Subsurface Reflectivity Research Articles

Assessing Ground Penetrating Radar's Ability to Image Subsurface Characteristics of Icy Debris Fans in Alaska and New Zealand

Icy debris fans have recently been described as fan shaped depositional landforms associated with (or formed during) deglaciation, however, the subsurface characteristics remain essentially undocumented. We used ground penetrating radar (GPR) to non-invasively investigate the subsurface characteristics of icy debris fans (IDFs) at McCarthy Glacier, Alaska, USA and at La Perouse Glacier, South Island of New Zealand. IDFs are largely unexplored paraglacial landforms in deglaciating alpine regions at the mouths of bedrock catchments between valley glaciers and icecaps. IDFs receive deposits of mainly ice and minor lithic material through different mass-flow processes, chiefly ice avalanche and to a lesser extent debris flow, slushflow, and rockfall. We report here on the GPR signal velocity observed from 15 different wide-angle reflection/refraction (WARR) soundings on the IDFs and on the McCarthy Glacier; the effect of GPR antenna orientation relative to subsurface reflections; the effect of spreading direction of the WARR soundings relative to topographic contour; observed differences between transverse electric (TE) and transverse magnetic (TM) antenna polarization; and a GPR profile extending from the McCarthy Glacier onto an IDF. Evaluation of the WARR soundings indicates that the IDF deposits have a GPR signal velocity that is similar to the underlying glacier, and that the antenna polarization and orientation did not prevent identification of GPR reflections. The GPR profile on the McCarthy Glacier indicates that the shallowest material is layered, decreases in thickness down fan, and has evidence of brittle failure planes (crevasses). The GPR profile and WARR soundings collected in 2013 indicate that the thickness of the McCarthy Glacier is 82 m in the approximate middle of the cirque and that the IDF deposits transition with depth into flowing glacial ice.

Least-squares Kirchhoff migration with non-smooth regularisation strategy for subsurface imaging

During the past several decades, many types of wave-equation migration methods arise for subsurface structure imaging. The classical Kirchhoff migration, however, is still widely adopted in the petroleum industry owing to its flexibility and computational efficiency. In constant density isotropic acoustic media, a basic assumption of the Kirchhoff migration is that every point of the subsurface model is supposed to be a diffractor which scatters wavefield energy to every direction, and hence collecting the scattered energy of all directions is the basic requirement for focusing the diffractor. Factors influencing the final image quality include incomplete data acquisition, multipathing from the surface to the imaging point, and insufficient illumination under complex overburden. All these factors can be theoretically taken into account in the migration weighting coefficient. However, computation of the weighting coefficient is hard work. In view of this difficulty, a fast regularising least-squares Kirchhoff migration algorithm is presented in this paper. It not only accounts for the irregular and incomplete data sampling (e.g. limited recording aperture, coarse sampling and acquisition gaps), but also compensates for the anomalous ray coverage and multipathing problem except for the shadow zone in the media. For the purpose of attenuating migration artefacts and providing a clear and accurate image of subsurface reflectivity, regularisation strategies are applied. The classical regularisation strategy may easily lead to over-regularisation or insufficient regularisation; we try to balance these two effects in this paper. The method is called the hybrid regularisation which incorporates smoothing and non-smoothing scale operators. The algorithm is implemented using a fast gradient decent solution method based on the Rayleigh quotient being used. Numerical experiments show that this hybrid regularisation method is powerful in handling the sparsity and smoothness of the model parameters.

Viscoacoustic reverse time migration using a time-domain complex-valued wave equation

During seismic wave propagation, intrinsic attenuation inside the earth gives rise to amplitude loss and phase dispersion. Without appropriate correction strategies in migration, these effects degrade the amplitudes and resolution of migrated images. Based on a new time-domain viscoacoustic wave equation, we have developed a viscoacoustic reverse time migration (RTM) approach to correct attenuation-associated dispersion and dissipation effects. A time-reverse wave equation is derived to extrapolate the receiver wavefields, in which the sign of the dissipation term is reversed, whereas the dispersion term remains unchanged. The difference between the forward and time-reverse wave equations is consistent with the physical insights of attenuation compensation during wavefield backpropagation. Due to the introduction of an imaginary unit in the dispersion term, the forward and time-reverse wave equations are complex valued. They are similar to the time-dependent Schrödinger equation, whose real and imaginary parts are coupled during wavefield extrapolation. The analytic property of the extrapolated source and receiver wavefields allows us to explicitly separate up- and downgoing waves. A causal imaging condition is implemented by crosscorrelating downgoing source and upgoing receiver wavefields to remove low-wavenumber artifacts in migrated images. Numerical examples demonstrate that our viscoacoustic RTM approach is capable of producing subsurface reflectivity images with correct spatial locations as well as amplitudes.

Multiple Elimination and Transmission Compensation in Primary Reflections in Data Domain

We retrieve transmission compensated subsurface primary reflections from the reflection response measured at the surface. This is achieved by filtering the reflection response. The application of this scheme does not require model information. In this process, the reflection response is convolved and correlated with itself. The result after each convolution and correlation is truncated in the time domain. Free-surface and internal multiple reflections are removed and the two-way transmission effects in the primary reflections are compensated for in one step. The output of this scheme is a data set that contains only transmission compensated primary reflections. The obtained data set can be used as input to retrieve an artefact-free image of the medium. We illustrate the method with a two-dimensional example that shows how free-surface and internal multiple reflections are removed and transmission loss in primary reflections are compensated for. The method can have a wide range of applications in 3D strongly scattering media that are accessible from one side only.

Above bandgap thermoreflectance for non-invasive thermal characterization of GaN-based wafers

GaN devices integrated with dissimilar substrates have transformed electronic and optoelectronic applications. However, an effective thermal resistance (TBReff) exists between the GaN layer and the dissimilar substrates typically, which can potentially cause a major heat transport bottleneck. A non-invasive method for monitoring the TBReff of bare wafers is a key enabler for process monitoring and for the reduction of TBReff through design optimization. The existing TBReff measurement techniques require metal deposition on the sample surface. Here, we demonstrate a generic non-invasive transient thermoreflectance technique which does not require modification of the GaN surface and can be applied to any GaN-based wafers, regardless of the substrate material. Above-bandgap pump and probe lasers are used to avoid any interference caused by sub-surface reflections, ensuring that this technique strictly follows the fundamental principle of thermoreflectance-based methods. Several GaN wafers on common substrates (SiC, Si, diamond, and sapphire) are measured to assess the validity of this technique.

Full waveform inversion with angle-dependent gradient preconditioning using wavefield decomposition

The main objective of the full waveform inversion (FWI) is to deliver a velocity model which produces accurate and high resolution depth images. An integral part of FWI is the iterative optimization process aiming at minimizing an objective function describing the misfit between the observed and modelled data with respect to the velocity model parameters. However, FWI commonly suffers from local minima due to errors in data fitting and the starting velocity model. In this study, we develop a methodology to enhance convergence and mitigate the risk of having solutions falling into local minima. We employ optical flow to decompose the source and residual receiver wavefields and map them into the subsurface angle domain. Having evaluated the propagation vectors of the respective cleaner wavefields, subsurface reflection and azimuth angles can be robustly computed. Using such information we can apply angle-dependent preconditioning within the inversion algorithm. During a conventional FWI workflow, larger angles (i.e., transmission wavepaths) are mainly responsible for long wavelength velocity anomalies whereas narrow angles (i.e., reflection wavepaths) influence short wavelength velocity anomalies. In the proposed FWI methodology, we apply an optimized weighting function based on these estimated subsurface reflection angles in order to weight certain angle directions needed for gradient estimation using in parameter updating. Following a hierarchical approach, allowing for larger angles at the early stage of the FWI application, we initially solve for the smooth and longer wavelength velocity updates. Relaxing the opening angle from large to mid to narrow, the gradient direction will first estimate long wavelength velocity model updates (transmission-based wavepaths), following by short wavelength velocity model updates (reflection-based wavepaths). Moreover, angle-dependent-based gradient preconditioning can reduce cycle skips and improve convergence during FWI iterations.

Automated reconstruction of subsurface interfaces in Promethei Lingula near the Martian south pole by using SHARAD data

Subsurface layers are preserved in polar regions on Mars, which are considered to be a record of past climate changes on Mars. Orbital radar instruments like the SHAllow RADar (SHARAD) on board Mars Reconnaissance Orbiter (MRO) transmit radar signals to Mars and receive a set of signals returned from interfaces having a contrast in dielectric properties in the probed subsurface regions. These subsurface layers which are preserved in the upper ≈ 1 km of the Martian Polar Layered Deposits (PLDs) can be observed in SHARAD radargrams. Extraction of these layering features is the preliminary work before interpreting and understanding their origins. In this study, we use a new method based on log-Gabor filtering and Continuous Wavelet Transform (CWT)-based peak detection to extract subsurface radar reflections and a workflow to remove clutter reflections in order to reconstruct 3-D subsurface layers. These methods and workflow are then tested on the SHARAD data in the Promethei Lingula region near the Martian south pole. The results show that following this workflow, the ground surface and six subsurface interfaces can be reconstructed, which aids in the interpretation of the depositional and erosional history of this region.

Multichannel band-controlled deconvolution based on a data-driven structural regularization

Sparse deconvolution methods frequently invert for subsurface reflection impulses and adopt a trace-by-trace processing pattern. However, following this approach causes unreliability of the estimated reflectivity due to the nonuniqueness of the inverse problem, the poor spatial continuity of structures in the reconstructed reflectivity section, and the suppression on the reflection signals with small amplitudes. We have developed a structurally constrained multichannel band-controlled deconvolution (SC-MBCD) algorithm to alleviate these three issues. The algorithm inverts for a high-resolution seismogram rather than the full-band reflectivity series, thereby reducing the multiple solutions in the inversion and enhancing the reliability of processing results. We also exploited a structural constraint term to guarantee the spatial continuity of the structures, and we enhanced the relatively weak signals. The reflection structure characteristics, defined and extracted from the observed stacked seismic data, are the core of the structural regularization item. We solved the cost function of the SC-MBCD by the alternating direction method of multipliers algorithm. Synthetic model and field data examples demonstrate the rationality of SC-MBCD and confirmed that the algorithm can provide a better inversion result than the conventional sparse spike inversion in terms of retrieving weak reflection events and guaranteeing stratal continuities.

Lateral Continuity of Layering in the Mars South Polar Layered Deposits From SHARAD Sounding Data

AbstractThe south polar layered deposits (SPLD) are composed of alternating layers of ice and dust in varying proportions. The accumulation of the layers is driven by orbital forcings, and the cadence and structure of these layers preserve a record of the past Martian climate. We use SHARAD data to examine the radar properties of SPLD reflectors and to infer their spatial correlations. Crossing orbit tracks are incoherently stacked to improve the echo signal‐to‐noise ratio and extend the delineation of reflectors, laterally and vertically, into areas where they are not evident in individual SHARAD traces. Three distinct radar reflection “facies” are identified: (a) shallow layers that are generally well focused in processed radargrams, (b) less densely spaced layers that occur over much of the depth of the SPLD but are blurred to varying degrees, and (c) low reflectivity zones. A pattern of diffuse echoes termed fog, which originates from an uncertain surface or volume scattering mechanism, extends to varying round‐trip delay times and is often correlated with blurring of subsurface reflections. The fog signature is pervasive, being present in some form over 64% of the SPLD. Unconformities are observed in stacks of reflectors that both intersect the surface and are confined to the subsurface. Only one major deviation from near‐horizontality of the reflectors, located to the east of Australe Mensa, was identified. There is no evidence for major unconformities that suggest multiple depositional centers that later merged into the SPLD. Instead, SHARAD data suggest that the materials of the SPLD were deposited regionally, superposing materials from previous depositional episodes.

Mapping the Basement of the Ebro Basin in Spain With Seismic Ambient Noise Autocorrelations

AbstractSingle‐station autocorrelations of seismic ambient noise allow to obtain the shallow subsurface reflection response without the need of any active source or earthquake. Recently, crustal‐scale studies successfully applied this method to map the crust‐mantle boundary. These studies employed different processing methodologies to stabilize and identify the weak‐amplitude reflections. Here we also analyze noise autocorrelations but use higher‐frequency bands to map the basement of the Ebro Basin in Spain. This basin has a nonuniform basement structure due to its complex evolution. We tested two autocorrelation methods (the classical and phase cross correlation) to retrieve the P wave reflection response for seismic broadband stations located in the basin. The phase correlation approach is amplitude unbiased since based on the instantaneous phase coherence of analytic signals. It is insensitive to the background seismicity from the Pyrenees and other noise and proved to be the more efficient approach to retrieve P wave reflections from the Paleozoic basement. The detected signals per station are quite stable and show only a small time variability. We also show that sidelobes caused by the convolution of a delta pulse at zero time lag with the effective noise source time function do not affect our measurements and compare the measured noise autocorrelations with synthetic data for lithological profiles from neighboring wells. The a priori information from well data was essential to identify the signals and to finally map the discontinuity in between and beyond the well positions. Our final result is a comprehensive map of the Paleozoic basement in the Ebro Basin.

Directional‐oriented wavefield imaging: a new wave‐based subsurface illumination imaging condition for reverse time migration

ABSTRACTThe key objective of an imaging algorithm is to produce accurate and high‐resolution images of the subsurface geology. However, significant wavefield distortions occur due to wave propagation through complex structures and irregular acquisition geometries causing uneven wavefield illumination at the target. Therefore, conventional imaging conditions are unable to correctly compensate for variable illumination effects. We propose a generalised wave‐based imaging condition, which incorporates a weighting function based on energy illumination at each subsurface reflection and azimuth angles. Our proposed imaging kernel, named as the directional‐oriented wavefield imaging, compensates for illumination effects produced by possible surface obstructions during acquisition, sparse geometries employed in the field, and complex velocity models. An integral part of the directional‐oriented wavefield imaging condition is a methodology for applying down‐going/up‐going wavefield decomposition to both source and receiver extrapolated wavefields. This type of wavefield decomposition eliminates low‐frequency artefacts and scattering noise caused by the two‐way wave equation and can facilitate the robust estimation for energy fluxes of wavefields required for the seismic illumination analysis. Then, based on the estimation of the respective wavefield propagation vectors and associated directions, we evaluate the illumination energy for each subsurface location as a function of image depth point and subsurface azimuth and reflection angles. Thus, the final directional‐oriented wavefield imaging kernel is a cross‐correlation of the decomposed source and receiver wavefields weighted by the illuminated energy estimated at each depth location. The application of the directional‐oriented wavefield imaging condition can be employed during the generation of both depth‐stacked images and azimuth–reflection angle‐domain common image gathers. Numerical examples using synthetic and real data demonstrate that the new imaging condition can properly image complex wave paths and produce high‐fidelity depth sections.

A structural rank reduction operator for removing artifacts in least-squares reverse time migration

Least-square reverse time migration (LSRTM) has been widely accepted because of its exceptional performance in mitigating migration artifacts and preserving the reflection amplitude. Due to the ill-posedness of the inverse problem, regularization methods or constraints must be applied to the reflectivity model. In this paper, we propose a novel iterative LSRTM framework that is regularized by a lowrank constraint. The lowrank constraint is applied along the geological structure of the subsurface reflectivity image and thus can also be called structural lowrank constraint. The lowrank constraint is applied by iteratively applying a rank reduction operator that is based on the lowrank approximation theory. The rank reduction operator applied along the structure direction can effectively remove those artifacts caused from sparse shot/receiver sampling or other circumstances. Compared with the traditionally used smoothness based constraint, the lowrank constraint is more capable of removing noise while preserving edge details. Since the constraint is applied in post-stack seismic image, the extra computational cost caused by the singular value decomposition (SVD) of the rank reduction operator is negligible compared with the computational cost of the migration operator. Numerical examples with different levels of structural complexity are used to demonstrate the effectiveness and validity of the proposed algorithm.

A wavefield-separation-based elastic least-squares reverse time migration

Elastic least-squares reverse time migration (ELSRTM) has the potential to provide improved subsurface reflectivity estimation. Compared with elastic RTM (ERTM), ELSRTM can produce images with higher spatial resolution, more balanced amplitudes, and fewer artifacts. However, the crosstalk between P- and S-waves can significantly degrade the imaging quality of ELSRTM. We have developed an ELSRTM method to suppress the crosstalk artifacts. This method includes three crucial points. The first is that the forward and backward wavefields are extrapolated based on the separated elastic velocity-stress equation of P- and S-waves. The second is that the separated vector P- and S-wave residuals are migrated to form reflectivity images of Lamé constants [Formula: see text] and [Formula: see text] independently. The third is that the reflectivity images of [Formula: see text] and [Formula: see text] are obtained by the vector P-wave wavefields achieved in the backward extrapolation of the separated vector P-wave residuals and the vector S-wave wavefields achieved in the backward extrapolation of the separated vector S-wave residuals, respectively. Numerical tests with synthetic data demonstrate that our ELSRTM method can produce images free of crosstalk artifacts. Compared with ELSRTM based on the coupled wavefields, our ELSRTM method has better convergence and higher accuracy.

Elastic least-squares reverse time migration using the energy norm

Incorporating anisotropy and elasticity into least-squares migration is an important step toward recovering accurate amplitudes in seismic imaging. An efficient way to extract reflectivity information from anisotropic elastic wavefields exploits properties of the energy norm. We derive linearized modeling and migration operators based on the energy norm to perform anisotropic least-squares reverse time migration (LSRTM) describing subsurface reflectivity and correctly predicting observed data without costly decomposition of wave modes. Imaging operators based on the energy norm have no polarity reversal at normal incidence and remove backscattering artifacts caused by sharp interfaces in the earth model, thus accelerating convergence and generating images of higher quality when compared with images produced by conventional methods. With synthetic and field data experiments, we find that our elastic LSRTM method generates high-quality images that predict the data for arbitrary anisotropy, without the complexity of wave-mode decomposition and with a high convergence rate.

Modern and relict sedimentary systems of the semi-arid continental shelf in NE Brazil

This paper describes the carbonate–siliciclastic system of the equatorial continental shelf of NE Brazil (East Ceará) based on X-ray fluorescence (XRF), grain size, CaCO3, shallow seismic and remotely operated vehicle (ROV) analyses. Data were obtained for two sectors: 1) Halimeda Bank (HB), inner shelf (−12 m), and 2) transverse profile (TP), inner to outer shelf-upper slope (−5 to −100 m). In total, 72 samples were collected, and 29 km of seismic lines (HB) and ROV profiles (HB and TP) were surveyed. The main chemical elements were Ca and Si (93%). These elements occur in two types of shallow marine sediments: carbonate (mainly autochthonous) and siliciclastics (terrigenous/allochthonous/relict). With respect to the chemical elements, a strong negative correlation was observed between calcareous (Ca and Sr) and siliciclastic (Si, Al, and K) components. Strontium does not always show a strong positive correlation with Ca. The average CaCO3 contents of 81% and 91% were determined for the HB and TP, respectively. The profiles show a predominance of carbonate sediments; however, the HB demonstrates a greater continental influence (inner shelf). The grain size presents a prevalence of sand (82%) in relation to gravel (18%). This particle size variation is mainly due to the breakdown of Halimeda nodules, siliciclastic sediments in the finer fraction (>2.5Φ), and the presence of gravel with iron coating (relict). Two types of echo-characters have been identified. Both are associated with the large presence of carbonate sediments. Echo I shows the bottom surface with continuity in the sub-bottom without a subsurface reflector. Echo II presents a discontinuous subsurface reflector. The ROV allowed the observation of algae patches in higher floors and gravelly and sandy bioclastics in the lowest sectors. Large patches of calcareous green algae, Halimeda, occur in the inner shelf below the 15 m isobath, mainly due to the semi-arid climate (weak sediment supply from the mainland), geographical position (equatorial) and oceanographic conditions (hydrodynamic and biogeochemistry). It has been concluded that the seafloor of the semi-arid continental shelf of East Ceará (NE Brazil) shows modern predominance of carbonate deposition based on the lack of contaminants, geochemical purity of carbonate sediments, and high percentage of CaCO3. The conditions for exploitation in the intermediate sector are provided. However, it would be ideal to perform punctual extraction and analyze the resilience and regeneration of Halimeda incrassata and the consequences for fisheries (important economic resource of the region).

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.

Assessing gloss perception of human facial skin across subject

We propose novel techniques for the evaluation of perceived facial gloss across subjects with varying surface reflections. Given a database of facial skin images from multiple subjects, ordered according to perceived gloss within each subject, we propose a head-tail (least and most glossy image of each subject) selective comparison approach for ordering the entire database. We conducted a two-alternative forced-choice empirical study to compare the facial gloss across subjects within each group. Using the gloss scores of selected candidates and the gloss range of a reference subject, we fit each within-subject gloss range to a global gloss range and quantized the scores into distinct gloss levels. We then conducted another empirical study to validate the quantized gloss levels. The results show that in 90% of the cases, the levels are consistent with human judgments. Based on the database with quantized gloss levels, we develop a max-margin learning model for facial skin gloss estimation. The model relies on gloss related statistics extracted from surface and subsurface reflection images obtained using multimodal photography. The predicted gloss level is decided by the nearest neighbors using the learned scoring function. Performance tests demonstrate that the best performance, with 82% accuracy, is obtained when we combine local statistics from both surface and subsurface reflections.

Applying of High-Resolution Geophysical Techniques for Drainage Investigations at El-Basateen Cemetery Area, Cairo, Egypt

Due to the collapse of some cemetery in Basateen area, South of Cairo, this paper presents the application of geoelectrical resistivity sounding and imaging, as well as ground penetrating radar techniques for outlining the reasons and the presence of draining water and groundwater at the investigated area. A Vertical Electrical Sounding (VES) survey was performed at 3 points through the studied site to investigate the vertical extent of the subsurface sequence and the saturation levels. A total of 9 Dipole-Dipole imaging profiles were surveyed to determine the lateral distribution of saturation of drain water and infiltrated groundwater, and a total of 6 GPR profiles with 100- and 200- MHz antennae were surveyed to evaluate and determine the depth and the degree of saturation of the subsurface layer/s. The qualitative and quantitative interpretation of the acquired VES's and dipole-dipole imaging profiles showing easily the levels of saturations at the studied site. From the interpretation of GPR profiles, it was possible to locate and determine the saturated zones and the level of the groundwater through the area. The radar signals are penetrated enough and enabled the identification of the subsurface reflectors. The results of GPR, VES's and Resistivity imaging showed a good agreement. The integrated interpretations were verified by local geology and information from several bores. Also, the study was supported by a chemical analysis from the drain water and Ein El-Seera spring (close to studied site), to determine the main source of the drain and infiltrated water at the studied site.

Modeling scattering effects from time-varying sea surface based on acoustic reciprocity

In marine seismic processing, the sea surface is often considered a flat mirror; hence, the effects of different weather conditions during the acquisition are largely ignored. However, studies have shown that rough sea-surface ghosts can severely damage the 4D signal, if not handled properly in data processing. To account for realistic sea-surface effects in processing, the impact of time-varying rough sea surfaces needs to be studied. We derive a method for modeling source and receiver ghosts from the time-varying rough sea surface and their interaction with subsurface reflections. This method is based on acoustic reciprocity and leads to integral equations of nonstationary wavefields. These modeling equations can also serve as a basis for investigating source and receiver deghosting methods for time-varying rough sea surfaces. Our developed modeling algorithm is validated against a frequency-domain approach for a “frozen” rough sea surface. For a moving simple sea surface, the Doppler shift produced by our method is in very good agreement with the analytical solution. Using a Pierson-Moskowitz spectrum, we derive a time-varying rough sea surface and model the receiver ghost, the source ghost, and the source-receiver ghost for the subsurface primary reflections of a heterogeneous geologic model. The results highlight that the source and receiver ghost interactions with a time-varying sea surface differently affect the subsurface reflections, and these effects can significantly impact the seismic repeatability of 4D studies.

Applications of least-squares pre-stack depth migration in complex geology around the world

Pre-stack depth migration has been an industrial imaging standard for decades, starting from the adoption of Kirchhoff migration in the early Nineties to the emergence of reverse-time migration (RTM) in the late 2000s. These algorithms map the recorded seismic reflection energy from a surface location to a subsurface location, through either a ray-based travel-time table or a waveequation-based propagation engine. In principle, by combining high-fidelity migration algorithms and accurate subsurface velocity models, we can achieve the ultimate goals of seismic imaging: the correct positioning and focusing of the seismic reflectivity of the subsurface geological structures. In reality, however, there are several challenges and issues that need to be addressed before we are able to achieve such an objective, not to mention the fact that most of the time we do not record all subsurface reflections sufficiently owing to limited coverage and sampling of the seismic recording spread. We can consider recorded seismic data to be the result of forward modelling experiments through subsurface structures. To image the reflectivity of the subsurface, we need to reverse the forward wave-propagation effects with an inverse of the forward modelling operator. Essentially, this is an inversion process. However, conventional imaging algorithms are formulated as adjoint operators rather than as true inverses (Claerbout, 1992). This approximation caused image degradation due to irregular and aliased acquisition sampling, limited receiver coverage, noise, and inhomogeneous or poor illumination caused by complex overburden. As a result, standard pre-stack depth migration algorithms suffer from migration artifacts with uncancelled swings, limited bandwidth, and distorted amplitude on subsurface reflectors (Gray, 1997). This is true even for stateof-the-art imaging technology such as RTM (Baysal et al., 1983; Zhang and Zhang, 2009).