Vertical Seismic Profile Data Set Research Articles

Assessing the value of combined use of distributed acoustic sensing (DAS) and multicomponent vertical seismic profiling (VSP) data with network-based full waveform inversion and uncertainty quantification: A case study in Alberta, Canada

Distributed acoustic sensing (DAS) technology, deployed in a vertical seismic profiling (VSP) experimental configuration, has emerged as a candidate for non-disruptive and low-cost seismic monitoring of CO2 geostorage and plume evolution. Full waveform inversion (FWI) has likewise received significant attention because it uses relatively complete physical models of wave propagation and because of its sample-by-sample incorporation of data information. Recent artificial neural network-based FWI algorithms (built with, for instance, recursive neural networks, or RNNs) have added to FWI a range of flexible and efficient tools for gradient computation and options for uncertainty assessment and initial model proxies. An important current research area for the use of DAS data is to better understand how they change our confidence levels in models selected through FWI. In particular, we seek to understand whether either DAS data or conventional geophone data alone are optimal for FWI model selection in the CO2 problem, and if not, to what degree they complement each other. The Snowflake 4D VSP dataset, which includes multi-offset and multi-azimuth broadband sources illuminating both fiberoptic cable and densely sampled accelerometer phones in the borehole, was acquired by our group to directly address these questions. In this study, we quantify uncertainty (UQ) by sampling the posterior model covariance matrix from the inverse Hessian matrix at the end of RNN-FWI runs on the Snowflake baseline data, invoking a velocity-density parameterization, and involving mixtures of accelerometer and DAS data. In this UQ context, the complementary effect of combining accelerometer and DAS data is evident in the Vp and Vs models. Our confidence in the approach is bolstered by its independent prediction of a region of known high uncertainty. In the overall pursuit of reliable and low-cost monitoring tools, this supports continued consideration of a multicomponent sensors supported by DAS approach.

Construction of pseudo-Hessian for vertical seismic profile full waveform inversion

The pseudo-Hessian matrix has been widely developed and applied to full waveform inversion to reduce the computational cost of obtaining the Hessian and its inverse matrix. Because the conventional pseudo-Hessian matrix assumes a surface seismic profiling geometry, this conventional method is compatible only with horizontally deployed sources and receiver geometries and cannot reflect the geometrical spreading effect of vertically deployed receivers. To enable the pseudo-Hessian to properly consider vertically deployed receiver locations and the geometrical spreading inherent in vertical seismic profiling data, we re-formulate part of the pseudo-Hessian matrix formulation. We verify our new scheme by directly calculating the Hessian matrices for a simple 1D model and conducting inversion tests with synthetic data sets. A comparison to the approximated Hessian matrix confirms that the vertical seismic profiling pseudo-Hessian provides better agreement with the approximated Hessian than the conventional pseudo-Hessian. In addition, we describe two numerical tests using multi-offset synthetic vertical seismic profiling data sets. When we apply the conventional pseudo-Hessian matrix to invert the synthetic data, we find that the inversion process cannot properly invert far offset data. However, we find that the pseudo-Hessian regarding vertical seismic profiling geometry allows the inversion process to invert far offset data and produces fewer artifacts than the conventional method. This study demonstrates that the vertical seismic profiling pseudo-Hessian matrix represents an alternative method that is necessary for the calculation of the pseudo-Hessian matrix for full waveform inversion with vertical seismic profiling using the Gauss–Newton method.

Time‐lapse VSP integration and calibration of subsurface stress field utilizing machine learning approaches: A case study of the morrow B formation, FWU

AbstractThis study aims to develop a methodology for calibrating subsurface stress changes through time‐lapse vertical seismic profiling (VSP) integration. The selected study site is a region around the injector well located within Farnsworth field unit (FWU), where there is an ongoing CO2‐enhanced oil recovery (EOR) operation. In our study, a site‐specific rock physics model was created from extensive geological, geophysical, and geomechanical characterization through 3D seismic data, well logs, and core assessed as part of the 1D MEM conducted on the characterization well within the study area. The Biot‐Gassmann workflow was utilized to combine the rock physics and reservoir simulation outputs to determine the seismic velocity change due to fluid substitution. Modeled seismic velocities attributed to mean effective stress were determined from the geomechanical simulation outputs, and the stress‐velocity relationship developed from ultrasonic seismic velocity measurements. A machine learning‐assisted workflow comprised of an artificial neural network and a particle swarm optimizer (PSO) was utilized to minimize a penalty function created between the modeled seismic velocities and the observed time‐lapse VSP dataset. The successful execution of this workflow has affirmed the suitability of acoustic time‐lapse measurements for 4D‐VSP geomechanical stress calibration pending measurable stress sensitivities within the anticipated effective stress changes and the availability of suitable and reliable datasets for petroelastic modeling. © 2023 Society of Chemical Industry and John Wiley & Sons, Ltd.

Fracture prediction based on walkaround 3D3C vertical seismic profiling data: A case study from the Tarim Basin in China

Natural fractures are well developed in the Sangtamu carbonate formation, which is the primary oil and gas production unit in the Tarim Basin, China. The analysis of converted waves via S-wave splitting (SWS) is an effective tool for predicting natural fractures in carbonate units. Compared with surface seismic data measurements, vertical seismic profiling (VSP) is more advantageous for acquiring and imaging converted waves. At present, there is a lack of robust methods on using 3D3C VSP data for fracture prediction. We propose an innovative workflow for predicting the spatial fracture distribution with the first ever application of SWS analysis to a 3D3C VSP data set. Instead of traditional Cartesian coordinates, we generate image bins based on a polar coordinate system to obtain accurate P-to-S converted waves of different azimuth angles. This is followed by a two-step SWS analysis. First, we conduct a multidirectional SWS analysis to estimate the fracture-induced anisotropy in the upper layers. Then, the wavefield of the target layer is corrected using time compensation and coordinate rotation. Finally, we apply SWS analysis again to obtain the azimuth and spatial intensity of the fractures in the target layer. We find that there is an overall good agreement in the fracture densities derived from the VSP waveforms and well-log data. The areas with high fracture development, as indicated by the SWS and ant-tracking analyses, also are consistent. Our study indicates that azimuth processing of walkaround 3D3C VSP combined with SWS analysis can serve as a quantitative diagnostic tool for fractures in a carbonate reservoir.

DAS-VSP interferometric imaging: CO2CRC Otway Project feasibility study

Recent advancements in distributed acoustic sensing (DAS) technology open new ways for borehole-based seismic monitoring of CO2 geosequestration. Compared to 4D surface seismic monitoring, repeated vertical seismic profiling (VSP) surveys with DAS receivers considerably reduce the cost and invasiveness of time-lapse CO2 monitoring. However, standard borehole imaging techniques cannot provide the same level of reservoir illumination as 3D surface seismic. The performance of VSP imaging can be significantly improved with interferometric utilization of free-surface multiples. We have developed a feasibility study of interferometric imaging with a synthetic walkaway VSP data set, followed by its application to field walkaway VSP data recorded by conventional borehole geophones and two types of DAS (standard and engineered fibers). Both experiments (synthetic and field) demonstrate that interferometric imaging is a viable method to extend the subsurface image beyond the coverage of standard VSP imaging. Specifically, the interferometry approach provides a more detailed upper section of the subsurface, whereas standard migration of primary reflections provides a more detailed bottom part of the image. Comparison of the standard and engineered fibers indicates that both fibers are sensitive to free-surface multiples, but the engineered fiber provides a much higher signal-to-noise ratio; thus, it is preferable for interferometric imaging with multiples. The result obtained with the engineered DAS cable indicates that in the depth range suitable for both methods, the VSP interferometric image of the reflectors is comparable to the surface seismic image. The experiment on the field DAS data proves that DAS is sensitive enough to record the nonprimary wavefield for imaging and monitoring of the subsurface.

Off-the-grid vertical seismic profile data regularization by a compressive sensing method

Different from the surface survey, the vertical seismic profile (VSP) survey deploys sources on the surface and geophones in a well. VSP provides higher resolution information of subsurface structures. The faults that cannot be imaged with surface seismic data may be detected with VSP data, and detailed analysis of fracture zones can be achieved with multicomponent VSP. However, one of the main problems is that the sources seldom are acquired on a regular grid in realistic VSP surveys. The irregular samplings cause serious artifacts in migration or imaging, such that data regularization must be implemented first. We have developed a compressive sensing (CS)-based method to regularize nonstationary VSP data. Our method directly operates on irregularly gridded data sets, which is a key contribution compared to the existing CS-based reconstruction methods that work on regular grids. The CS framework consists of a sparsity constraint and a penalty term. We have used the curvelet transform for sparsity constraint of nonstationary events in the regularization term and the nonequispaced Fourier transform to regularize the VSP data in a penalty term. An alternative directional method of multipliers is used for solving the optimization problem. Our method is tested on synthetic, field 2D and 3D VSP data sets. Our method obtains improved reconstructions on continuities of the events and produces fewer artifacts compared to the well-known antileaking Fourier transform method.

Imaging improvements from subsalt 3D VSP acquisitions in the Gulf of Mexico

From 2015 through 2018, BP acquired six large-scale 3D vertical seismic profile (VSP) data sets at their Gulf of Mexico assets, two at each of the Thunder Horse, Mad Dog, and Atlantis fields. The acquisition of these large-scale data sets was enabled by the development of a 100-level wireline tool and the adoption of simultaneous shooting. With those two developments, it became feasible to acquire data sets with the coverage and data density needed to build high-quality images of the subsurface using 3D VSP acquisitions. There have been recent advances in finite difference modeling to guide the survey design and the high-quality processing that is required to create the 3D VSP image volumes. These volumes have two main advantages over conventional surface seismic data. First, in 3D VSP acquisition, the receiver can be located below the overlying salt bodies, which allows for illumination of the reservoirs that cannot be achieved using surface seismic data. Second, the location of the receivers closer to the imaging targets enables higher frequency content of the resulting VSP data compared to conventional surface seismic images. Both imaging enhancements can have a significant business value, and the resulting VSP data sets have demonstrated a clear impact on business decisions. In the three case studies, we demonstrate the business impact of the 3D VSP data acquired through improvement of imaging of stratigraphic edges, improved interpretation of fault geometry and orientation, and related improvement of the quality of well planning and targeting. We conclude with discussion on cost, global impact, and present recommendations and lessons learned for future surveys.

Distributed acoustic sensing coupling noise removal based on sparse optimization

The industry treats the distributed acoustic sensing (DAS) system, which uses an optical fiber cable in vertical seismic profiling (VSP) data acquisition, as a new and fast-growing technology. The high-quality data set acquired from the DAS acquisition system can produce high-precision VSP images and obtain more detailed checkshots. However, in field data, the acquired VSP data set suffers from strong coherent DAS coupling noise. Many factors may cause coherent DAS coupling noise, such as the cable slapping and ringing due to the physical placement, the regular swing of the wireline in the well, and the uncoupling between the fiber cable and the casing. This DAS coupling noise reduces the signal-to-noise ratio and affects the subsequent processing and interpretation. Removing the DAS coupling noise can help to improve the quality of the VSP data set acquired with the DAS system. We have developed a sparse-optimization-based DAS coupling noise removing method. In the DAS-based VSP data set, the effective signal and the coupling noise have distinct morphological characteristics. The effective VSP signal has a wide bandwidth, whereas the DAS coupling noise appears in some narrow frequency bands in the frequency domain. The continuous wavelet transform and the discrete cosine transform can sparsely represent the effective VSP signal and DAS coupling noise, respectively. Therefore, we choose these two transforms as two sparse dictionaries and combine them to form an overcomplete dictionary. The morphological component analysis (MCA) can use the morphological difference between different components and the overcomplete dictionary to sparsely represent all components in the complicated signal. Based on the MCA theory, we use the block coordinate relaxation algorithm to separate the effective VSP signal and DAS coupling noise. Applications on a synthetic data set and two field data sets have validated the effectiveness of our method.

Potential of full waveform inversion of vertical hard rock environment seismic profile data in

Complex structure of the subsurface in hard rock environment often complicates traditional processing and interpretation of seismic datasets based on the analysis of reflected waves. Full-waveform inversion (FWI), in turn, utilizes the whole wavefield, including the transmitted waves and reflections, to build the models of physical properties (such as P wave velocity and density), which is one of its main advantages over traditional methods of seismic imaging. We conduct a feasibility study of 2D full-waveform inversion (FWI) applied to vertical seismic profile (VSP) synthetic data computed in a model that is based on a real hard-rock survey site for the purpose of identification of heterogeneities. Using this complex model of the subsurface that contains steep interfaces, high seismic wave velocities and densities, we generate a synthetic VSP dataset with a finite-difference code. Multi-offset VSP geometry is considered due to the abundance of transmitted waves. We then apply FWI to this dataset. We use finite-difference modelling for the forward problem in FWI, optimization is conducted using the limited-memory BFGS method. FWI is applied in a multiscale manner, from 10 Hz to 190 Hz. Inversion results suggest that FWI of VSP data is a suitable tool for building the models of physical properties of the subsurface that are crucial for mineral exploration and mine planning.

Application of time-lapse full waveform inversion of vertical seismic profile data for the identification of changes introduced by CO2 sequestration

Seismic methods are frequently used for the purpose of monitoring of time-lapse changes introduced by CO2 sequestration. Surface seismic is often considered as the main tool for monitoring. Vertical Seismic Profile (VSP) is occasionally applied as an auxiliary method. Standard VSP data processing workflow does not provide a quantitative estimate of the time-lapse changes in the physical properties. However, full waveform inversion (FWI) may be used for the purpose of quantitative interpretation. Its ability to employ the whole seismic wavefield (including transmitted, reflected and converted waves) for the purpose of building the models of physical properties can be considered one of its main advantages.We show that time-lapse elastic FWI of VSP data is capable of providing quantitative estimates of time-lapse changes in the medium. A feasibility study is carried out on 2D and 3D synthetic datasets created using full-earth models of the CO2CRC Otway CO2 sequestration site. The inversion workflow obtained from the feasibility study is successfully applied to a field single-offset time-lapse VSP dataset. As a result, FWI provides an image of the time-lapse changes introduced by the injection of supercritical CO2.

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.

An Iterative Zero-Offset VSP Wavefield Separating Method Based on the Error Analysis of SVD Filtering

Wavefield separation is one critical step in the vertical seismic profiling (VSP) data processing. In this letter, we present an iterative zero-offset VSP wavefield separating method based on analyzing the error of the singular value decomposition (SVD) low-pass filtering. The error of the SVD low-pass filtering can be divided into the incomplete error and the truncated error. The incomplete error is caused by the incompleteness of subspace, while the truncated error is related to discarding small singular values and corresponding eigenimages. Flattening the strongly correlated component in the 2-D signal can reduce these two errors, and the flattened component can be extracted precisely with the SVD low-pass filtering. The zero-offset VSP data set in seismic data processing records downgoing and upgoing wavefields, which have different propagating directions. By flattening the downgoing and upgoing wavefields alternatively, we propose one iterative zero-offset VSP wavefield separating method. In each iteration, we first flatten the downgoing wavefield to increase its correlation and estimate the downgoing wavefield by using the SVD low-pass filtering, and then, we flatten the upgoing wavefield in the residual to increase its correlation and estimate the upgoing wavefield by using the SVD low-pass filtering. The proposed method is applied to one synthetic data set and one real zero-offset VSP data set. Compared with the commonly used wavefield separation method, our method can have better separation results and reduce the separation error.

Compressional- and shear-wave studies of distributed acoustic sensing acquired vertical seismic profile data

Understanding the strengths and limitations of rapidly advancing distributed acoustic sensing (DAS) technology used for recording vertical seismic profile (VSP) data is achieved by comparing DAS and geophone data sets using both compressional-wave (P-wave) and shear-wave (S-wave) VSP data and their corresponding geophysical answer products. We validate the kinematics (time) and dynamics (amplitude) of DAS VSP data by examining the extracted slowness values, response-to-incident angles, corridor stacks, and common-depth-point (CDP) transforms. For kinematics validation, the slowness values computed from P- and S-wave components of DAS VSP data agree with the geophone slowness values. For dynamics validation, we confirm the cos2 θ response of the fiber to the incident angle of the seismic wavefield for P-waves and sin 2θ for S-waves. The amplitudes of the P-wave corridor stacks are comparable; the S-wave corridor stacks are similar for shallow events and differ for later events due to the limited response of the fiber to S-waves at near-vertical angles of incidence. High-quality CDP transform images are obtained for P- and S-waves. These analyses indicate that properly acquired DAS VSP data sets are reliable for the kinetics and dynamics of both P- and S-waves. Once the fiber-optic cable is installed in the well, VSP acquisition costs are greatly reduced because DAS data may be acquired with no additional well intervention. The extensive spatial coverage obtained using fiber-optic cables, the ease of acquiring time-lapse (4D) VSP data, and the reliability of the resulting DAS VSP data sets are making DAS technology an extremely important VSP acquisition tool.

VSP wavefield separation using the gray-scale Hough transform: synthetic data

The principal objective in Vertical Seismic Profile (VSP) processing is the separation of the downgoing and upgoing wavefields. Several methods have been suggested in this area. This paper presents a new approach based on the gray-scale Hough transform (GSHT) which is an extension of the conventional Hough transform used to detect straight lines and other curves. The technique, we suggest here, directly maps the gray-scale VSP image, including the downgoing and upgoing linear events, in image coordinate space (x,t,g) to the gray Hough parameter counting space (θ,ρ,g), where θ and ρ are the polar parameters and g is the gray-scale value. In this new space, the downgoing events appear in the negative angles θ quadrant and the upgoing in the positive quadrant, owning to their opposite apparent velocities. The inverse GSHT algorithm, we developed in this study, is performed for extracting separately these two wavefields by considering the straight lines that satisfy the corresponding filtering conditions. The experimental results on synthetic VSP datasets are convincing. The wave separation is well performed, even in the presence of loud noise levels, with signal to noise ratio improvement and amplitude preservation, in contrast to median filtering.

Walkaway VSP using multimode optical fibers in a hybrid wireline

Distributed acoustic sensing (DAS) is a novel technology that uses an optical fiber cable as a sensor for acoustic signals and can take almost any downhole fiber-optic installation or deployment and turn the fiber-optic cable into a large downhole seismic array. This array can provide enhanced vertical seismic profile (VSP) imaging and monitor fluids and pressure changes in the hydrocarbon-production reservoir. Walkaway VSP data acquired over a formerly producing well in northeastern China provided a rich set of high-quality DAS walkaway VSP data. A standard VSP data preprocessing workflow was applied, followed by prestack Kirchhoff time migration. In the DAS preprocessing step, we were faced with additional challenges: strong coherent noise due to cable slapping and ringing along the borehole casing. Compared with an earlier offset VSP data set using 327 levels acquired with conventional 3C downhole geophones in the same well, the final preprocessed DAS walkaway VSP has a larger vertical aperture, resulting in a wider lateral image. The single-well DAS walkaway VSP images provide a good result with higher vertical and lateral resolution than the surface seismic in the objective area. The vertical-well environment, which lacks the ability to effectively “clamp” the sensor to the borehole-casing wall by touching, creates a unique set of challenges. Although earth signal was recorded with almost all the shots, there was also a considerable amount of noise. Much of the noise was due to the physical placement of the wireline in the well and was expressed by slapping and ringing. Reported here are lessons learned in handling the wireline cable and subsequent special DAS data processing steps developed to remediate some of the practical wireline deployment issues. Optical wireline cable as a conveyance of fiber-optic cables for VSP in vertical wells will open the use of the DAS system to wider applications.

Case History: Using time‐lapse vertical seismic profiling data to constrain velocity–saturation relations: the Frio brine pilot CO2 injection

ABSTRACTCO2 sequestration projects benefit from quantitative assessment of saturation distribution and plume extent for field development and leakage prevention. In this work, we carry out quantitative analysis of time‐lapse seismic by using rock physics and seismic modelling tools. We investigate the suitability of Gassmann's equation for a CO2 sequestration project with 1600 tons of CO2 injected into high‐porosity, brine‐saturated sandstone. We analyze the observed time delays and amplitude changes in a time‐lapse vertical seismic profile dataset. Both reflected and transmitted waves are analyzed qualitatively and quantitatively. To interpret the changes obtained from the vertical seismic profile, we perform a 2.5D elastic, finite‐difference modelling study. The results show a P‐wave velocity reduction of 750 m/s in the proximity of the injection well evident by the first arrivals (travel‐time delays and amplitude change) and reflected wave amplitude changes. These results do not match with our rock physics model using Gassmann's equation predictions even when taking uncertainty in CO2 saturation and grain properties into account. We find that time‐lapse vertical seismic profile data integrated with other information (e.g., core and well log) can be used to constrain the velocity–saturation relation and verify the applicability of theoretical models such as Gassmann's equation with considerable certainty. The study shows that possible nonelastic factors are in play after CO2 injection (e.g., CO2–brine–rock interaction and pressure effect) as Gassmann's equation underestimated the velocity reduction in comparison with field data for all three sets of time‐lapse vertical seismic profile attributes. Our work shows the importance of data integration to validate the applicability of theoretical models such as Gassmann's equation for quantitative analysis of time‐lapse seismic data.

SV-P and S-S imaging at a CO2 storage site using vertical seismic profiling data

Only compressional (P) waves are typically used to illuminate the geology of land-based carbon dioxide (CO2) storage sites because the costs associated with horizontal-force vibrators needed to emit shear (S) waves deters the use of that mode. However, S-waves are highly sensitive to fractures and provide clues to the porosity and permeability of the reservoir and seal. Shear wave energy may also be produced by vertical-force vibrators, and the resulting up-going direct-S waves may be recorded either as reflected S-S modes or as converted SV-P modes. These two data components can contribute information not available in P-wave components. In particular, the SV-P mode makes converted-wave analysis possible when working with seismic data generated by vertical vibrators and recorded with only vertical geophones.In this paper, we present a method for extracting S-waves emitted by vertical-force vibrators. This is a low-cost opportunity for full seismic wavefield analysis that enhances understanding of geologic reservoirs. We illustrate S-wave seismic imaging with a vertical seismic profiling dataset acquired at a CO2 storage site in Decatur, Illinois. We discuss a data processing flow that segregates direct-S modes. We compare SV-P and S-S images generated by a vertical vibrator source with P-P, P-SV, and P-SH images – the typical images made with vertical-vibrator sources. All images appear consistent and complement each other, indicating the method presented here allows the use of S-waves in CO2 storage site screening without requiring horizontal geophones.

Reverse time migration of 3D vertical seismic profile data

Reverse time migration (RTM) has shown increasing advantages in handling seismic images of complex subsurface media, but it has not been used widely in 3D seismic data due to the large storage and computation requirements. Our prime objective was to develop an RTM strategy that was applicable to 3D vertical seismic profiling (VSP) data. The strategy consists of two aspects: storage saving and calculation acceleration. First, we determined the use of the random boundary condition (RBC) to save the storage in wavefield simulation. An absorbing boundary such as the perfect matching layer boundary is often used in RTM, but it has a high memory demand for storing the source wavefield. RBC is a nonabsorbing boundary and only stores the source wavefield at the two maximum time steps, then repropagates the source wavefield backwards at every time step, and hence, it significantly reduces the memory requirement. Second, we examined the use of the graphic processing unit (GPU) parallelization technique to accelerate the computation. RBC needs to simulate the source wavefield twice and doubles the computation. Thus, it is very necessary to realize the RTM algorithm by GPU, especially for a 3D VSP data set. GPU and central processing unit (CPU) collaborated parallel implementation can greatly reduce the computation time, where the CPU performs serial code, and the GPU performs parallel code. Because RBC does not need the same huge amount of storage as an absorbing boundary, RTM becomes practically applicable for 3D VSP imaging.

Velocity analysis with vertical seismic profile data using migration of surface-related multiples

We have developed an original method for migration velocity analysis for vertical seismic profile (VSP) data. The method is based on VSP imaging with the primary reflected data and surface-related multiples. Velocity updates are carried out by matching the images obtained by these two types of waves. To do it automatically, we have introduced an objective function of the crosscorrelation type and developed a gradient-based maximization algorithm. On synthetic walk-away VSP data sets, we found that maximization of the crosscorrelation of the images provided by the two different types of waves allowed the retrieval of the interval velocities below the borehole receivers — a problem that was considered to be challenging with a VSP acquisition. Also, the possibility of the lateral velocity gradient reconstruction was developed on a simple synthetic model. On the real walk-away VSP data set from the North Sea, we found that the method could also be used for estimation of effective anisotropy parameters below the borehole receivers. In all of our examples, the velocity model refinement based on the presented method led to significant improvements of the seismic images.

Vertical seismic profile waveform inversion

Waveform inversion of vertical seismic profile (VSP) data is studied in this paper. In this study, finite-difference acoustic wave modelling in the frequency-domain is used for seismic forward modelling and a classical iterative Gauss-Newton algorithm is used for inversion. The inversion algorithm in the frequency-domain allows a multiscale approach in which individual frequency components from low to high are inverted. This reduces nonlinearity of the inverse problem and decreases the computational costs by converging to a favourable solution via a limited number of frequency components. Here, the algorithm is applied to synthetic and real VSP datasets. The synthetic model includes both smooth and sharp features. It is observed that although satisfactory results can be obtained without including the higher-frequency components, these are essential in preserving the edges of the sharp discontinuities in the velocity model. Seismic preconditioning was applied to the real VSP dataset prior to inversion to mitigate the effects of noise and unwanted wave modes. By comparing the results of inversion with the sonic log data, it is shown that waveform inversion is capable of capturing the small scale variations in the velocity model, whereas traveltime inversion fails to capture the true range of velocity variations.