Kirchhoff Prestack Depth Migration Research Articles

Imaging of thrust structures under Colombian foothills landscape through Marchenko approach

The Marchenko imaging approach successfully deals with multiple scattering during seismic migration, obtaining clear images in structurally complex geological zones below at a specific depth. Through the Marchenko equation, the method retrieves Green's function of a virtual source in profundity using reflections recorded on the surface and a smoothed velocity model. According to the theorem of reciprocity, Green's function represents the medium's response to a source on the surface recorded by a virtual receiver in-depth and decomposes it into a down-going wavefield and an up-going wavefield. Both wave fields' deconvolution provides the reflection response of virtual sources and virtual receivers repositioned in the subsurface, mimicking redatumming. The result is an image free of multiple internal reflections from the area below virtual both sources and receivers. After successfully testing with synthetic seismograms generated in a plane-horizontal layers model, we applied the Marchenko algorithm to seismic data of the Upper Magdalena Valley project using an available velocity model. Compared to an image supplied by a Kirchhoff pre-stack depth migration algorithm, the new image correctly positions the seismic events avoiding misleading interpretations in locating complex structures.

From FWI to ultra-high-resolution imaging

In recent years, the development of time-lag full-waveform inversion (FWI) has enabled the use of the full wavefield (primary reflections, diving waves, and their multiples and ghosts) in the inversion process. With this advancement, it is possible to obtain a very detailed velocity model, ultimately reaching the point of deriving from the velocity a migration-like reflectivity image called the FWI image. When the FWI maximum frequency is increased, high-resolution velocity models are obtained, revealing superior reservoir information compared to conventional imaging results. Two case studies will be discussed in this paper. The first is in the Greater Castberg area where the 150 Hz FWI image greatly surpassed the Q Kirchhoff prestack depth migration image from the water-bottom level down to the reservoir (located at a depth of about 1.5 km). The second case study is over the Nordkapp Basin. The use of the full wavefield for the shallow ultra-high-resolution (UHR) FWI image (run at 200 Hz) revealed reverse faulting and pockmark details that were invisible with Kirchhoff prestack depth migration and reverse time migration. By using additional information present in multiples, ghosts, and diving waves, a spatial resolution down to 3 m was achieved. This made it possible to image very thin features without the need for a dedicated high-resolution acquisition design. The current UHR FWI image workflow provides velocity and reflectivity information in the near surface that is important in identifying optimal locations for various purposes such as well placement and wind-turbine installation.

Superior resolution through multiparameter FWI imaging: A new philosophy in seismic processing and imaging

Seismic processing and imaging workflows have been refined over many decades to attenuate aspects of the recorded wavefield which would be improperly mapped into the image domain by legacy migration algorithms such as Kirchhoff prestack depth migration. These workflows, which include techniques such as deghosting, designature, demultiple, and regularization, have become increasingly complex and time-consuming due to the sequential fashion in which they must be tested and applied. The single-scattering (primary-only) preprocessed data are then migrated and used in extensive model building workflows, including reflection residual moveout tomography, to refine low-frequency subsurface models. Obtaining optimal results at each stage requires subjective assessment of a wide range of parameter tests. Results can be highly variable, with different decisions resulting in very different outcomes. Such workflows mean that projects may take many months or even years. Full-waveform inversion (FWI) imaging offers an alternative philosophy to this conventional approach. FWI imaging is a least-squares multiscattering algorithm that uses the raw field data (transmitted and reflected arrivals as well as their multiples and ghosts) to determine many different subsurface parameters, including reflectivity. Because this approach uses the full wavefield, the subsurface is sampled more completely during the inversion. Here, we demonstrate the application of a novel multiparameter FWI imaging technique to generate high-resolution amplitude variation with angle reflectivity simultaneously with other model parameters, such as velocity and anisotropy, directly from the raw field data. Given that these results are obtained faster than the conventional workflow with a higher resolution, improved illumination, and reduced noise, we highlight the potential of multiparameter FWI imaging to supersede the conventional workflow.

Elastic anisotropic finite-difference full-wave modeling and imaging of 2D tilted transversely isotropic (TTI) media

Imaging below the tilted transversely isotropic (TTI) media pose serious problems and distortions of the subsurface geological targets of interest for hydrocarbon exploration, which is very common in fold-thrust belts or active tectonic areas like the Rocky Mountain foothills of the Canada or foothills of the Himalaya. To model and image below the TTI media having symmetry axis orthogonal to dipping anisotropic layers, a 2D TTI thrust sheet is considered for elastic anisotropic finite-difference full-wave modeling and generation of synthetic seismic data using the robust staggered-grid scheme of wave propagation. Free-surface boundary conditions at the top and absorbing boundary conditions for the other three sides of the model have been imposed to reduce undesirable edge effects and suppress dispersions. The synthetic seismic data generated for the 2D TTI thrust model are migrated using the anisotropic Kirchhoff pre-stack time (PSTM) and depth migration (PSDM) technique followed by the migration velocity analysis (MVA) algorithm. The traveltime computations are made using robust eikonal equations with fourth-order elastic anisotropic finite-difference solutions to handle large tilts (ν) along with anisotropic ray-tracing to image below the TTI thrust sheet. The MVA algorithm adopted also estimates the anisotropic parameters ε and δ accurately within the acceptable error limit through successive iterations of inversion and parameter update, which results in sufficient flattening of the reflection events in the common image gathers (CIGs). This is a powerful and stable methodology to handle large tilt (ν = 60°) of the steeply dipping reflectors in complex geological structure like the TTI thrust model without much distortion of CIGs for which the symmetry axis of each TTI block is set orthogonal to the bottom of the reflectors having different tilts.

4D seismic co-processing pre-stack depth migration for scarce acquisition repeatability

Time-lapse (4D) seismic processing is routinely used to monitor hydrocarbon reservoir production. Seismic reflections are sensitive to formation pressure and fluid content. This means that repeated seismic surveys can theoretically detect pressure changes and fluid changes associated with field production. These measurements can help optimize production strategy and identify areas where hydrocarbons have been bypassed. However, the seismic signal associated with such changes can be negligible, especially in heterogeneous carbonate reservoirs. To measure this 4D signal, the seismic acquisition must be repeated. Data vintages should be processed together to minimize differences unrelated to production. Repeatability of data acquisition is sometimes impossible to achieve in the Middle East due to environmental changes (e.g., dunes, currents, field facilities). Due to high cost and inadequate sampling, attempts to permanently bury seismic sources and receivers have failed.In this study, least-square pre-stack depth migration (LSM) co-processing was applied to remove the influence of survey design on the final image and pinching mark compared to conventional Kirchhoff pre-stack depth migration (KPSDM). The 4D physical, geometric, and seismic attributes are analyzed in the field as key diagnostic tools to evaluate the probability of a sighted 4D difference independent of two different acquisition geometries. The 4D analysis was performed on two case studies offshore Abu Dhabi, to determine which workflow and algorithm are most likely to ensure that the complete and optimal 4D processing sequence relaxes the need for seismic acquisition repeatability.

Three-dimensional reflection seismic imaging of the iron oxide deposits in the Ludvika mining area, Sweden, using Fresnel volume migration

Abstract. We present pre-stack depth-imaging results for a case study of 3D reflection seismic exploration at the Blötberget iron oxide mining site belonging to the Bergslagen mineral district in central Sweden. The goal of the study is to directly image the ore-bearing horizons and to delineate their possible depth extension below depths known from existing boreholes. For this purpose, we applied a tailored pre-processing workflow and two different seismic imaging approaches, Kirchhoff pre-stack depth migration (KPSDM) and Fresnel volume migration (FVM). Both imaging techniques deliver a well-resolved 3D image of the deposit and its host rock, where the FVM image yields a significantly better image quality compared to the KPSDM image. We were able to unravel distinct horizons, which are linked to known mineralization and provide insights on their possible lateral and depth extent. Comparison of the known mineralization with the final FVM reflection volume suggests a good agreement of the position and the shape of the imaged reflectors caused by the mineralization. Furthermore, the images show additional reflectors below the mineralization and reflectors with opposite dips. One of these reflectors is interpreted to be a fault intersecting the mineralization, which can be traced to the surface and linked to a fault trace in the geological map. The depth-imaging results can serve as the basis for further investigations, drilling, and follow-up mine planning at the Blötberget mining site..

Ultrasonic Echo Localization Using Seismic Migration Techniques in Engineered Barriers for Nuclear Waste Storage

In the framework of non-destructive-testing advanced seismic imaging techniques have been applied to ultrasonic echo data in order to examine the integrity of an engineered test-barrier designed to be used for sealing an underground nuclear waste disposal site. Synthetic data as well as real multi-receiver ultrasonic data acquired at the test site were processed and imaged using Kirchhoff prestack depth migration reverse time migration (RTM). In general, both methods provide a good image quality as demonstrated by various case studies, however deeper parts within the test barrier containing inclined reflectors were reconstructed more accurately by RTM. In particular, the image quality of a specific target reflector at a depth of 8 m in the test-barrier has been significantly improved compared to previous investigations using synthetic aperture focusing technique, which justifies the considerable computing time of this method.

Full-Waveform Inversion for Imaging Faulted Structures: A Case Study from the Japan Trench Forearc Slope

Full-waveform inversion (FWI) of limited-offset marine seismic data is a challenging task due to the lack of refracted energy and diving waves from the shallow sediments, which are fundamentally required to update the long-wavelength background velocity model in a tomographic fashion. When these events are absent, a reliable initial velocity model is necessary to ensure that the observed and simulated waveforms kinematically fit within an error of less than half a wavelength to protect the FWI iterative local optimization scheme from cycle skipping. We use a migration-based velocity analysis (MVA) method, including a combination of the layer-stripping approach and iterations of Kirchhoff prestack depth migration (KPSDM), to build an accurate initial velocity model for the FWI application on 2D seismic data with a maximum offset of 5.8 km. The data are acquired in the Japan Trench subduction zone, and we focus on the area where the shallow sediments overlying a highly reflective basement on top of the Cretaceous erosional unconformity are severely faulted and deformed. Despite the limited offsets available in the seismic data, our carefully designed workflow for data preconditioning, initial model building, and waveform inversion provides a velocity model that could improve the depth images down to almost 3.5 km. We present several quality control measures to assess the reliability of the resulting FWI model, including ray path illuminations, sensitivity kernels, reverse time migration (RTM) images, and KPSDM common image gathers. A direct comparison between the FWI and MVA velocity profiles reveals a sharp boundary at the Cretaceous basement interface, a feature that could not be observed in the MVA velocity model. The normal faults caused by the basal erosion of the upper plate in the study area reach the seafloor with evident subsidence of the shallow strata, implying that the faults are active.

The Design of Payload Lunar Regolith Penetrating Radar on Chang'E-5 Lander

Sampling return in Chang'E-5 (CE-5) mission is the third phase of three strategic steps of China's lunar program. The three strategic steps are orbiting, landing, and returning. The sampling and drilling device is mounted on the Lander. One task of the CE-5 Lunar Regolith Penetrating Radar (LRPR) is to provide information support for the drilling and sampling device. This article introduces the scientific objectives of CE-5 LRPR and the difference with Chang'E-3 lunar penetrating radar. The system design, working principle, imaging, and calibration methods of LRPR are the highlight. Considering that the Lander is stationary, and its bottom is about 90 cm from the lunar surface, an antenna array is adopted to probe the subsurface structure and the regolith thickness for supporting the drilling. The design uses a pre-amplifier circuit to increase the dynamic range of the whole system, which enhances the detection effect of shallow lunar soil structure. For verifying the probing ability of LRPR, the marble slabs, metal balls, and stones are buried in the volcanic ash pool in advance for detection and verification. The pre-stack Kirchhoff depth migration imaging method is adopted to identify the burial depth and thickness of the target. The verification results meet the task requirements.

PRE STACK DEPTH MIGRATION UNTUK KOREKSI EFEK PULL UP DENGAN MENGGUNAKAN METODE HORIZON BASED DEPTH TOMOGRAPHY PADA LAPANGAN ‘A1 DAN A2’

In the case of seismic data processing with sandstone lithology such as shale and carbonate often get the result of data processing which have pull up effect especially on the time domain migration result. Pre stack depth migration is a processing based on focusing the amplitude according to the actual depth by using the input interval velocity. Migration is performed using kirchhoff pre stack depth migration algorithm. Pre stack depth migration is done with modeling of horizontal based depth tomography method. This method uses residual moveout correction applied along the horizon-picking line. This research uses two field data that is A1 and A2 Field. A1field has characteristics of carbonate rock that produce pull up shaped similar to carbonate layer. A2 field has a pull-up effect that is not very clear but has build up because of the layer above it. Stages performed starting from the processing of pre stack time migration in the form of velocity picking, generate rms velocity and migration time domain. The pre stack depth migration process begins with a velocity transformation with the dix transformation equation to generate interval velocity, migrate Pre stack depth migration, perform horizon interpretations and perform velocity modeling using the horizon based depth tomography method. The iteration is done 4 times and resulted in the final section of pre stack depth migration which has been corrected by pull up effect.

Anisotropic Kirchhoff pre-stack depth migration at the COSC-1 borehole, central Sweden

SUMMARYA remarkably well preserved representation of a deeply eroded Palaeozoic orogen is found in the Scandinavian Caledonides, formed by the collision of the two palaeocontinents Baltica and Laurentia. Today, after 400 Ma of erosion along with uplift and extension during the opening of the North Atlantic Ocean, the geological structures in central western Sweden comprise far transported allochthonous units, the underlying Precambrian crystalline basement, and a shallow west-dipping décollement that separates the two and is associated with a thin layer of Cambrian black shales. These structures, in particular the Seve Nappes (upper part of the Middle Allochthons), the Lower Allochthons and the highly reflective basement are the target of the two approximately 2.5 km deep fully cored scientific boreholes in central Sweden that are part of the project COSC (Collisional Orogeny in the Scandinavian Caledonides). Thus, a continuous 5 km tectonostratigraphic profile through the Caledonian nappes into Baltica’s basement will be recovered. The first borehole, COSC-1, was successfully drilled in 2014 and revealed a thick section of the seismically highly reflective Lower Seve Nappe. The Seve Nappe Complex, mainly consisting of felsic gneisses and mafic amphibolites, appears to be highly anisotropic. To allow for extrapolation of findings from core analysis and downhole logging to the structures around the borehole, several surface and borehole seismic experiments were conducted. Here, we use three long offset surface seismic profiles that are centred on the borehole COSC-1 to image the structures in the vicinity of the borehole and below it. We applied Kirchhoff pre-stack depth migration, taking into account the seismic anisotropy in the Seve Nappe Complex. We calculated Green’s functions using an anisotropic eikonal solver for a VTI (transversely isotropic with vertical axis of symmetry) velocity model, which was previously derived by the analysis of VSP (Vertical Seismic Profile) and surface seismic data. We show, that the anisotropic results are superior to the corresponding isotropic depth migration. The reflections appear significantly more continuous and better focused. The depth imaging of the long offset profiles provides a link between a high-resolution 3-D data set and the regional scale 2-D COSC Seismic Profile and complements these data sets, especially in the deeper parts below the borehole. However, many of the reflective structures can be observed in the different data sets. Most of the dominant reflections imaged originate below the bottom of the borehole and are situated within the Precambrian basement or at the transition zones between Middle and Lower Allochthons and the basement. The origin of the deeper reflections remains enigmatic, possibly representing dolerite intrusions or deformation zones of Caledonian or pre-Caledonian age.

Sparse 3D Seismic Imaging in the Kylylahti Mine Area, Eastern Finland: Comparison of Time Versus Depth Approach

A 10.5 km2 3D seismic survey was acquired over the Kylylahti mine area (Outokumpu mineral district, eastern Finland) as a part of the COGITO-MIN (COst-effective Geophysical Imaging Techniques for supporting Ongoing MINeral exploration in Europe) project, which aimed at the development of cost-effective geophysical imaging methods for mineral exploration. The cost-effectiveness in our case was related to the fact that an active-source 3D seismic survey was accomplished by using the receiver spread originally designed for a 3D passive survey. The 3D array recorded Vibroseis and dynamite shots from an active-source 2D seismic survey, from a vertical seismic profiling experiment survey, as well as some additional “random” Vibroseis and dynamite shots made to complement the 3D source distribution. The resulting 3D survey was characterized by irregular shooting geometry and relatively large receiver intervals (50 m). Using this dataset, we evaluate the effectiveness of the standard time-imaging approach (post-stack and pre-stack time migration) compared to depth imaging (standard and specialized Kirchhoff pre-stack depth migration, KPreSDM). Standard time-domain processing and imaging failed to convincingly portray the first ~1500 m of the subsurface, which was the primary interest of the survey. With a standard KPreSDM, we managed to obtain a good image of the base of the Kylylahti formation bordering the extent of the mineralization-hosting Outokumpu assemblage rocks, but otherwise the image was very noisy in the shallower section. The specialized KPreSDM approach (i.e., coherency-based Fresnel volume migration) resulted in a much cleaner image of the shallow, steeply dipping events, as well as some additional deeper reflectors, possibly representing repetition of the contact between the Outokumpu assemblage and the surrounding Kalevian metasediments at depth.

Accelerating Kirchhoff Pre-stack depth migration on a GPU by overlapping ray tracing and imaging

Kirchhoff-based depth migration is in great demand for imaging at large scales and high-density seismic data exploration. A Graphic Processing Unit, or GPU, can compose a heterogeneous hardware that contains a traditional Central Processing Unit (CPU), and it can greatly accelerate migration calculations. An improved acceleration method is proposed here that uses overlapped ray tracing, which provides two-way travel times, and an imaging kernel. In our method, ray tracing is calculated by the CPU due to its complicated divergences. The imaging kernel is passed to the GPU by unlooping the imaging volume. Streams and asynchronous calculation functions are used to overlap the imaging kernel of a previous trace to the ray tracing of the next trace. The nvprof profiling tool, along with the elapsed time, are used to measure the efficiency of the accelerated work, and it is found that the GPU code results in a speedup factor of 60 relative to single thread CPU code, and when using the overlapped computation, the GPU efficiency is improved by 30%. This method shows great potential for further application in large scale seismic data imaging with GPU.

Matrix-free anisotropic slope tomography: Theory and application

Slope tomography uses traveltimes, source, and receiver slopes of locally coherent events to build subsurface velocity models. Locally coherent events by opposition to continuous reflections are suitable for semiautomatic and dense picking, which is conducive to better resolved tomographic models. These models can be further used as background/initial models for depth migration or full-waveform inversion. Slope tomography conventionally relies on ray tracing for traveltimes and slopes computation, where rays are traced from scatterers in depth to sources and receivers. The inverse problem relies on the explicit building of the sensitivity matrix to update the velocity model by local optimization. Alternatively, slope tomography can be implemented with eikonal solvers, which compute efficiently finely sampled traveltime maps from the sources and receivers, whereas slopes are estimated by finite differences of the traveltime maps. Moreover, a matrix-free inverse problem can be implemented with the adjoint-state method for the estimation of the data-misfit gradient. This new formulation of slope tomography is extended to tilted transverse isotropic (TTI) acoustic media, in which the model space is parameterized by four anisotropic parameters (e.g., vertical wavespeed, Thomson’s parameter [Formula: see text], [Formula: see text], and tilt angle) and the coordinates of the scatterers. A toy synthetic example allows for a first assessment of the crosstalk between anisotropic parameters and scatterer coordinates. A more realistic synthetic example indicates the feasibility of the joint update of the vertical wavespeed and [Formula: see text]. The slope tomography is finally applied to real broadband towed-streamer data to build the vertical velocity and the scatterers, while anisotropic parameters [Formula: see text] and [Formula: see text] are used as background parameters. The velocity model quality is assessed through common-image gathers computed by TTI Kirchhoff prestack-depth migration.

Geomechanical prestack depth migration of the Kraken 3D (Browse Basin, Australia)

Conventional pre-stack depth migration applied to the broadband Kraken 3D Marine Seismic Survey was unable to fully resolve short-wavelength velocity anomalies below the sea floor causing obvious imaging problems and limiting depth conversion and amplitude interpretation. Improved imaging was achieved by initiating tomography using a velocity model built by combining geomechanics with rock physics appropriate for shallow carbonates and mudrocks. 3D gravity modelling using high-resolution bathymetry and compaction trends constitutes a new approach for iteratively building a 3D geomechanical model. Effective stress is derived by applying Terzaghi’s principle within an integration (along depth) involving the model bulk and fluid densities and the vertical component of gravity (all of which may vary spatially, using more refined models). Carbonate and mudrock rock physics models, believed to be appropriate for Neogene sediments along much of the NW Shelf of Australia were derived from abundant core and wireline data acquired during the recent IODP Expedition 356. These models provide the necessary link between effective stress and P-wave velocity with Backus averaging handling the “seismic scale” mixing of different lithologies expected in the Kraken 3D area. Kirchhoff prestack depth migration was revisited from archived preprocessed gathers using the geomechanical model combined with Common reflection angle gathers (CRAM) to initiate tomography. CRAM gathers were very effective in the presence of multiples and complex near surface topography to achieve a better update in tomography. Heavy smoothing of velocities was imposed where sequence stratigraphic interpretation suggests only distal mudstone facies. Tomography in shallower layers was then revisited to restore geologically plausible depth structures and deliver a clear improvement in imaging relative to previous processing efforts.

Migration-based microseismic event location in the Schlema-Alberoda mining area

Mining operations in the Schlema-Alberoda uranium mine located in south-west Saxony (Germany) stopped in 1990, and the mine was then allowed to flood. The region is seismically active and has been monitored for a long time. We have located some of the microseismic events which occurred between 2005 and 2012 in the mining area to investigate the nature of the seismicity, as well as the long-term role of mining-induced and triggered seismicity. In this study, we used pseudo-synthetic data obtained from the vertical component records of a local seismic network, to accurately locate the hypocenters. The location procedure is based on a Kirchhoff Prestack Depth Migration approach. In order to assess the accuracy of the migration results, a homogeneous and a 3-D velocity model are tested in the migration algorithm. Both of these velocity models were previously used to migrate data acquired by a 3-D reflection seismic survey in this area. The resulting images were comparable, with minor differences to the reflectors in our area of interest. In contrast, we found that the errors in the velocity model can strongly affect the migration-based earthquake localization. The located hypocenters are compared to the 3-D reflection seismic image of the area to determine possible correlations between the seismicity and reflectivity. This comparison shows that some of reflectors can be directly correlated with the induced and triggered seismicity of the area. The results also indicate that the main causes of the post-mining seismicity are changes in the mine flooding level and the consequent changes in the pore pressure of the subsurface structures. Finally, we confirm that the hypocenters are often bound to preexisting subsurface structures like faults and fractures in the area. In particular, the spatial pattern of the hypocenters proves the existence of a previously unmapped extension of the Ruhmvoll fault. This pattern also suggests a connection between this structure and the Roter Kamm fault, a major component of the larger Gera-Jàchymov fault zone.

Imaging the crustal structure along the KCRT-2008 profile in the Southern Korean Peninsula using regularisation

Information regarding crustal structure is important for geological and geophysical research. Several attempts have been made to delineate the crustal structure of the Korean Peninsula, but the resolution in these studies has generally been too low. To acquire detailed images of the regional subsurface structure, we applied seismic data processing tools that are commonly used in oil exploration to crustal refraction data recorded along the Korea Crust Research Team 2008 (KCRT-2008) profile at irregular intervals. To use conventional seismic data processing tools, the data should be sampled regularly in both time and space domains. In this study, we applied the matching pursuit interpolation technique to regularise the KCRT-2008 data in the space domain, followed by dip filtering to attenuate coherent noise. Then, Kirchhoff prestack depth migration was applied using both refracted and reflected waves to image the subsurface structure at higher signal-to-noise ratios and increase spatial resolution using far offset data. The migrated section shows the interfaces of three mid-crustal layers at depths of 14.27 and 24.37–25.34 km and the downwarped Moho at a depth range of 29.3–36.1 km.

Imaging challenges and processing solutions in the Brazilian Equatorial Margin: A case study in the Barreirinhas Basin

The Barreirinhas Basin is located in northeast Brazil and is part of the Brazilian Equatorial Margin, a new exploration frontier with complex geology. This basin is characterized by a rugose water bottom, a fast carbonate platform, shallow gas pockets, and a complex channel network. All of these elements represent a significant challenge for velocity model building and imaging of the depositional system. From preprocessing to final imaging, high-end technologies were required to meet the processing objectives. The 3D designature and 3D deghosting were crucial to remove bubble energy and ghosts related to canyon diffractions. The velocity model building exploited offset-dependent dip information in the nonlinear slope tomography — i.e., dip-constrained tomography (DCT) — to deal with small-scale lateral velocity variations. The full-waveform inversion, up to 20 Hz, was able to efficiently capture small velocity anomalies and resolve high-spatial-resolution variations that DCT could not totally solve. Even with a detailed velocity model, some dim zones and amplitude variations were still observable in the depth-migrated image. Gas pockets, responsible for the absorption and phase distortion of the seismic signal (commonly denoted by the quality factor of attenuation, Q), were detected and delineated using volumetric Q tomography. The resultant interval Q model was consistent with the geology, and its use was beneficial in a Q-compensating Kirchhoff prestack depth migration.

Angle-domain common imaging gather extraction via Kirchhoff prestack depth migration based on a traveltime table in transversely isotropic media

Angle-domain common imaging gather extraction via Kirchhoff prestack depth migration based on a traveltime table in transversely isotropic media

Super-resolution least-squares prestack Kirchhoff depth migration using the L0-norm

Least-squares migration (LSM) is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground reflectivity models. LSM reduces the migration artifacts, enhances the spatial resolution of the migrated images, and yields a more accurate subsurface reflectivity distribution than that of standard migration. The introduction of regularization constraints effectively improves the stability of the least-squares offset. The commonly used regularization terms are based on the L2-norm, which smooths the migration results, e.g., by smearing the reflectivities, while providing stability. However, in exploration geophysics, reflection structures based on velocity and density are generally observed to be discontinuous in depth, illustrating sparse reflectance. To obtain a sparse migration profile, we propose the super-resolution least-squares Kirchhoff prestack depth migration by solving the L0-norm-constrained optimization problem. Additionally, we introduce a two-stage iterative soft and hard thresholding algorithm to retrieve the super-resolution reflectivity distribution. Further, the proposed algorithm is applied to complex synthetic data. Furthermore, the sensitivity of the proposed algorithm to noise and the dominant frequency of the source wavelet was evaluated. Finally, we conclude that the proposed method improves the spatial resolution and achieves impulse-like reflectivity distribution and can be applied to structural interpretations and complex subsurface imaging.