Inaccurate Velocity Model Research Articles

Improving the least-squares image by using angle information to avoid cycle skipping

In the past few decades, the least-squares reverse time migration (LSRTM) algorithm has been widely used to enhance images of complex subsurface structures by minimizing the data misfit function between the predicted and observed seismic data. However, this algorithm is sensitive to the accuracy of the migration velocity model, which, in the case of real data applications (generally obtained via tomography), always deviates from the true velocity model. Therefore, conventional LSRTM faces a cycle-skipping problem caused by a smeared image when using an inaccurate migration velocity model. To address the cycle-skipping problem, we have introduced an angle-domain LSRTM algorithm. Unlike the conventional LSRTM algorithm, our method updates the common source-propagation angle image gathers rather than the stacked image. An extended Born modeling operator in the common source-propagation angle domain is was derived, which reproduced kinematically accurate data in the presence of velocity errors. Our method can provide more focused images with high resolution as well as angle-domain common-image gathers (ADCIGs) with enhanced resolution and balanced amplitudes. However, because the velocity model is not updated, the provided image can have errors in depth. Synthetic and field examples are used to verify that our method can robustly improve the quality of the ADCIGs and the finally stacked images with affordable computational costs in the presence of velocity errors.

The adaptive particle swarm optimization technique for solving microseismic source location parameters

Abstract. An intelligent method is presented for locating a microseismic source based on the particle swarm optimization (PSO) concept. It eliminates microseismic source locating errors caused by the inaccurate velocity model of the earth medium. The method uses, as the target of PSO, a global minimum of the sum of squared discrepancies between differences of modeled arrival times and differences of measured arrival times. The discrepancies are calculated for all pairs of detectors of a seismic monitoring system. Then, the adaptive PSO algorithm is applied to locate the microseismic source and obtain optimal value of the P-wave velocity. The PSO algorithm adjusts inertia weight, accelerating constants, the maximum flight velocity of particles, and other parameters to avoid the PSO algorithm trapping by local optima during the solution process. The origin time of the microseismic event is estimated by minimizing the sum of squared discrepancies between the modeled arrival times and the measured arrival times. This sum is calculated using the obtained estimates of the microseismic source coordinates and P-wave velocity. The effectiveness of the PSO algorithm was verified through inversion of a theoretical model and two analyses of actual data from mine blasts in different locations. Compared with the classic least squares method (LSM), the PSO algorithm displays faster convergence and higher accuracy of microseismic source location. Moreover, there is no need to measure the microseismic wave velocity in advance: the PSO algorithm eliminates the adverse effects caused by error in the P-wave velocity when locating a microseismic source using traditional methods.

Reflection-Waveform Inversion Regularized with Structure-Oriented Smoothing Shaping

Restricted by the limited length of the receiver arrays, estimating the seismic properties of deep targets requires inverting reflection data. Reflection-waveform inversion (RWI) utilizes reflection data to recover the background velocity. RWI splits the Earth model into a long-wavelength background velocity and short-wavelength reflectors. Because of the limited apertures of reflection data illuminating targets, and the trade-off between the depth of reflectors and the average velocity above the reflectors, RWI is inherently ill-posed and contains a large null space. One manifestation of the ill-posedness is the existence of characteristic artificial blob-shaped or column-like anomalies in the velocity models estimated with RWI. That erroneous background velocity, which still fits the travel time of reflection arrivals in the recorded data, can lead to inaccurate velocity models and distorted migration images in the subsequent processes. In order to mitigate those artifacts and improve the conditioning of RWI, we incorporate a piece of prior information into RWI, i.e. slow property variation along geological structures. This prior information is expressed mathematically as structure-oriented smoothing. We achieved this smoothing by solving an anisotropic diffusion equation with a finite-difference method. Thus, we formulated a method for RWI regularized with structure-oriented smoothing shaping by alternating the following three steps: building temporary reflectors, updating background velocity, and solving the diffusion equation. We successfully tested this scheme on the Marmousi model and a modified overthrust model. The results show that the regularized RWI yields a stable and accurate background velocity, and it is more effective than conventional Tikhonov regularization approaches. The estimated background model leads to a high-quality final velocity model when used as an initial model in conventional full-waveform inversion.

Pre-stack elastic parameter inversion of ray parameters

P is a ray parameter. Seismic wave path of P gather spreads nearly along the ray path. Compared with angle gather, P gather can be obtained directly from seismic data and is independent of overlying strata velocity, which avoids the inversion error caused by inaccurate velocity models. Based on P stacked gather, ray elastic impedance of different P values and pre-stack elastic parameters have been computed using Bayesian sparse pulse inversion and constrained search method, respectively. The method has been applied to reservoir prediction of the Yuanba area in the north of Sichuan depression. Exploration results indicated that P stacked data can better delineate the geological body compared with angle stacked data. In addition, stable solutions are easier to be obtained by Bayesian sparse pulse inversion and constrained search method. The pre-stack elastic parameters of P gather showed higher precision and more authenticity than that of angle gather. This methodology has achieved excellent results in reservoir prediction of the Yuanba area and has huge potential for future application in exploration and development.

Inversion for Focal Mechanisms Using Waveform Envelopes and Inaccurate Velocity Models: Examples from Brazil

Inversion for Focal Mechanisms Using Waveform Envelopes and Inaccurate Velocity Models: Examples from Brazil

Volume source-based extended waveform inversion

Full-waveform inversion (FWI) faces the persistent challenge of cycle skipping, which can result in stagnation of the iterative methods at uninformative models with poor data fit. Extended reformulations of FWI avoid cycle skipping through adding auxiliary parameters to the model so that a good data fit can be maintained throughout the inversion process. The volume-based matched source waveform inversion algorithm introduces source parameters by relaxing the location constraint of source energy: It is permitted to spread in space, while being strictly localized at time [Formula: see text]. The extent of source energy spread is penalized by weighting the source energy with distance from the survey source location. For transmission data geometry (crosswell, diving wave, etc.) and transparent (nonreflecting) acoustic models, this penalty function is stable with respect to the data-frequency content, unlike the standard FWI objective. We conjecture that the penalty function is actually convex over much larger region in model space than is the FWI objective. Several synthetic examples support this conjecture and suggest that the theoretical limitation to pure transmission is not necessary: The inversion method can converge to a solution of the inverse problem in the absence of low-frequency data from an inaccurate initial velocity model even when reflections and refractions are present in the data along with transmitted energy.

Automated seismic waveform location using multichannel coherency migration (MCM)–I: theory

With the proliferation of dense seismic networks sampling the full seismic wavefield, recorded seismic data volumes are getting bigger and automated analysis tools to locate seismic events are essential. Here, we propose a novel Multichannel Coherency Migration (MCM) method to locate earthquakes in continuous seismic data and reveal the location and origin time of seismic events directly from recorded waveforms. By continuously calculating the coherency between waveforms from different receiver pairs, MCM greatly expands the available information which can be used for event location. MCM does not require phase picking or phase identification, which allows fully automated waveform analysis. By migrating the coherency between waveforms, MCM leads to improved source energy focusing. We have tested and compared MCM to other migration-based methods in noise-free and noisy synthetic data. The tests and analysis show that MCM is noise resistant and can achieve more accurate results compared with other migration-based methods. MCM is able to suppress strong interference from other seismic sources occurring at a similar time and location. It can be used with arbitrary 3D velocity models and is able to obtain reasonable location results with smooth but inaccurate velocity models. MCM exhibits excellent location performance and can be easily parallelized giving it large potential to be developed as a real-time location method for very large datasets.

Waveform-based source location method using a source parameter isolation strategy

We have developed a novel acoustic-wave-equation-based full-waveform source location method to locate microseismic events. With the acoustic-wave equation and source signature independent inversion strategy, source location parameters (hypocenter locations) can be isolated from others and can then be retrieved independently and accurately, even when the origin time and source signature are not correct. Based on the acoustic-wave equation, new Fréchet derivatives of seismic waveforms with respect to the location parameters are derived to better accelerate the inversion process. To ease the cycle-skipping problem, a correlation is applied to select the best starting source positions. Some 2D and 3D numerical examples are presented to demonstrate the validity of our method. Compared with the waveform-based grid-search method, our method is effective in isolating the hypocenter locations from the source signature and origin time. The computational cost is nearly negligible compared with the waveform-based grid-search method. The robustness of our method is also tested for cases with inaccurate velocity models or using microseismic data with a signal-to-noise ratio of ≥[Formula: see text]. Finally, field data are used to indicate the practical applicability of our method.

Moment Tensor Inversion Based on the Principal Component Analysis of Waveforms: Method and Application to Microearthquakes in West Bohemia, Czech Republic

ABSTRACT We develop and test a new hybrid approach of the amplitude and waveform moment tensor inversions, which utilizes the principal component analysis of seismograms. The proposed inversion is less sensitive to noise in data, being thus more accurate and more robust than the amplitude inversion. It also suppresses other unmodeled phenomena, like a directivity of the source, errors caused by local site effects at individual stations, and by time shifts in arrivals of observed and synthetic signals due to an inaccurate velocity model. This inversion is computationally less demanding than the full waveform inversion and thus applicable to large sets of earthquakes. The approach is numerically tested on synthetic data with various levels of noise. The applicability of the inversion is demonstrated on inverting more than 800 microearthquakes that occurred during the 2014 activity in West Bohemia, Czech Republic. The analysis revealed several distinct clusters of moment tensors. Focal mechanisms corresponding to moment tensors of three clusters are left‐lateral strike slips associated with the most active fault in the focal zone. Another cluster is characterized by right‐lateral strike slips associated with the fault conjugate to the main fault. Finally, we identified a cluster with pure reverse focal mechanisms that are anomalous and not expected to occur in the region. These mechanisms were not detected in previous seismic activity, and they have an unfavorable orientation with respect to regional tectonic stress. This might indicate a presence of local stress heterogeneities caused, for example, by an interaction of faults or fault segments in the focal zone.

Diffraction imaging method by Mahalanobis-based amplitude damping

Clarifying and locating small-scale discontinuities or inhomogeneities in the subsurface, such as faults and collapsed columns, plays a vital role in safe coal mining because these discontinuities or inhomogeneities may destroy the continuity of layers and result in dangerous mining accidents. Diffractions carry key information from these objects and therefore can be used for high-resolution imaging. However, diffracted/scattered waves are much weaker than reflected waves and consequently require separation before being imaged. We have developed a Mahalanobis-based diffraction imaging method by modifying the classic Kirchhoff formula with an exponential function to account for the dynamic differences between reflections and diffractions in the shot domain. The imaging method can automatically account for destroying of reflected waves, constructive stacking of diffracted waves, and strengthening of scattered waves. The method can overcome the difficulties in handling Fresnel apertures, and it is suitable for high-resolution imaging because of the consistency of the waveforms in the shot domain. Although the proposed method in principle requires a good migration velocity model for calculating elementary diffraction traveltimes, it is robust to an inaccurate migration velocity model. Two numerical experiments demonstrate the feasibility of the proposed method in removing reflections and highlighting diffractions, and one field application further confirms its efficiency in resolving masked faults and collapsed columns.

Automated microseismic event location using Master-Event Waveform Stacking.

Accurate and automated locations of microseismic events are desirable for many seismological and industrial applications. The analysis of microseismicity is particularly challenging because of weak seismic signals with low signal-to-noise ratio. Traditional location approaches rely on automated picking, based on individual seismograms, and make no use of the coherency information between signals at different stations. This strong limitation has been overcome by full-waveform location methods, which exploit the coherency of waveforms at different stations and improve the location robustness even in presence of noise. However, the performance of these methods strongly depend on the accuracy of the adopted velocity model, which is often quite rough; inaccurate models result in large location errors. We present an improved waveform stacking location method based on source-specific station corrections. Our method inherits the advantages of full-waveform location methods while strongly mitigating the dependency on the accuracy of the velocity model. With this approach the influence of an inaccurate velocity model on the results is restricted to the estimation of travel times solely within the seismogenic volume, but not for the entire source-receiver path. We finally successfully applied our new method to a realistic synthetic dataset as well as real data.

부정확한 속도 모델을 가정한 진원 결정 방법의 성능평가: 지표면 미소지진 모니터링 사례

The hypocenter distribution of microseismic events generated by hydraulic fracturing for shale gas development provides essential information for understanding characteristics of fracture network. In this study, we evaluate how inaccurate velocity models influence the inversion results of two widely used location programs, hypoellipse and hypoDD, which are developed based on an iterative linear inversion. We assume that 98 stations are densely located inside the circle with a radius of 4 km and 5 artificial hypocenter sets (S0 ~ S4) are located from the center of the network to the south with 1 km interval. Each hypocenter set contains 25 events placed on the plane. To quantify accuracies of the inversion results, we defined 6 parameters: difference between average hypocenters of assumed and inverted locations, ; ratio of assumed and inverted areas estimated by hypocenters, r; difference between dip of the reference plane and the best fitting plane for determined hypocenters, ; difference between strike of the reference plane and the best fitting plane for determined hypocenters, ; root-mean-square distance between hypocenters and the best fitting plane, ; root-mean-square error in horizontal direction on the best fitting plane, . Synthetic travel times are calculated for the reference model having 1D layered structure and the inaccurate velocity model for the inversion is constructed by using normal distribution with standard deviations of 0.1, 0.2, and 0.3 km/s, respectively, with respect to the reference model. The parameters , r, , and show positive correlation with the level of velocity perturbations, but the others are not sensitive to the perturbations except S4, which is located at the outer boundary of the network. In cases of S0, S1, S2, and S3, hypoellipse and hypoDD provide similar results for . However, for other parameters, hypoDD shows much better results and errors of locations can be reduced by about several meters regardless of the level of perturbations. In light of the purpose to understand the characteristics of hydraulic fracturing, error of velocity structure should be under 0.2 km/s in hypoellipse and 0.3 km/s in hypoDD.

Seismic prism waves generated by seafloor canyons and their effects on subsurface imaging

SUMMARY Complex seafloor bathymetry can create significant challenges for subsurface imaging and geologic interpretation of seismic exploration and monitoring data. Steep seafloor canyons that cut through continental shelf areas can produce very strong seismic wavefield distortions. Neglecting such wavefield complexity can result in inaccurate velocity models, significant imaging errors, misleading amplitudes and uncertain geologic interpretations. In this paper we investigate the kinematic and dynamic effects of seismic “prism waves” generated by seafloor canyons. Prism waves are waves that undergo multiple primary reflections at scattering interfaces before propagating to the recording sensor array. We demonstrate that strong prism waves can be generated for realistic seafloor canyon geometries, and show how their adverse effects can contaminate the seismic imaging process.

Prism waves in seafloor canyons and their effects on seismic imaging

Complex seafloor bathymetry can create significant challenges for subsurface imaging and geologic interpretation of seismic exploration and monitoring data. Steep seafloor canyons that cut through continental shelf areas can produce very strong seismic wavefield distortions. Neglecting such wavefield complexity can result in inaccurate velocity models, significant imaging errors, misleading amplitudes, and erroneous geologic interpretations. We have evaluated the kinematic and dynamic effects of seismic prism waves generated by seafloor canyons. Prism waves are seismic waves that undergo consecutive reflections at a scattering interface before propagating to the recording sensor array. We have demonstrated that strong prism waves can be generated for realistic seafloor canyon geometries, and we determined how their adverse effects can contaminate seismic imaging and velocity estimation.

Kirchhoff prestack depth migration in 3-D simple models: comparison of triclinic anisotropy with simpler anisotropies

We use Kirchhoff prestack depth migration to calculate migrated sections in 3-D simple anisotropic homogeneous velocity models in order to demonstrate the impact of anisotropy on migrated images. The recorded wave field is generated in models composed of two homogeneous layers separated by one either non-inclined or inclined curved interface. The anisotropy in the upper layer is triclinic. We apply Kirchhoff prestack depth migration to velocity models with different types of anisotropy: a triclinic anisotropic medium, an isotropic medium, transversely isotropic media with a horizontal (HTI) and vertical (VTI) symmetry axis. We observe asymmetry in migration caused by triclinic anisotropy and we show the errors of the migrated interface caused by inaccurate velocity models used for migration. The study is limited to P-waves.

Local vertical seismic profiling (VSP) elastic reverse-time migration and migration resolution: Salt-flank imaging with transmitted P-to-S waves

To avoid the defocusing effects of propagating waves through salt and overburden with an inaccurate overburden velocity model, we introduce a vertical seismic profiling (VSP) local elastic reverse-time-migration (RTM) method for salt-flank imaging by transmitted P-to-S waves. This method back-projects the transmitted PS waves using a local velocity model around the well until they are in phase with the back-projected PP waves at the salt boundaries. The merits of this method are that it does not require the complex overburden and salt-body velocities and it automatically accounts for source-side statics. In addition, the method accounts for kinematic and dynamic effects, including anisotropy, absorption, and all other unknown rock effects outside of this lo-cal subsalt velocity model. Numerical tests on an elastic salt model and offset 2D VSP data in the Gulf of Mexico, using a finite-difference time-domain staggered-grid RTM scheme, partly demonstrate the effectiveness of this method over interferometry PS-PP transmission migration and local acoustic RTM. Our method separates elastic wavefields to vector P- and S-wave velocity components at the trial image point and achieves better resolution than local acoustic RTM and interferometric transmission migration. The analytical formulas of migration resolution for local acoustic and elastic RTM show that the migration illumination is limited by data frequency and receiver aperture, and the spatial resolution is lower than standard poststack and prestack migration. This new method can image salt flanks as well as subsalt reflectors.

Performance of the Radial Semblance Method for the Location of Very Long Period Volcanic Signals

We investigate the performance of a source location method that com- bines multichannel semblance and particle motions and is being increasingly used to obtain estimates of the source locations of very long period (VLP) seismic signals recorded on volcanoes. The method makes use of the radial particle motions and large wavelengths that characterize the VLP events. To assess the capabilities of this radial semblance method, and to better understand its limitations, we quantify the effects of window length, noise contents of the signal, inaccurate velocity models, receiver coverage, and orientation errors in the horizontal components of the receiv- ers. Our results show that the semblance method performs best when (1) the noise level is low enough to allow a good characterization of the waveforms, (2) the sources are located at distances between one half of the average receiver spacing and about two times the network aperture, and (3) the orientations of the horizontal components of the seismometers are known with relative accuracy. When these requirements are met, the radial semblance method constitutes an adequate tool to obtain preliminary locations of VLP volcanic signals recorded by broadband networks. Moreover, we provide a formula to determine the radial semblance level that should be used to define error regions associated to the estimated source locations.

Pitfalls in seismic interpretation: Depth migration artifacts

Editor's note: This series is designed to update the classic Pitfalls in Seismic Interpretation by Tucker and Yorstan, first published by SEG in 1973. Contact Steve Henry (geolearn@aol.com) for information about contributing to this series. Interpretation of depth‐migrated data has become increasingly common owing to advances in both post‐ and prestack depth processing. It is well known that depth processing can provide better imaging of complex subsurface geology than conventional time processing, depending largely on the accuracy of the depth‐migration velocity model. This paper briefly describes an example of an artifact in a prestack depth‐migrated image caused by an inaccurate velocity model. Depth migration moves reflections to their correct subsurface positions based on traveltimes calculated from the migration velocity model. In comparison to time migration, which provides accurate images in areas where velocity is predominantly a function of depth and does not have large lateral variations, a depth migration velocity model contains …

Pre-stack depth migration of seismic multiples

Seismic multiples still present a major impediment to exploration on the North West Shelf of Western Australia. Considerable effort is being expended on the removal of multiple events from the seismic record to improve the quality of the image of the subsurface, hence reducing the risk of drilling dry holes. Most of the published multiple attenuation techniques to date are based on the premise that multiples are noise and hence need to be removed. The technique presented in this paper is based on the assumption that multiples are signal, and that image quality will be enhanced by assigning their energies to the appropriate place in the final migrated section. A new procedure has been developed for the pre-stack depth migration (PSDM) of seismic multiples which correctly images both primary and multiple energy to give a depth section without visible multiples. The three key processes in the PSDM process are the determination of a suitable velocity model, a method for the computation of travel-times, and a method of mapping seismic shot record data to the final output depth section. The velocity model in the new procedure can include horizontal, dipping planar, and irregular boundaries. Travel-time mapping is achieved by implementing Huygen’s principle (Podvin and Lecomte, 1991) while also incorporating the curved wavefront approach of Schneider et al. (1992). By extending the work of Zhao (1996), reflections are modelled using the generalised exploding reflector model (Lambert, 1996) which was used by Manuel (1998) for modelling multiple reflections. This technique is capable of handling large velocity contrasts in structures with irregular boundaries. Zhao et al. (1998) showed how to map first and later arrivals arising from different travel paths in the subsurface. This new procedure treats primary and multiple events as first and later arrivals respectively, and maps them to the final depth section. Examples based on synthetically modelled data show that significant multiple content can be removed by using this new migration technique. The velocity models used for these examples are reasonably complex which enables the new technique to be tested quite rigorously. In most, if not all, depth migration procedures the resultant image quality is dependent on an accurate velocity model. A slightly inaccurate velocity model was used with the new procedure which still resulted in a reasonably accurate depth migrated section.

I.S.C. mislocation of earthquakes in Iran and geometrical residuals

P-wave arrival-time data from earthquakes in the Zagros Fold Belt area of western Iran, recorded at as many as 20 local stations temporarily in operation during September 1976, are used to find errors in epicentre locations issued by the International Seismological Centre (ISC). Assuming that Zagros earthquakes are generally confined to the crust (Jackson and Fitch 1981), it was possible to obtain accurate epicentres for these earthquakes, and to conclude that they are mislocated towards the northeast by the ISC and that the ISC P n velocity is inappropriate for Zagros. It is shown that when inaccurate velocity models are used in earthquake locations, the geometry of the network of stations used induces a new type of travel-time residuals, called “geometrical residuals” here, which will disappear if the velocity models are corrected. The geometrical residuals contain information about the correct velocity structure and appear in the routine epicentre locations issued by the ISC. Identification of these residuals can lead to a wealth of new data for accurate velocity determinations.