Kirchhoff Migration Research Articles

Pre‐stack Kirchhoff depth migration local space‐shift imaging condition: synthetic and data examples

ABSTRACTExtracting accurate common image angle gathers from pre‐stack depth migrations is important in the generation of any incremental uplift to the amplitude versus angle attributes and seismic inversions that can lead to significant impacts in exploration and development success. The commonly used Kirchhoff migration outputs surface common offset image gathers that require a transformation to angle gathers for amplitude versus angle analysis. The accuracy of this transformation is one of the factors that determine the robustness of the amplitude versus angle measurements. Here, we investigate the possibility of implementing an extended imaging condition, focusing on the space‐lag condition, for generating subsurface reflection angle gathers within a Kirchhoff migration. The objective is to determine if exploiting the spatial local shift imaging condition can provide any increase in angle gather fidelity relative to the common offset image gathers. The same restrictions with a ray‐based approach will apply using the extended imaging condition as both the offset and extended imaging condition method use travel times derived from solutions to an Eikonal equation. The aims are to offer an alternative ray‐based method to generate subsurface angle gathers and to understand the impact on the amplitude versus angle response. To this end, the implementation of the space‐shift imaging condition is discussed and results of three different data sets are presented. A layered three‐dimensional model and a complex two‐dimensional model are used to assess the space shift image gathers output from such a migration scheme and to evaluate the seismic attributes relative to the traditional surface offset common image gathers. The synthetic results show that the extended imaging condition clearly provides an uplift in the measured amplitude versus angle over the surface offset migration. The noise profile post‐migration is also improved for the space‐lag migration due to the double summation inside the migration. Finally, we show an example of a space‐lag gather from deep marine data and compare the resultant angle gathers with those generated from an offset migration and a time‐shift imaging condition Kirchhoff migration. The comparison of the real data with a well log shows that the space‐lag result is a better match to the well compared to the time‐lag extended imaging condition and the common offset Kirchhoff migration. Overall, the results from the synthetics and real data show that a Kirchhoff migration with an extended imaging condition is capable of generating subsurface angle gathers with an incremental improvement in amplitude versus angle fidelity and lower noise but comes at a higher computational cost.

Efficient Parallel Implementation of Multi-Arrival 3D Prestack Seismic Depth Migration

The goal of seismic migration is to reconstruct the image of Earth's depth inhomogeneities on the base of seismic data. Seismic data is obtained using shots in shallow wells that are located in a dense grid points. Those shots could be considered as special point sources. A reflected and scattered seismic waves from the depth inhomogeneities are received by geophones located also in a dense grid points on a surface. A seismic image of depth inhomogeneities can be constructed based on these waves. The implementation of 3-D seismic migration implies the solution of about 10 4÷5 3-D direct problems of wave propagation. Hence efficient asymptotic methods are of a great practical importance. The multi-arrival 3-D seismic migration program is implemented based on a new asymptotic method. It takes into account multi-pass wave propagation and caustics. The program uses parallel calculations in an MPI environment on hundreds and thousands of processor cores. The program was successfully tested on an international synthetic SEG salt data set and on real data. A seismic image cube for Timan-Pechora region is given as an example.

The influence of irregular seafloor topography on the seismic wave field and migration imaging

One of the problems experienced in marine geophysical exploration is that the layered features in the migration imaging profile are blurred and the seismic energy reflected is weaker in the middle or lower parts. In this study we model the seismic wavefield records in the undulating seafloor when there is both a slight change and significant change in seafloor topography to analyze its influence on the seismic reflection data and migration imaging profiles. We compare and analyze the wave field records collected at the same point on the original and modified velocity models, and the cross-bonding resulting migration imaging profiles. The results show that whether the seismic reflection data collection is performed along the direction of the survey line or against the direction of the survey line, slight changes in the seafloor topography have little effect on the wave field records and the migration profile, while significant changes in the seafloor topography have great effect on both the wave field records and migration profile.

Late Quaternary vertical slip rates along the Southern Yadong–Gulu Rift, Southern Tibetan Plateau

Determination of vertical slip rate on different timescales is one of the critical issues along north-trending rifts in Southern Tibet. The Yadong–Gulu rift, a typical example of these north-trending rifts, lacked sufficient quantitative data about the vertical slip rate along its southern portion. The southern Yadong–Gulu rift is comprised of the Relong, Nieru and the Pagri–Duoqing Co grabens, which are controlled by a normal fault along its eastern boundary. To determine the vertical slip rate, we measured the average height of fault scarps along the main fault trace and dated sediments displaced by the scarps by Optically Stimulated Luminescence (OSL) dating. The results indicated that the ages of these fault scarps clustered at late Pleistocene, and the vertical separation of scarps ranged from about 5.5 m to 22 m. After abandoning distinctly inaccurate displacements, we estimate that the average vertical slip rate of Relong graben is 0.7 ± 0.1 mm/yr and Nieru graben is 0.8 ± 0.1 mm/yr, while that of Pagri–Duoqing Co graben is 2.0 ± 0.5 mm/yr since the latest Quaternary (ca. 15 ka) by weighting mean slip rate with error. It is considered that the different slip rates derive from the dispersed deformation of other faults around the Nieru and Relong graben and ductile deformation within the lower crust and northern Himalaya gneiss dome. Besides, the lack of large earthquakes in historical documents compared with the northern part of Yadong-Gulu rift, the inferred pattern of seismic migration and triggering of MHT to north-trending rifts, together indicate that the southern Yadong–Gulu rift is at high risks for middle to large earthquakes (M ≥ 6) possibly.

2-D and 3-D Reconstruction Algorithms in the Fourier Domain for Plane-Wave Imaging in Nondestructive Testing.

Time-domain plane-wave imaging (PWI) has recently emerged in medical imaging and is now taking to nondestructive testing (NDT) due to its ability to provide images of good resolution and contrast with only a few steered plane waves. Insonifying a medium with plane waves is a particularly interesting approach in 3-D imaging with matrix arrays because it allows to tremendously reduce the volume of data to be stored and processed as well as the acquisition time. However, even if the data volume is reduced with plane wave emissions, the image reconstruction in the time domain with a delay-and-sum algorithm is not sufficient to achieve low computation times in 3-D due to the number of voxels. Other reconstruction algorithms take place in the wavenumber-frequency (f-k) domain and have been shown to accelerate computation times in seismic imaging and in synthetic aperture radar. In this paper, we start from time-domain PWI in 2-D and compare it to two algorithms in the f-k domain, coming from the Stolt migration in seismic imaging and the Lu theory of limited diffraction beams in medical imaging. We then extend them to immersion testing configurations where a linear array is facing a plane water-steel interface. Finally, the reconstruction algorithms are generalized to 3-D imaging with matrix arrays. A comparison dwelling on image quality and algorithmic complexities is provided, as well as a theoretical analysis of the image amplitudes and the limits of each method. We show that the reconstruction schemes in the f-k domain improve the lateral resolution and offer a theoretical and numerical computation gain of up to 36 in 3-D imaging in a realistic NDT configuration.

Research on seismic wave reverse time migration data regularization and parallel computing in cloud environment

Research on seismic wave reverse time migration data regularization and parallel computing in cloud environment

SOLUTION OF HIGH VELOCITY ANOMALIES IMPERCEPTIBLE TO SEISMIC RESOLUTION, BY MEANS OF SYNTHETIC MODELS, PENOBSCOT FIELD, CANADA

Penobscot Field is located in the Sable Sub-basin in Nova Scotia, Canada, where a 3D seismic acquisition campaign was carried out in 1991 and also two oil wells were previously drilled (L-30 and B-41). In the interpreted seismic data, a discrepancy was found in the travel times of the seismic waves near well B-41, causing a false structural height in the Naskapi Member, Mississauga Formation (Early Cretaceous or Lower Cretaceous) and deeper formations (10 to 15 ms, i.e. approximately 25 m). It was decided to find a solution of this problem using synthetic models. First, making a delimitation of the study area by means of a seismic subcube, which were later interpreted surfaces of interest, through the well data. The average velocity and density properties were found for each interpreted strata. Subsequently, a 2D seismic acquisition was simulated, choosing a line that crossed both wells and through the use of ray traces, synthetic shot gathers were obtained and processed through the use of different seismic migration tests, and the final solution was found to be Kirchhoff pre-stacking migration in depth.

Porosity Prediction Using Neural Network Based on Seismic Inversion and Seismic Attributes

It has done a study of porosity prediction by using neural network. The study uses 2D seismic data post-stack time migration (PSTM) and 2 well data at field “T”. The objective is determining distribution of porosity. Porosity in carbonate reservoir is actually heterogeneous, complex and random. To face the complexity the neural network method has been implemented. The neural network algorithm uses probabilistic neural network based on best seismic attributes. It has been selected by using multi-attribute method with has high correlation. The best attributes which have been selected are amplitude envelope, average frequency, amplitude weighted phase, integrated absolute amplitude, acoustic impedance, and dominant frequency. The attribute is used as input to probabilistic neural network method process. The result porosity prediction based on probabilistic neural network use non-linear equation obtained high correlation coefficient 0.86 and approach actual log. The result has a better correlation than using multi-attribute method with correlation 0.58. The value of distribution porosity is 0.05–0.3 and it indicates the heterogeneous porosity distribution generally from the bottom to up are decreasing value.

Kinematic migration for determination of velocity model of the medium while solving practical problems of seismic exploration

Seismic migration allows solving different problems of seismic exploration and depending on the properties of the wave field which take part during the processing is subdivided into two types: kinematic and dynamic. Kinematic migration allows to determine seismic velocities and interfaces in geological medium for further implementation of dynamic migration can be enabled while solving different problems of seismic exploration where fast information on a priori parameters of velocity model of the study medium is needed. Kinematic migration for both fields of refracted and reflected waves is based on the continuation of temporal field which is implemented by finite-differential solution of eikonal equation. The values of temporal field are determined by distinct scheme which has quadratic degree of approximation and conditional stability that is proved during the studies. In this case the algorithm of kinematic migration of the field of refracted waves envisages two reverse continuations of temporal fields observed from two opposite sources while algorithm of kinematic migration of the field of reflected waves includes both direct continuation of temporal field from dotted source and reverse continuation from seismic receivers. Particularly urgent problem in this direction is the study of feasibility of finite-differential kinematic migration in case of determination of velocity model of multiple-structured geological medium while processing seismic data observed in different range of distances from the source. Possibilities of application of elaborated finite-differential kinematic migration for solving practical problems of seismic exploration have been considered in the paper. Effectiveness of elaborated techniques is demonstrated by model and real examples.

Optimal coding of blended seismic sources for 2D full waveform inversion in time

Full Waveform Inversion (FWI) schemes are gradually becoming more common in the oil and gas industry, as a new tool for studying complex geological zones, based on their reliability for estimating velocity models. FWI is a non-linear inversion method that iteratively estimates subsurface characteristics such as seismic velocity, starting from an initial velocity model and the preconditioned data acquired.
 Blended sources have been used in marine seismic acquisitions to reduce acquisition costs, reducing the number of times that the vessel needs to cross the exploration delineation trajectory. When blended or simultaneous without previous de-blending or separation, stage data are used in the reconstruction of the velocity model with the FWI method, and the computational time is reduced. However, blended data implies overlapping single shot-gathers, producing interference that affects the result of seismic approaches, such as FWI or seismic image migration.
 In this document, an encoding strategy is developed, which reduces the overlap areas within the blended data to improve the final velocity model with the FWI method.

An optimized space-time Gaussian beam migration method with dynamic parameter control

In the Gaussian beam (GB) method, initial beam parameters are principal factors influencing the accuracy and computational efficiency of seismic depth imaging. Various optimized beam parameter strategies for Gaussian beam migration (GBM) have been proposed to improve imaging quality as well as computational efficiency, while optimized space-time Gaussian beam schemes for seismic migration have still not been fully investigated. In this paper, an optimized space-time Gaussian beam approach with dynamic parameter control for seismic depth imaging is developed. We first provide an expression for dynamic beam parameter by taking in account the effect of velocity field variation on the beam forming. Based on dynamic beam parameters, the new space-time adaptive Gaussian beam generated by an arbitrary source wavelet is obtained, which can adaptively calculate the beam width to make the seismic beam energy better focused in the central ray neighborhood. Then, the forward wavefield is constructed in two-dimensional (2D) acoustic media by space-time adaptive Gaussian beam for the implementation of migration. Adhering to the framework of conventional space-time Gaussian beam method, we perform the up-going ray tracing from subsurface imaging points to the receiver surface to compute the asymptotic Green function for the construction of the backward wavefield. Numerical experiments demonstrate that the new presented approach has a superior accuracy for seismic depth imaging in both shallow and deep regions compared to the conventional space-time Gaussian beam migration scheme.

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.

An introduction to seismic exploration of the Micang-Dabashan foothill belt in the Sichuan Basin

Geologic studies indicate that the platform-margin reef-shallow facies in Permo-Triassic marine strata in the Micang-Dabashan foothill belt in the Sichuan Basin are favorable exploration targets for oil and gas exploration. However, the typical dual-complexity problem (complex surface condition and subsurface structure) brings a great challenge for seismic technology targeting of those potential oil and gas reservoirs. To overcome this problem, varieties of advanced seismic acquisition and processing methods have been used to improve the imaging quality of piedmont seismic data since 2000. Some improvements have been achieved: The reflection waves from the far offset and deep layer can be acquired in shot gathers from limestone outcropped areas, and the signal-to-noise ratio (S/N) of reflection and diffraction waves in the stack section has been enhanced significantly so as to reveal amounts of valuable geologic information. The resolution and the S/N of seismic migration imaging for the strong fold zone in marine strata have been improved partially, so that the structure of the step-fault zone and the enveloping of gypsum rock are clearer than those revealed by the old seismic section. Even so, actual drilling data demonstrate that the subsurface structures of the foothill belt are far more complex than those revealed by the current seismic imaging results. Therefore, postdrilling evaluation for the validity of seismic techniques implemented in the Nanjiang and Zhenba piedmont zone has been carried out. The results indicate that the current acquisition scheme and processing workflow cannot completely fulfill the requirements of high-precision velocity modeling and migration imaging of complex structures (such as footwalls of thrust fault and small-scale fault blocks) in the piedmont zone, especially when the rugged surface and the widespread limestone outcrop appear simultaneously. Finally, we have developed some potential needs of seismic theories and techniques in the foothill belt, including seismic wave propagation, acquisition, and processing technology.

A parameter-modified method for implementing surface topography in elastic-wave finite-difference modeling

Accurate seismic modeling with a realistic topography plays an essential role in onshore seismic migration and inversion. The finite-difference (FD) method is one of the most popular numerical tools for seismic modeling. But implementing the free surface on topography using the FD method is nontrivial. We have developed a stable and efficient parameter-modified (PM) method for modeling elastic-wave propagation in the presence of complex topography. This method is based on a standard staggered-grid scheme, and the stress-free condition is implemented on the rugged surface by modifying the redefined medium parameters at the discrete topography boundary points. This numerical treatment for topography needs to be performed only once before the wave simulation. In this way, we avoid the tedious handling of wavefield variables in every time step, and this boundary treatment can be integrated easily into existing staggered-grid FD modeling codes. A series of numerical tests in two dimensions and three dimensions indicate that with a spatial sampling of 15 grid points per minimum wavelength, our method is good enough to eliminate staircase diffractions and produces more accurate results than those obtained by some other staggered-grid-based numerical approaches. Numerical experiments on some more complex models also demonstrate the feasibility of our method in handling topography with strong variation and Poisson’s ratio discontinuity. In addition, this PM method can be used in a discontinuous-grid scheme in which only the regions near the irregular topography need to be oversampled, which is very important for improving its efficiency in real applications.

Imaging the high-temperature geothermal field at Krafla using vertical seismic profiling

Geophysical exploration and in particular active-source seismic imaging of geothermal fields is important to assess and optimize the exploitation of natural heat sources for energy production and direct use. The first multi-offset (moving-source) vertical seismic profiling (VSP) experiment over the high-temperature geothermal field in Krafla (Iceland) was carried out in spring 2014 with the aim to test whether VSP is a suitable method to map volcanic stratigraphy, fractures, dykes, steam zones and magmatic bodies at this site and for volcanic environments in general. In this study, we present a workflow for processing the sparse Krafla VSP dataset recorded with receivers in either of two boreholes. The analysis involved first-arrival traveltime inversion and seismic reflection processing. The seismic velocity model obtained by traveltime tomography reveals structural information between the two boreholes and can be linked to an existing geological model, showing that the seismic velocities are mainly controlled by lithology. The zero-offset seismic reflection data were processed into two corridor stacks. Walk-away VSP reflection data were migrated with a novel multicomponent Kirchhoff migration algorithm that includes P- and S-wave isolation to obtain separate PP, PS and SS migrated images. The reflections imaged in the corridor stacks can be linked to the main lithological units known from borehole logging information. Migrated images from the walk-away data reveal reflectors below and to the sides of the two boreholes. Considering à priori information, such as hypocenter locations from earthquake seismology studies, the reflectors can be related to changes in lithology, fault zones, dykes and possibly the top of the Krafla magma chamber. We found that VSP is potentially a useful method to image the key lithological boundaries and volcanic stratigraphy in the complex magmatic environment at Krafla, but à priori information proved to be essential to constrain the processing and interpretation of the sparse array dataset.

Resolving range aliasing in Omega-K synthetic aperture beamforming

The Omega-K algorithm is a beamforming algorithm that exploits Stolt migration in the wavenumber domain to focus stripmap synthetic aperture data. Because of its efficiency and its inherently broad-band properties it has been a common solution for synthetic aperture beamforming problems, especially in situations where trajectory perturbations are small and computational resources are limited. The algorithm is commonly divided into two stages: a bulk compression stage leveraging a phase multiplication in the wavenumber domain (sometimes used in isolation for resonance and shadow enhancement), which focuses data at the scene center, and Stolt migration which brings the entire scene into focus. For systems with very broad beamwidth the bulk compression stage can lead to spatial aliasing for close range scatterers, causing a loss of spatial spectrum information and increased noise. The cause of this frequently overlooked aliasing problem, its manifestation in SAS images, and methods for its avoidance will be discussed and demonstrated using both simulations and ClutterEX17 sonar data.

Source-independent extended waveform inversion based on space-time source extension: Frequency-domain implementation

Source signature estimation from seismic data is a crucial ingredient for successful application of seismic migration and full-waveform inversion (FWI). If the starting velocity deviates from the target velocity, FWI method with on-the-fly source estimation may fail due to the cycle-skipping problem. We have developed a source-based extended waveform inversion method, by introducing additional parameters in the source function, to solve the FWI problem without the source signature as a priori. Specifically, we allow the point source function to be dependent on spatial and time variables. In this way, we can easily construct an extended source function to fit the recorded data by solving a source matching subproblem; hence, it is less prone to cycle skipping. A novel source focusing annihilator, defined as the distance function from the real source position, is used for penalizing the defocused energy in the extended source function. A close data fit avoiding the cycle-skipping problem effectively makes the new method less likely to suffer from local minima, which does not require extreme low-frequency signals in the data. Numerical experiments confirm that our method can mitigate cycle skipping in FWI and is robust against random noise.

Imaging small polarizable scatterers with polarization data

We present a method for imaging small scatterers in a homogeneous medium from polarization measurements of the electric field at an array. The electric field comes from illuminating the scatterers with a point source with known location and polarization. We view this problem as a generalized phase retrieval problem with data being the coherency matrix or Stokes parameters of the electric field at the array. We introduce a simple preprocessing of the coherency matrix data that partially recovers the ideal data where all the components of the electric field are known for different source dipole moments. We prove that the images obtained using an electromagnetic version of Kirchhoff migration applied to the partial data are, for high frequencies, asymptotically identical to the images obtained from ideal data. We analyze the image resolution and show that polarizability tensor components in an appropriate basis can be recovered from the Kirchhoff images, which are tensor fields. A time domain interpretation of this imaging problem is provided and numerical experiments are used to illustrate the theory.

Locating wind farms by seismic interferometry and migration

We present a case study on the detection and quantification of seismic signals induced by operating wind turbines (WTs). We spatially locate the sources of such signals in data which were recorded at 11 seismic stations in 2011 and 2012 during the TIMO project (Deep Structure of the Central Upper Rhine Graben). During this time period, four wind farms with altogether 12 WTs were in operation near the town of Landau, Southwest Germany. We locate WTs as sources of continuous seismic signals by application of seismic interferometry and migration of the energy found in cross-correlograms. A clear increase of emitted seismic energy with rotor speed confirms that the observed signal is induced by WTs. We can clearly distinguish wind farms consisting of different types of WTs (different hub height and rotor diameter) corresponding to different stable frequency bands (1.3–1.6 Hz, 1.75–1.95 Hz and 2.0–2.2 Hz) which do not depend on wind speed. The peak frequency apparently is controlled by the elastic eigenmodes of the structure rather than the passing of blades at the tower. From this we conclude that vibrations are coupled into the ground at the foundation and propagate as Rayleigh waves (and not as infrasound). The migration velocity of 320 m/s corresponds to their group velocity. The applied migration method can contribute to the assessment of local sources of seismic noise. This topic gets growing attention in the seismological community. In particular, the recent boost of newly installed wind farms is a threat to seismological observatories such as the Black Forest Observatory (BFO) and the Grafenberg array (GRF) or gravitational wave observatories (e.g. LIGO, VIRGO) in terms of a sensitivity degradation of such observatories.

A generalized average-derivative optimal finite-difference scheme for 2D frequency-domain acoustic-wave modeling on continuous nonuniform grids

The frequency-domain finite-difference (FDFD) method is an effective tool for implementing frequency-domain seismic modeling, inversion, and migration. However, the computational cost for the FDFD method dealing with large models is prohibitive, limiting its application. As a common strategy to improve the computational efficiency, a nonuniform grid is usually adopted in the time-domain finite-difference method instead of the FDFD method. We have developed a generalized average-derivative optimal scheme (GADOS) that can perform frequency-domain acoustic-wave modeling on continuous nonuniform grids in the vertical and horizontal directions. Before we begin the calculations, we optimize numerous stencils in which the grid spacing ratios are different to obtain a large dictionary composed of many groups of optimal coefficients. We consider the continuous nonuniform grids as a gathering of nonuniform nine-point stencils (i.e., the stencil of the GADOS) and select the proper weighted coefficients for every stencil to ensure that the numerical dispersion is minimal in the global area. All the phase-velocity errors of the GADOS for different grid spacing ratios are less than [Formula: see text] even if the number of grid points per wavelength is as small as four after the weighted coefficients are optimized by minimizing the numerical dispersion. Compared with the average-derivative optimal scheme (ADOS), simulating seismic waves with the GADOS on nonuniform grids reduce the computational cost with the premise of ensuring sufficient accuracy. Several numerical examples are presented to illustrate the feasibility and efficiency of the GADOS on continuous nonuniform grids.