way migration. Etgen (2012) extended this method as Kirchhoff migration usually fail to provide high-quality from 2D to 3D and optimized the computational efficiency by recycling one-way Green’s functions via extrapolating them from the surface. Giboli et al. (2012) upgraded Green’s Edited by Jie Hao and Chun-Yan Tang function from one-way to two-way and created SOGs via stationary-phase extraction of an encoded attribute. Yang * Yang Zhao et al. (2015) proposed a simple but expensive method. zhaoyang@cup.edu.cn This method divided a common-shot gather into offset sets (Duquet and Lailly 2006) and back-propagated the wavefield State Key Laboratory of Petroleum Resources and Prospecting, Unconventional Petroleum Research for each offset set separately. Zhao et al. (2020a) extended Institute, China University of Petroleum, Beijing 100083, it to the elastic cases and perform a comprehensive elastic China migration velocity analysis. Each offset gathers can survive Department of Earth, Environmental and Planetary Sciences, the destructive interference from neighboring offsets; there - Rice University, Houston, TX, USA fore RTM SOGs can provide reliable moveouts since each Department of Earth and Planetary Science, University source-receiver section is migrated independently (Zhao of California, Berkeley, CA, USA et al. 2018). Aramco Research Center, Aramco Services Company, All previous works were suffered from significant com- Houston, TX, USA putational cost, which prevents this technology from being Institute of Geology and Geophysics, Chinese Academy widely used in practice, even for 2D applications. For of Sciences, Beijing 100029, China Vol.:(0123456789) 1 3 774 Petroleum Science (2021) 18:773–782 example, for one shot, RTM SOGs with 20 offsets are about partial images that are kept separately. In 2D, it becomes the 10 times more expensive than regular RTM with cross- following integral over time: correlation imaging conditions. As a result, mitigating the SOGs cost is particularly essential and is the main objective I(x, z, h)= src(x, z, t)rec(x + h, z, t)dt (1) of this article. One potential way to mitigate this problem is to use sparse offsets. A sparse offset system can significantly reduce the computational cost but can produce migration where I(x, z, h) is the surface-offset image gathers. x and z operators. To compensate for the sparse offset, an effective are the image-point location. src and rec denote the source interpolation is critical to make this proposed workflow fea- wavefield and receiver wavefield, respectively. T is the record sible in practice. Various approaches were established for duration. rec (x + h, z, t) gives the receiver wavefields using data interpolations in the geophysical community (Yilmaz data at each offset h . Equation (1) is performed indepen- 2001), in which a variety of data volumes to interpolate data dently on each offset h and the size of I(x, z, h) depends on at the target positions to regularize and increase the spatial the offset selection. SOGs are well-known essential outputs density of the geophysical datasets. For example, the fre- of pre-stack depth migration used for velocity estimation. quency-space (FX) domain (Spitz 1991) interpolation, based The local reflected events are selected on the migrated gather on complex spatial prediction filters (Ronen 1987), does volume. They are characterized by their dips in the common- not require any attempt to determine the geological dips. In offset panels and residual moveout curve. Migration veloc- contrast, many interpolation methods were developed along ity analysis aims to invert the velocity model by flattening with geologic structures, such as the energy-scanning local the residual moveouts of picked local events. Definitions of dip method (Marfurt 2006), local structure tensors (Fehmers parameters associated with events x, z, h to ray trajectories and Höcker 2003), and plane-wave destruction (PWD) filters and residual moveouts in the context of migration velocity (Fomel 2002b). In this study, we select PWD as the inter- analysis are summarized in Fig. 1. As observed in Fig. 1, the polation method since most gathers present a non-complex following requirement of the travel time needs to be satisfied curvature structure. In summary, the image gathers at additional offsets are generated by structural-dip-guided interpolation. The pro- calc calc posed workflow consists of the following five steps: a SOGs p p src rec Far offset, h computations. Each shot-domain seismic records is divided obs obs p p src rec src rec Surface-offset, h into different groups with sparse offsets to mitigate the cost. Near offset, h RTM is performed on each offset group independently. b Ray tracing in the depth domain. Rays are shooting from T (src,rec) obs migrated events up to the corresponding shot/receiver loca- tions. These parameters, such as geological dip, reflection angle, locations, and ray travel time are determined by this T (src,x,z) T (rec,x,z) calc calc h ray-tracing process. c Dip calculations in the time domain. The process of depth-to-time mapping provides time-domain parameters such as recorded time, source and receiver loca- CDP(x,z) tions, ray-traced emerging angles at source, and receiver. We may, therefore, estimate the observed dip of local events at each sparse offset by PWD. d Residual dip calculation. We then calculate the misfits of surface angles between ray- Fig. 1 Geometry of a local event with geological dip and its traced and observed results and yield the residual dips at residual moveout from common-image gather via ray tracing. The these sparsely offsets. e Gather interpolation. Finally, we depth perturbation δz is exaggerated to depth z, offset h for illus- perform the PWD interpolation using the obtained residual tration purpose. The far-offset source (src) ray, with the travel time T (src, x, z) (the left red solid line), forms the incident angle θ to dips as a guide and rebuild the gathers at denser spatial calc the normal direction (the purple dot line), and so as the receiver (rec) samplings. ray, with the travel time T (rec, x, z) . In contrast, the far-offset ray calc of the observed seismic data (the blue lines), with the travel time T (src, rec) , shoot from a shallower reflector and reach the src and obs rec at the same h. The near-offset ray path (yellow solid line) forms 2 Local reflection events from RTM SOGs similarly and share the same reflector with the observed ray path. The corresponding CIGs range from the near-offset (yellow lines) to the Similar to Kirchhoff migration, offset-domain partial images far-offset ray (red lines) presenting a residual dip ϕ (the solid green are straightforward to produce by RTM. The migration inte- lines) is shown on the right. By performing tomographic updates for slowness χ, the local event is shifted vertically by δz to the location of gral is performed on separate subsets of the data and the the observed event by flattening the residual dips 1 3 Depth, z 2 Petroleum Science (2021) 18:773–782 775 with a local event T (src, rec) migrated to a 2D position surface-offset h via the relation h = src∕2 − rec∕2 (Claer- obs x, z, h: bout 1985). Equation (1) can be rewritten as obs calc obs calc T (src, rec)= T (src, x, z, )+ T (rec, x, z, ) (2) (p − p )− (p − p ) obs calc calc src src rec rec tan = (5) 2 cos cos where T (src, x, z, ) and T (rec, x, z, ) are the calculated calc calc one-way travel time (dependent of slowness ) from the obs calc obs calc where (p − p )−(p − p ) is the surface angle src src rec rec source and the receiver locations to the image location x, z , misfit caused by the velocity errors, and 2 cos cos is respectively. Similarly, T (src, rec) is the observed two-way a stretching factor at the place of the local event (x, z, h). obs travel time (independent of slowness ) for the given event Chauris et al. (2002) derived this connection between local from the seismic records in the time domain. The depth per- events in the pre-stack time domain and the events in the turbation z is applied to depth z , offset h for illustration depth domain. A full RTM SOG using Equation (5) is fairly purpose. Figure. 2a shows a synthetic example of collected expensive. Figure. 2b shows a sparse and muted version of SOGs from Fig. 1 of different CDPs (common-depth points). Fig. 2a with selected offsets. The gathers are generated with It shows the relationship of different dips of one local event only 1/10 cost comparing to a full operation but an effective in three dimensions (CDP, offsets, and depth), specifically, interpolation is required to compensate for the sparsity. A is apparent geological migrated dip measured in the com- dip-guided interpolation is selected for the relatively simple mon offset axis and is the residual dip in the SOG. and structure as CIGs. Equation (5) is the key equation providing are defined as: the residual dip to perform gather interpolation. calc calc These measurements p , p , cos , cos are deter- z z src rec tan = , tan = (3) mined by ray tracing in depth-domain (red lines in Fig. 1). h x Specifically, rays are traced from each image point to the source and receiver locations for the given dip and reflection For the correct velocity, the SOG should be flat and angle. Each ray possesses five parameters: apparent geologi- should be zero. The dip information (blue lines in Fig. 1) cal dip cos , reflection angle cos , horizontal and vertical is given by positions x, z , and ray travel time T (src, rec) . Source-side calc calc calc dip p and receiver-side dip p can be determined dur- src rec T (src, rec) T (src, rec) obs obs obs obs = p , = p (4) ing ray tracing and used for the depth delay estimation. In src rec src rec obs obs contrast, these time-domain measurements p , p require src rec designed techniques to be directly measured in the common In tomography, Stork (1992) established that the rela- shot and receiver domains, respectively (red lines in Fig. 2a). tionships mapping traveltime perturbations to depth devia- In the next section, we will discuss the dip estimation and tions are T (src, x, z)+ T (rec, x, z)= 2z cos cos . calc calc how to use the dip to perform the dip-guided interpolation. The source and receiver locations are switched to the (a) (b) 1000 1000 2000 2000 3000 3000 4000 4000 5000 5000 6000 6000 7000 7000 z z 4000 4000 3000 h 3000 h x x 5000 5000 2000 2000 z z z z tan = 0 tan = 0 1000 1000 x x -5000 z -5000 z 0 0 tan = tan = CDP, m CDP, m h h Offset, mOffset, m Fig. 2 Geometry relationship of the local migrated event from Fig. 1 mapping from time to depth time. a Definitions of the residual dip and apparent geological dip associated with a local event in CIGs in depth domain. The Y axis represents the CDP location, whereas the XZ plane is equivalent to Fig. 1, with is apparent geological migrated dip measured in the common offset (Y) axis, and is the residual dip in the CIGs. b Sparse SOG with 1/8 of the offset groups as in (a) 1 3 Depth, m Depth, m 776 Petroleum Science (2021) 18:773–782 The depth perturbation z is exaggerated to depth z , offset dominant dip is then determined by minimizing the predic- h for illustration purpose. The far-offset source ( src ) r ay, tion error (Fomel 2010; Xue et al. 2019). Shaping regulariza- with the travel time T (src, x, z) (the left red solid line), tion limits the assessed dips to change smoothly in neighbor- calc forms the incident angle to the normal direction (the ing traces for the interpolated records. We can formularize it obs purple dot line), and so as the receiver ( rec) ray, with the as a regularized least-squares problem as ≈ , where travel time T (rec, x, z) . In contrast, the far-offset ray of is the dip field between traces, associated with the PWD calc obs the observed seismic data (the blue lines), with the travel operator, the delta is the prediction error, and is the time T (src, rec) , shoot from a shallower reflector and reach original seismic trace in time-domain. This approximated obs the src and rec at the same h . The near-offset ray path (yel- equality can be achieved by solving the least-squares prob- obs T obs −1 obs T low solid line) forms similarly and share the same reflector lem ≈ (( ) ) ( ) . with the observed ray path. The corresponding CIGs range Dip calculation of time-domain gathers is challenging due from the near-offset (yellow lines) to the far-offset ray (red to its low S/N ratio. Preprocessing steps should be applied lines) presenting a residual dip (the solid green lines) is before the estimation for accurate dip extraction. The pre- shown on the right. By performing tomographic updates for processing steps include low-pass filtering, removal of slowness , the local event is shifted vertically by z to the coherent noise, and estimation in the common-offset domain location of the observed event by flattening the residual dips. with dip constraints within a realistic range. Figure 3a shows local migrated events in the corresponding time domain with record time T (src, rec) . Events are identified by the soft obs 3 Dip estimation and dip‑guided thresholding of the semblance within sliding windows. A interpolation simple example of the resultant picking of a common-shot gather is illustrated in Fig. 3a. Figure 3b illustrates the cal- obs obs Local reflected events, either in time-domain or depth- culated dip from the input data and provides p , p for src rec calc calc domain gathers, contain not only temporal and spatial Equation (5). Other measurements p , p , cos , cos can src rec information but also dip information. Seismic dips can be be achieved via ray tracing in the depth domain. We can then used for velocity model building, gather interpolation, and obtain tan using Equation (5). Parameter calculations are conditioning. These measurements of seismic dips can be the most crucial step in the entire workflow. completed by PWD filters and are valuable tools for numer - The next task is to use tan to perform dip-guided ous geophysical applications (Fomel 2002a, 2010; Fomel interpolation to fill in the missing offset. We again need and Guitton 2006). PWD predicts the next trace by phase- to solve the regularized least-squares problem by switch- shifting from the previous trace along with the dominant ing matrix position ≈ , where is still the dip field event dip while maintaining the amplitude. The estimated containing tan but is sparse SOGs. Instead of solving 0 0 0.10 (a) (b) 0.08 1 1 0.06 0.04 2 2 0.02 3 3 −0.02 4 4 −0.04 −0.06 5 5 −0.08 rec rec 6 6 −0.10 −8000 −6000 −4000 −2000 0 2000 4000 6000 8000 −8000 −6000 −4000 −2000 02000 40006000 8000 Offset, m Offset, m T (src,rec) T (src,rec) obs obs obs obs p = p = rec rec rec rec obs obs Fig. 3 A local event defined in the time domain. a The dip p of observed data is measured in common shot gather at the receiver position. p rec src can be computed similarly but in common receiver gathers. b Dip estimation and event identification using PWD. Red and blue represent the slope of local events dipping in different directions 1 3 Time, s T (src,rec) obs T (src,rec) obs Time, s T (src,rec) obs T (src,rec) obs Petroleum Science (2021) 18:773–782 777 for , we solve for this interpolation purpose. This linear As we discussed earlier, PWD is suitable for the gath- T −1 problem can be solved efficiently by ≈( ) . To ers with simple curvatures since this technique assumes demonstrate this dip estimation and interpolation process, smooth amplitude variances and a single plane-wave direc- a classic synthetic image (Claerbout and Fomel 2006) is tion. Other advanced interpolation methods, such as cubic selected to validate our proposed dip-guided interpolation spline interpolation (Zhang and Zheng 2014), can also be procedure. This classic image contains dipping beds, an used. Cubic splines offer more stable and smooth results as unconformity, and a fault. Figure 4a shows the subsampled well as continuous second-order derivatives for given input version (1/4 sampling rate), and we want to recover the points. Cubic splines thus produce continuous results for original image from this image. Figure 4b shows the dip smoothly varying shapes. The shape of migration gathers estimated from the input image, and it has been smoothed along offsets are generally varying smoothly and generate similarly to generate a dip that has the same dimension as continuous spatial derivatives. Taking advantage of high- the target image (Zhao et al. 2020c). We can easily obtain order nonlinearity, the cubic-spline interpolation may serve the interpolation result following the derived equations as a great option to interpolate gathers with complex curva- above. Figure 4c and d show the interpolation images and tures (e.g., mixed up-down curve). their difference from the true reference image, respec- Figure 5 demonstrates this dip-guided interpolation pro- tively. The interpolated results act as a smoother version cess, where Fig. 5a is a selected sparse SOG from Fig. 2b. of the inputs, and residuals only around the unconformity The ray-tracing procedure described in the previous section and fault can be observed. A comprehensive analysis can was carried out for each local event individually. The result- be found in Zhao et al. (2020b). ing values overlapping with its associated event in sparse (a) Distance, km (b) Distance, km 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 0.5 1.0 1.5 0 0 0.2 0.2 0.4 0.4 -1 0.6 0.6 -2 (c) Distance, km (d) Distance, km 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 0 0.2 0.2 0.4 0.4 0.6 0.6 Fig. 4 A classic synthetic image for the dip-guided PWD interpolation process. a Synthetic input image containing steep structures and a fault (56 traces, 30 m spacing); b dip estimation using the proposed PWD operator; c interpolation result (224 traces, 7.5 m spacing); d difference compared to the true reference image. In addition to an improved resolution and SNR, residuals only around the unconformity and fault can be found 1 3 Time, s Time, s Time, s Time, s Slope (samples) 778 Petroleum Science (2021) 18:773–782 0 0 (a) (b) 1000 1000 2000 2000 3000 3000 4000 4000 5000 5000 6000 6000 7000 7000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 -8000 -6000 -4000 -2000 02000400060008000 Offset, m Offset, m 0 0 (c) (d) 1000 1000 2000 2000 3000 3000 4000 4000 5000 5000 6000 6000 7000 7000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 -8000 -6000 -4000 -2000 02000400060008000 Offset, m Offset, m (e) Offset, m Fig. 5 Dip-guided interpolation process a a selected offset gather (11 offsets) from Fig. 2a before interpolation; b calculated dip of the sparse offsets using Equation (5); Red lines with varied tilted angles displayed on top of identified events indicate the dip values; c after interpolations (81 offsets) using dip-guided PWD operator; d original full offset RTM SOGs; e a waveform comparison between our proposed method (green lines) and the original SOG (blue lines) at the same selected sections. The detailed comparison (e) demonstrates that our method provides very similar waveforms to the original SOGs but with significantly reduced costs SOG are shown in Fig. 5b. The sparse needs to be popu- linear smoothing. Figure 5c shows the interpolated results lated with the desired offset grid. We applied linear interpo- using in the sparse offset grid as the initial dips with the lation to fill in in the offset gaps, followed by horizontal PWD. A total of 81 offsets of SOG have been recovered. The 1 3 Depth, m Depth, m Depth, m Depth, m Depth, m Petroleum Science (2021) 18:773–782 779 reference SOG is shown in Fig. 5d. The interpolated gather SOGs. The efficiency is mainly attributed to three factors: shows a comparable quality and preserves the slope com- sparse offsets we selected, the cheap cost of 3D ray-tracing, paring with full SOGs. The proposed method successfully and fast dip-guided interpolation. recovers the missing traces and removes the aliased events, but with only one-eighth of the computation cost. 5 Conclusions 4 Examples We proposed a dip-based method to gather interpolations to mitigate the heavy cost of generating RTM SOGs. The main In this section, we aim to demonstrate the proposed method idea of our proposed method is mapping the local events using synthetic and field data examples. The first example between time and depth domains via ray tracing. The local is a transition-zone model with a shallow water environ- events are defined by these depth-domain parameters: geo- ment. The model contains sediments with strong velocity logical dip, reflection angle, locations, and ray travel time; anomalies such as salt bodies and islands. 250 shot gath- and time-domain parameters: recorded time, source and ers were preprocessed with refraction-wave muting and FK receiver locations, ray-traced emerging angles at source, noise removal. We separated the common-shot data with an and receiver. Compared with traditional techniques, our pro- offset ranging from -8 to 8 km into 11 groups with a spac - posed workflow accomplishes comparable gather quality, ing of 1.6 km. Similar to the example in Fig. 5, the migrated but with considerably lower cost as demonstrated by these CIGs are shown in Fig. 6 generated the input SOGs by sub- synthetic and field data examples. The proposed workflow sampling the original offsets shown in Fig. 6a, which has offers a practically realistic approach for velocity model severe aliasing issues in the offset dimension; Fig. 6b shows building in the presence of complex geological settings. The the dip estimated with the PWD filter. We used it to perform computation cost ratio highly depends on the percentage of dip-oriented interpolation, resulting in the result shown in sparse offsets to the full, and the optimum number of the Fig. 6c. To perform high-quality picking of residual moveout sparse offsets are related to curvatures caused by velocity for tomography, the target output gathers have 81 offsets inaccuracy. In the simplest case of a constant velocity error with 0.2 km spacing. The difference between the full offsets in a homogeneous medium, we may only need two offsets in Fig. 6d is very small. The interpolation has reconstructed to reconstruct residual moveouts because the curvature is the original SOGs with a much smaller cost. In the second controlled by the tangent function of the incident ray angle. example, a field data experiment with a real transition-zone In the presence of complex velocity error in a heterogene- environment was performed, and the results are shown in ous medium, however, the gather may experience up-down Fig. 7. We used the same parameters as the previous syn- curvatures rather than a single curve-down (up) moveout. thetic example to examine the robustness of our proposed These complicated scenarios require dense offsets among method. Comparing the interpolated SOGs (Fig. 7c) with each peak-trough to fully reconstruct the correctness of kin- full SOGs (Fig. 7d), the recovery quality is very comparable ematic information from these gathers. We are currently in a to the synthetic example, which further demonstrates the preliminary interpolation stage, in which the offset selection robustness of our workflow. The computation time of these is determined in a heuristic way instead of through system- two datasets is listed in Table 1. Compared to the computa- atic optimization. A more robust and self-adaptive approach tion time for standard GOSs, our proposed method indicates is one of our ongoing research directions. a speedup factor of about 5 times over standard full-volume 1 3 780 Petroleum Science (2021) 18:773–782 0 0 (a) (b) 3500 3500 0 0 2000 2000 4000 4000 30000 30000 6000 6000 25000 20000 -5000 0 5000 -8000-6000-4000-2000 0 2000 4000 6000 8000 Offset, m Offset, m 0 0 33400 33400 (c) (d) 3500 3500 0 0 2000 2000 4000 4000 30000 30000 6000 6000 25000 25000 -5000 0 5000 -5000 0 5000 Offset, m Offset, m (e) 0 1000 2000 3000 4000 5000 6000 Offset, m Fig. 6 Dip-guided PWD interpolation process of synthetic transition zone example. Y-axis represents the CDP location in addition to SOG shown in Fig. 5. a RTM SOGs with sparse offsets. Comparing this with Fig. 2, only 10 offsets are selected for RTM SOG computations. Other traces are filled with zeros. b the calculated dip of the sparse offsets using equation (5); c Interpolated results. Seven additional traces were inserted between each of the neighboring input traces. d Original SOG with dense 81 offset traces. e a waveform comparison between our pro- posed method (green lines) and the original SOG (blue lines) at a selected section. The detailed comparison (e) demonstrates that our method provides a highly comparable quality to the original SOGs and the kinematic moveout matches closely with the proposed method 1 3 Midpoint, m Midpoint, m Midpoint, m Midpoint, m Depth, m Depth, m Depth, m Depth, m Depth, m Petroleum Science (2021) 18:773–782 781 100 100 1.0 (a) (b) 41400 41400 0.5 5020 5020 0 0 5000 5000 -0.5 10000 10000 -5000 0 5000 -5000 0 5000 Offset, m Offset, m 0 100 (c) 41400 (d) 36420 5020 5020 0 0 5000 5000 10000 10000 -5000 0 5000 -5000 0 5000 Offset, m Offset, m (e) 0 500 1000 1500 2000 2500 3000 Offset, m Fig. 7 Dip-guided PWD interpolation process of real transition zone example. Plots in the same fashion as Fig. 6 1 3 Midpoint, m Midpoint, m Midpoint, m Midpoint, m Depth, m Depth, m Depth, m Depth, m Depth, m 782 Petroleum Science (2021) 18:773–782 Etgen JT. 3D wave equation Kirchhoff migration. 82nd Annual Inter - Table 1 The comparison of computation CPU cost between original national Meeting. 2012:755-60. doi:https://doi. or g/10. 1190/ seg am and our proposed methods, where calculations are based on a Linux 2012- 0755.1. cluster consisting of 64 2.6G GHz dual-core processor nodes. Fehmers GC, Höcker CFW. Fast structural interpretation with struc- ture-oriented filtering. Geophysics. 2003;68(4):1286–93. https:// Numerical tests Original SOGs Dip-guided Saving rate % doi. org/ 10. 1190/1. 15981 21. interpolated Fomel S. Applications of plane-wave destruction filters. Geophysics. SOGs 2002;67(6):1946–60. 2D synthetic test 11 hours 2.375 hours 78 Fomel S. Predictive painting of 3D seismic volumes. Geophysics. 2010;75(4):A25–30. https:// doi. org/ 10. 1190/1. 34538 47. 3D field data test 92 hours 25 hours 72 Fomel S, Guitton A. Regularizing seismic inverse problems by model reparameterization using plane-wave construction. Geophysics. 2006;71(5):A43–7. https:// doi. org/ 10. 1190/1. 23356 09. Acknowledgements We specifically express our appreciation to Cris- Giboli M, Baina R, Nicoletis L, Duquet B. Reverse time migra- tina Young for her critical work on improving this paper. We would tion surface offset gathers part 1: a new method to produce like to thank the three anonymous reviewers for their comments and ‘classical’common image gathers. 82nd Annual International suggestions, which significantly improved the quality of this paper. Meeting. 2012:1007-12. doi: https:// doi. or g/ 10. 1190/ seg am This study is jointly supported by the National Key R&D Program of 2012- 1007.1 China (2017YFC1500303 and 2020YFA0710604), the Science Foun- Marfurt KJ. Robust estimates of 3D reflector dip and azimuth. Geo- dation of China University of Petroleum, Beijing (2462019YJRC007 physics. 2006;71(4):P29–40. https://d oi.o rg/1 0.1 190/1.2 21304 9. and 2462020YXZZ047), and the Strategic Cooperation Technology Ronen J. Wave-equation trace interpolation. Geophysics. Projects of CNPC and CUPB (ZLZX2020-05). 1987;52(7):973–84. https:// doi. org/ 10. 1190/1. 14423 66. Spitz S. Seismic trace interpolation in the FX domain. Geophysics. Open Access This article is licensed under a Creative Commons Attri- 1991;56(6):785–94. https:// doi. org/ 10. 1190/1. 14430 96. bution 4.0 International License, which permits use, sharing, adapta- Stork C. Reflection tomography in the postmigrated domain. Geophys- tion, distribution and reproduction in any medium or format, as long ics. 1992;57(5):680–92. as you give appropriate credit to the original author(s) and the source, Xue ZG, Zhang HZ, Zhao Y, Fomel S. Pattern-guided dip estima- provide a link to the Creative Commons licence, and indicate if changes tion with plane-wave destruction filters. Geophys Prospect. were made. The images or other third party material in this article are 2019;67(7):1798–810. https://doi. or g/10. 1111/ 1365- 2478. 12798 . included in the article’s Creative Commons licence, unless indicated Yang Z, Huang S, Yan R. Improved subsalt tomography using RTM otherwise in a credit line to the material. If material is not included in surface offset gathers. 85th Annual International Meeting. the article’s Creative Commons licence and your intended use is not 2015:5254-8. doi:https://d oi.o rg/1 0.1 190/s egam2 015-5 84836 6.1. permitted by statutory regulation or exceeds the permitted use, you will Yilmaz Ö. Seismic data analysis: Processing, inversion, and interpreta- need to obtain permission directly from the copyright holder. To view a tion of seismic data. Society of exploration geophysicists; 2001. copy of this licence, visit http://cr eativ ecommons. or g/licen ses/ b y/4.0/ . Zhang J, Zheng T. Receiver function imaging with reconstructed wavefields from sparsely scattered stations. Seismol Res Lett. 2014;86(1):165–72. https:// doi. org/ 10. 1785/ 02201 40028% JSeis molog icalR esear chLet ters. References Zhao Y, Liu T, Jia XY, Liu HW, Xue ZG, Zhang HZ, Zhu HJ, Liang H. Surface-offset gathers from elastic reverse time migration and Chauris H, Noble MS, Lambaré G, Podvin P. Migration velocity analy- velocity analysis. Geophysics. 2020;85(1):S47–64. https://doi. or g/ sis from locally coherent events in 2-D laterally heterogeneous 10. 1190/ Geo20 18- 0676.1. media Part I: Theoretical aspects. Geophysics. 2002;67(4):1202– Zhao Y, Niu FL, Liu HW, Jia XY, Yang JD, Huo SD. Source-receiver 12. https:// doi. org/ 10. 1190/1. 15003 82. interferometric redatuming using sparse buried receivers to Claerbout J, Fomel S. Image estimation by example: Geophysical address complex near-surface environments: a case study of seis- soundings image construction. Stanford Exploration Project; mic imaging quality and Time-lapse repeatability. J Geophys Res- Solid Earth. 2020. https:// doi. org/ 10. 1029/ 2020J B0194 96. Claerbout JF. Imaging the earth’s interior. UK: Blackwell Scientific Zhao Y, Niu FL, Zhang ZS, Li X, Chen JH, Yang JD. Signal detection Inc; 1985. and enhancement for seismic crosscorrelation using the wavelet- Duquet B, Lailly P. Ec ffi ient 3D wave-equation migration using virtual domain kalman filter. Surv Geophys. 2020. https:// doi. org/ 10. planar sources. Geophysics. 2006;71(5):S185–97. https://doi. or g/ 1007/ s10712- 020- 09620-6. 10. 1190/1. 23356 28. Zhao Y, Zhang HZ, Yang JD, Fei T. Reducing artifacts of elastic Ehinger A, Lailly P, Marfurt KJ. Green’s function implementa- reverse time migration by the deprimary technique. Geophysics. tion of common-offset, wave-equation migration. Geophysics. 2018;83(6):S569–77. https:// doi. org/ 10. 1190/ Geo20 18- 0260.1. 1996;61(6):1813–21. https:// doi. org/ 10. 1190/1. 14440 97. 1 3
Petroleum Science – Springer Journals
Published: Mar 30, 2021
Keywords: Surface-offset gathers; Reverse-time migration; Dip-guided interpolation; Reduced costs; Local-event raytracing
You can share this free article with as many people as you like with the url below! We hope you enjoy this feature!
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.