Kirchhoff Migration Algorithm Research Articles

Fast Factorized Kirchhoff Migration Algorithm for Near-Field Radar Imaging With Sparse MIMO Arrays

Fast Factorized Kirchhoff Migration Algorithm for Near-Field Radar Imaging With Sparse MIMO Arrays

Multi-image, reverse time, and Kirchhoff migrations with compact Green’s functions

Using compact representations of Green’s functions we derive a common framework for reverse time migration (RTM) and Kirchhoff migration. These compact Green’s functions (CGFs) are 3D volumes containing traveltimes and amplitudes for the N most representative events in the upcoming/downgoing decomposed 4D wavefields originating from a point source. Within this framework, we implement an RTM algorithm using a multivalued excitation time/amplitude imaging condition. This new approach produces four complementary imaging volumes (different combinations of source and receiver decomposed wavefields) and angle/azimuth gathers with computational effort less than 15% greater than that of plain (one image and no gathers) RTM algorithms. The advantages of separating the image volume into four complementary volumes are well established in the literature (low-frequency noise separation and turning wave imaging); however, its use has been limited by the computational cost. Despite using two source propagations to decompose the source wavefield, we reduce the computations to less than 20% of a single source propagation by performing finite-difference propagation with half the frequency limit used in the receiver wavefield propagation. The combination of CGF and an excitation time/amplitude imaging condition allows receiver wavefield decomposition with only one wavefield propagation. Our RTM algorithm constructs angle/azimuth gathers using a postmigration computation of the source and receiver wavefield’s propagation directions. To compute the propagation directions after migration, we use a new concept: the cumulative wavefield volumes, which are 3D, imaging-condition-guided compressions, of the 4D source and receiver wavefields. We also use CGF to implement a Kirchhoff migration algorithm that produces four complementary image volumes with RTM-like quality. Furthermore, we present synthetic and field data examples to clarify the new concepts and illustrate the results obtained using these methods.

3D deep geothermal reservoir imaging with wireline distributed acoustic sensing in two boreholes

Abstract. Geothermal exploration will help move towards a low-carbon economy and provide a basis for green and sustainable growth. The development of new practical, reliable methods for geophysical characterization of a reservoir has the potential to facilitate a broader application of deep geothermal energy. At the Groß Schönebeck in situ laboratory, a unique vertical seismic profiling (VSP) dataset was recorded in two 4.3 km deep geothermal boreholes using fibre-optic cables in early 2017. The experiment set-up consisted of 61 vibrator points organized in a spiral pattern around the well site to ensure a proper offset and azimuth distribution in the target reservoir section. Data were processed using a standard workflow for VSP. As a result, a detailed three-dimensional 0.75km×1km×4.5 km image around the existing boreholes was created using the Kirchhoff migration algorithm with restricted aperture. The imaging resolved small-scale features in the reservoir essential for the future exploration of the geothermal research site. Borehole data with vertical resolution up to 16 m revealed the existing depth variations of the Elbe reservoir sandstone horizon at 4.08–4.10 km depth and indications of an unconformity in the area where we expect volcanic rocks. In addition, in the borehole data a complex interlaying with numerous pinch-outs in the Upper Rotliegend reservoir section (3.8 to 4 km depth) was discovered. Thereby, we demonstrate that wireline fibre-optic data can significantly contribute to exploration by providing an efficient and reliable method for deep geothermal reservoir imaging.

Nondestructive Inspection of Tree Trunks Using a Dual-Polarized Ground-Penetrating Radar System

In recent years, trees in European countries have been increasingly endangered by emerging infectious diseases (EIDs). In the United Kingdom, this has been observed to affect whole woodlands and forests, threatening the existence of some types of trees. Although quarantine measures have been taken to limit the spreading of such diseases, this has not yet been effectively controlled leading to millions of trees affected by EIDs. Ground-penetrating radar (GPR) has proven effective in identifying critical features on diseased trees for detection of EIDs spread. However, the irregular shape of tree trunks and their complex internal structure represent real challenges for conventional GPR measurements and data processing methodologies. In this research, a dual-polarised GPR system is used to detect internal decay in tree trunks using novel signal processing methodologies. A polarimetric correlation filter based on Bragg Scattering on a 3D Pauli feature vector and an arc-shaped Kirchhoff migration are discussed in detail. The proposed polarimetric correlation filter is utilised to enhance the signal-to-noise ratio (SNR) of B-scans due to bark and tree trunk high-loss properties of tree trunks. Meanwhile, an arc-shaped Kirchhoff migration algorithm is performed to counteract the influence of the bark irregularity. The proposed data processing framework is successfully validated with measurements on a real tree trunk, where cross-sections were subsequently cut for comparison purposes. Outcomes from the proposed methodology demonstrate a high consistency with the features observed on the tree trunk cross-sections, indicating the reliability of the proposed detection scheme for assessing tree-decay associated with EIDs.

Radar imaging of fractures and voids behind the walls of an underground mine

Two- and three-dimensional rock-penetrating-radar data were acquired on the wall of a pillar in an underground limestone mine. The objective was to test the ability of radar to image fractures and karst voids and to characterize their geometry, aperture, and fluid content, with the goal of mitigating mining hazards. Strong radar reflections in the field data correlate with fractures and a cave exposed on the pillar walls. Large pillar wall topography was included in the steep-dip Kirchhoff migration algorithm because standard elevation corrections are inaccurate. The depth-migrated 250 MHz radar images illuminate fractures, karst voids, and the far wall of the pillar up to approximately 25 m depth into the rock, with a spatial resolution of <0.5 m. Higher frequency radar improved the image resolution and aided in the interpretation, but at the cost of shallower depth of penetration and extra acquisition effort. Due to the strong contrast in physical properties between the rock and the fracture fluid, fractures with apertures as thin as a 50th of a radar wavelength were imaged. Water-filled fractures with mm-scale aperture and air-filled fractures with cm-scale apertures produce strong reflections at 250 MHz. A strong variation in the reflection amplitude along each fracture is interpreted to represent the variable fracture aperture and the nonplanar fracture structure. Fracture apertures were quantitatively measured, but distinguishing water from air-filled fractures was not possible due to the complex radar wavelet and fracture geometry. Two conjugate fracture sets were imaged. One of these fracture sets dominates the rock mass stability and water inrush challenges throughout the mine. All of the detected voids and a large cave are at the intersection of two fractures, indicating preferential water flow and dissolution along conjugate fracture intersections. Detecting, locating, and characterizing fractures and voids prior to excavation can enable miners to mitigate potential collapse and flood hazards before they occur.

Comparing between KM and RTM Algorithms to Pre- Stack Migrate Seismic Data

Creating a clear seismic section to explore the underground is the primary goal of seismic surveys. The seismic section is created by processing the data obtained from the seismic survey. Migration is an important seismic data process, as it puts reflections in place. In this research, the Kirchhoff Migration (KM) algorithm and the Reverse Time Migration (RTM) algorithm were applied using MatlabR2019 software on two industrial models, comparing the results by calculating the brightness on the resulting image and after calculating the contrast and adjusting the seismic section. The results showed that the use of the RTM algorithm gives more clear results than the results obtained when applying the KM algorithm.

Estimated Lunar Regolith Structure Based on the Least-Squares Kirchhoff Migration of CE-3 Lunar Penetrating Radar Data

The lunar penetrating radar (LPR) carried on the Chang E-3 Yutu Rover observations at 500 MHz successfully reveals the thickness and geological structure of the shallow lunar regolith. Previous work used the calculated permittivity and the migration image to estimate the layer interface and local target. In this letter, a least-squares Kirchhoff migration (LSM) algorithm is presented to reduce the migration artifacts (i.e., recording footprints) due to incomplete data. Both synthetic and CE-3 LPR data are used to test the effectiveness of the LSM method. The numerical results show that LSM can achieve a much superior image quality than Kirchhoff migration and frequency-wavenumber (F-K) migration results. Based on the LSM result of CE-3 LPR data, we can find evident strata reflection and continuous distinct layers in the shallow lunar subsurface below the CE-3 site. It provides a more reliable and robust way to interpret the lunar regolith structure.

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.

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.

Offshore imaging with complex overburden: Understanding gather complexity and resulting attribute accuracy through synthetics

The objectives of this study are to determine the effect of complex overburden in offshore continental settings on the seismic wavefield and on the resultant seismic images and attributes. Seismic waves exhibit complex wave paths when propagating through heterogeneous geologic structures. A key step in understanding the consequences for imaging and, more importantly, amplitude versus angle behavior is to model this complexity in a known earth-velocity model. The earth model used, represented by the seismic velocities, should exhibit similar behavior to the real data but still remain as simple as possible. This is also the case in velocity-model building. However, the inability to include subtle geologic features leads to inaccuracy and uncertainty in the velocity model. Understanding how this inaccuracy manifests itself is vital in any predictive exercise using seismic attributes. To improve this understanding, several synthetic data sets were simulated using full-wavefield synthetics. It is evident from the results that subtle velocity features are required in the imaging velocity field to ensure accurate angle gather behavior whether output is from a ray-based Kirchhoff migration or full-wave equation algorithm. If this requirement is met, seismic attributes from an amplitude-preserving migration can be used as a facies prediction in conjunction with the correct imaging algorithm.

Passive detection of scatterer using autocorrelation of surf noise

When a scatterer is located in a diffuse noise field, time domain Green's function between two different receivers can be extracted from cross-correlation of ambient noise which is recorded by the two receivers so that target detection can be implemented. However, the method based on cross-correlation strongly depends on timing synchronization of each receiver, otherwise there will be a time drift in the cross-correlation result, which can bring error in the positioning detection. Besides, two receivers that are far from each other must communicate with each other to implement cross-correlation in real-time data processing, but big data transmission is difficult in the ocean. Compared with cross-correlation, autocorrelation means that each receiver works independently and only the final autocorrelation result is to be transmitted. Actually, the scattered wave of target is always so weak that it is submerged in the autocorrelation result of the ambient noise. In this paper, we propose a method of processing the autocorrelation of the ambient noise. When the averaging noise autocorrelation of all receivers is subtracted from the autocorrelation result of the noise recorded by each receiver, the signalnoise ratio of the scattered wave will be significantly enhanced. With the help of Kirchhoff migration algorithm, detection of a scatterer can be implemented. We have conducted a scatterer passive detection experiment in Shilaoren beach, Qingdao, and accurately detected the position of a polyviny chloride pipe (about 8 m away from the nearest receiver) using only 12 min surf noise data. The experimental result shows that the processing of autocorrelation could replace cross-correlation in passive target detection when the ambient noise is time steady and the statistical characteristics of the background noise at different receivers are the same. Unlike Green's function extracted from cross-correlation of ambient noise, each receiver can work independently without considering the problems of massive data transmission and timing synchronization, which may be suitable for target detection using multi-receivers and mobile platform.

A comparison on initial-value ray tracing and fast marching eikonal solver for VTI traveltime computing

The Earth's subsurface is an anisotropic medium where the velocity of seismic waves alters in different propagation angles. Omitting anisotropy in seismic imaging not only brings mis-positioning of migrated dipping events but also fails to retain dipping energy during dip-moveout. To account for the efficacy of seismic anisotropy in imaging, an anisotropic wave equation must be engaged. Seismic traveltime computing is fundamental of both Kirchhoff migration and tomography algorithms. Two main categories of traveltime computing involve traditional ray tracing methods and finite difference eikonal solvers. In this study, we present two techniques of initial-value ray tracing and fast marching eikonal solver in isotropic and vertical transverse isotropy (VTI) media, and a comparison between results is demonstrated for more evaluation. Although the ray tracing approach is able to compute multiple arrivals with great precision, the eikonal solver is faster and more robust for traveltime computation. Since the ray tracing result is not a deterministic solution and it depends on the initial circumstance, employing the eikonal solver method are more preferred and suggested.

Experimental Studies on Monitoring and Metering of Radial Deformations on Transformer HV Winding Using Image Processing and UWB Transceivers

In this paper, a novel method based on image processing is proposed for detecting the presence and location of mechanical deformations on an actual power transformer winding. A vertical imaging setup is used to obtain a two-dimensional (2-D) image of the transformer winding using synthetic aperture radar (SAR) imaging method and Kirchhoff migration algorithm. The main goal of the image processing method is to detect the location of the radial deformation on the transformer high-voltage (HV) winding. Two different deformations are applied on the winding under the test in this paper. The first one is a modeled bulgy mechanical deformation and the second one is an actual concave buckling made on the actual transformer HV winding. The experimental results for different cases show the effectiveness of the proposed method to detect the presence and location of the deformation on the transformer winding.

Efficient Near-Field Imaging for Single-Borehole Radar With Widely Separated Transceivers

In this paper, the formulation of Stolt migration is modified for impulse borehole radar near-field imaging in the subsurface scenarios where the transceiver is widely separated with respect to the detection range. The proposed approach consists of the following aspects. First, the locations of the transmitter and receiver in the survey are regarded as independent sample dimensions, and the original sample set is converted to an enlarged virtual sample set. The frequency–wavenumber spectrum (FWS) of the virtual sample set is available via multidimensional fast Fourier transform (FFT). Then, the relation between the angular frequency and wavenumbers of the transmitter and receiver is derived in the frame of the virtual sample set, which provides the basis for the interpolation in angular frequency and weighting process of FWS. By applying multidimensional inverse FFT (IFFT) to the interpolated and weighted FWS of the virtual sample set, the energy of target responses will focus in some profile of the IFFT result, the position of which is related with the separation between the transmitter and receiver. Finally, the desired target space can be extracted from the IFFT result. The improved Stolt migration technique is compared with the conventional Stolt migration algorithm, back-projection method, and Kirchhoff migration algorithm on synthetic data and validated by single-borehole radar experiment in the subsurface scenario. The results show that the developed Stolt migration is superior to the conventional methods in cross-range resolution, computational cost, and the ability to reconstruct locations and shapes of targets.

An efficient parallel algorithm: Poststack and prestack Kirchhoff 3D depth migration using flexi-depth iterations

This paper presents an efficient parallel 3D Kirchhoff depth migration algorithm suitable for current class of multicore architecture. The fundamental Kirchhoff depth migration algorithm exhibits inherent parallelism however, when it comes to 3D data migration, as the data size increases the resource requirement of the algorithm also increases. This challenges its practical implementation even on current generation high performance computing systems. Therefore a smart parallelization approach is essential to handle 3D data for migration. The most compute intensive part of Kirchhoff depth migration algorithm is the calculation of traveltime tables due to its resource requirements such as memory/storage and I/O. In the current research work, we target this area and develop a competent parallel algorithm for post and prestack 3D Kirchhoff depth migration, using hybrid MPI+OpenMP programming techniques. We introduce a concept of flexi-depth iterations while depth migrating data in parallel imaging space, using optimized traveltime table computations. This concept provides flexibility to the algorithm by migrating data in a number of depth iterations, which depends upon the available node memory and the size of data to be migrated during runtime. Furthermore, it minimizes the requirements of storage, I/O and inter-node communication, thus making it advantageous over the conventional parallelization approaches. The developed parallel algorithm is demonstrated and analysed on Yuva II, a PARAM series of supercomputers. Optimization, performance and scalability experiment results along with the migration outcome show the effectiveness of the parallel algorithm.

Application of pre-stack reverse time migration based on FWI velocity estimation to ground penetrating radar data

Abstract Reverse-time migration (RTM) is used for subsurface imaging to handle complex velocity models including steeply dipping interfaces and dramatic lateral variations and promises better imaging results compared to traditional migration method such as Kirchhoff migration algorithm. RTM has been increasingly used in seismic surveys for hydrocarbon resource explorations. Based on the similarity of kinematics and dynamics between electromagnetic wave and elastic wave, we develop pre-stack RTM method and apply it to process ground penetrating radar (GPR) data. Finite-difference time domain (FDTD) numerical method is used to simulate the electromagnetic wave propagation including forward and backward extrapolations, the cross-correlation imaging condition is used to obtain the final image. In order to provide a velocity model with relatively higher accuracy as the initial velocity model for RTM, we apply a full waveform inversion (FWI) in time domain to estimate the subsurface velocity structure based on reflection radar data. For testing the effectiveness of the algorithm, we have constructed a complex geological model, common-offset radar data and common-shot profile (CSP) radar reflection data are synthesized. All data are migrated with traditional Kirchhoff migration method and pre-stack RTM method separately, the migration results from pre-stack RTM show better coincidence with the true model. Furthermore, we have performed a physical experiment in a sandbox where a polyvinyl chloride (PVC) box is buried in the sand, the obtained common-offset radar data and common-shot radar data are migrated by using Kirchhoff migration method and pre-stack RTM algorithm separately, the pre-stack RTM result shows that RTM algorithm could get better imaging results.

P-Wave Reflection Imaging of Submerged Soil Models Using Ultrasound

An ultrasonic p -wave reflection imaging system is used to noninvasively image submerged soil models with embedded anomalies and complex geometric layer contacts. The ultrasonic transducers emit compressive waves into water that subsequently transmit into the underlying soil, and measurements of the reflections are used to construct the images. The properties of the transducers and data acquisition hardware and software are explained. Fast signal stacking is used to improve signal-to-noise ratio and provide clearer images. Transducer directivity is explained as a wave passage effect, and transfer functions are derived for square and circular transducers to quantify directivity. The transfer functions agree reasonably with measured amplitude data. The cause of errors in the imaged position of dipping reflectors is explained, and a Kirchhoff migration algorithm is implemented to correct these errors. A soil model consisting of embedded high- and low-impedance anomalies, dipping soil layer contacts, and an u...

Water velocity estimation using inversion methods

It is known that the propagation velocity of sound waves in water can vary over time. For a 3D seismic survey, if data are acquired in adjacent lines but at different dates, this implies the same reflection point will be recorded at different times. To take this effect into account in seismic processing, it is necessary to measure the sound velocity in water. I have developed a 3D tomographic method that directly estimates it. It assumes a constant sound velocity for a group of shots belonging to a single sail line. Using a picked water-bottom reflection and an initial depth and velocity model, results good for use in subsequent processing can be obtained by estimating only two parameters: the variation of the propagation velocity and a constant vertical shift of the reflector depth in relation to the initial model. The method was tested with both synthetic and real data. The real data results were validated using two methods. First, I analyzed the histogram of the residuals of the final updated model. Second, I used a specially modified Kirchhoff migration algorithm to migrate the sea bottom. The main advantages of this method are that it takes into account the sea-bottom dips to estimate the velocities and it can be applied to each sail line separately. Also, the inversion is not ill-conditioned provided that data with large enough offsets are used. As a result, the method is simple to apply.

Improving lateral and vertical resolution of seismic images by correcting for wavelet stretch in common-angle migration

Long-offset or high-incident-angle seismic reflections provide us with improved velocity resolution, better leverage against multiples, less contamination by ground roll, and information that is often critical when estimating lithology and fluid product. Unfortunately, high-incident-angle seismic reflections suffer not only from nonhyperbolic moveout but also from wavelet stretch during imaging, resulting in lower-resolution images that mix the response from adjacent lithologies. For an arbitrary acoustic medium, wavelet stretch from prestack migration depends only on the cosine of the reflection angle, such that the amount of wavelet stretch will be the same for all samples of a common-reflection-angle migrated trace. Thus, we are able to implement a wavelet stretch correction by applying a simple stationary spectral shaping operation to common-angle migrated traces. We obtain such traces directly by a prestack Kirchhoff migration algorithm. Correcting for stretch effectively increases the fold of imaged data, far beyond that achieved in conventional migration, resulting in improved signal-to-noise ratio of the final stacked section. Increasing the fidelity of large incident angles results in images with improved vertical and lateral resolution and with increased angular illumination, valuable for amplitude variation with angle (AVA) and amplitude variation with offset (AVO) analysis. Finally, such large-angle images are more sensitive to and therefore provide increased leverage over errors in velocity and velocity anisotropy. These ideas were applied to prestack time migration on seismic data from the Fort Worth basin, in Texas.

A visual based connection between seismic inversion and seismic migration

The Kirchhoff migration algorithm is heuristically derived using the mathematics of least squares inversion and the concept of matched filters. These concepts are visualized with cartoon descriptions that describe inversion using linear algebra and time-varying deconvolution. The time varying wavelets are then replaced with diffractions, to form a diffraction matrix that is used to model seismic data. The product of the transpose of this diffraction matrix with the seismic data produces a band-limited inversion that is identical to a Kirchhoff migration. Simple modification to the diffraction matrix illustrate the use of variable velocities and constant offset prestack migration.