Accurate Velocity Model Research Articles

Increasing the robustness and applicability of full-waveform inversion: An optimal transport distance strategy

Full-waveform inversion starts being used as a standard stage of the seismic-imaging workflow, at the exploration scale, for the reconstruction of high-resolution wave velocity models. However, its successful application still relies on the estimation of an accurate enough initial velocity model, as well as on the design of a suitable hierarchical workflow, allowing it to feed the inversion process progressively with data. These two requirements are mandatory to avoid the cycle-skipping or phase-ambiguity problem when comparing observed and synthetic data. This difficulty is due to the definition of the full-waveform inversion problem as the least-squares minimization of the data misfit. The resulting misfit function has local minima, which correspond to the interpretation of the seismic data up to one or several phase shifts. In this article, we review an alternative formulation of full-waveform inversion based on the optimal transport distance we have proposed in recent studies. We propose to use a particular instance of the optimal transport problem, which is adapted to the interpretation of real seismic data and for which we design an efficient low-complexity numerical strategy. Numerical results in 2D and 3D configurations (BP 2004, Chevron 2014 benchmark model, SEG/EAGE overthrust model) show that this reformulation should yield a more convex misfit function, less prone to cycle skipping. In this study, we present a simple illustration on the Marmousi model, which illustrates how this new distance strongly relaxes the requirement on the initial model design. Starting from a rather simplistic approximation of the initial model, the method is able to reconstruct a meaningful estimation of the Marmousi model, while the standard least-squares formulation is trapped into a local, meaningless minimum.

Near-surface velocity modeling using a combined inversion of surface and refracted P-waves

We propose an innovative workflow based on the complementary use of Rayleigh waves alongside standard P-wave refraction tomography, which better depicts the shallow part of the near-surface P-wave velocity model. Our surface-wave processing sequence led to an S-wave near-surface velocity field that can be used as a constraint for P-wave tomography and can improve P-wave statics determination. Rayleigh waves are processed in three steps. The first step consists of an accurate frequency-dependent traveltime measurement for each selected source-receiver pair in which the phase difference between two adjacent traces is used to derive the phase velocity. Then, a frequency-dependent surface-wave velocity tomography is performed from the picked traveltimes. Finally, after surface-wave tomography, the frequency-dependent phase velocity volume output by the tomography is inverted to deliver an S-wave near-surface velocity model. This model is used to constrain the first-arrival P-wave tomography. To illustrate our method, we use a 3D narrow-azimuth land data set, acquired along a river valley. Strong lateral velocity variations exist in the shallow part, with slow velocities around the unconsolidated sediments of the riverbed and faster velocities in the consolidated sediments of the surrounding hills. A combined first-arrival tomography using the S-wave velocity model, the initial unconstrained refracted P-wave velocity model, and the original first arrivals is used to obtain a more accurate near-surface P-wave velocity model. This new approach led to a constrained P-wave velocity model from which primary statics are derived and then applied, leading to an improved image with better focusing and continuity of thin layers in the shallowest part.

Velocity model building challenges and solutions in a SE Asian basin: beyond reflection tomography

Brunei Darussalam, on the South-East Asian island of Borneo, has a long history of oil and gas production. Oil was first discovered in the onshore Seria field in 1929. Other sizeable fields have been discovered since, such as Champion and Ampa, and a high level of exploration and development activities are continuing. To ensure the challenges that come with these activities can be addressed adequately, a large part of Brunei’s offshore has recently been covered by modern broadband acquisition. Remaining parts offshore are covered by older 3D seismic. The coastal strip of Brunei, encompassing among others the large Seria field, is covered by wide-azimuth 3D land and transition-zone data. Brunei’s subsurface geology poses some specific challenges for seismic imaging for hydrocarbon exploration and development purposes. Shallow gas accumulations – gas clouds or gas bags – absorb much of the seismic energy and cause a wipe-out zone below them. Many exploration and development targets lie in relatively shallow (less than 200m deep) water where the (sub-)seabed is characterized by corals and near-surface channels. This impacts the seismic image through the resulting variation of near-surface velocities as well as attenuation owing to scattering and negatively impacts the deeper structural imaging. An illustration of these challenges is shown in Figure 1. The subsurface offshore and onshore Brunei is also heavily faulted and large anticlines often have steep flanks, and suffer from crestal collapses. Drilling targets can be relatively narrow (few 100 m wide) fault blocks near the crestal collapses, which makes accurate fault imaging and positioning and thus an accurate seismic velocity model absolutely crucial for confident well placement. Figure 2 shows the importance of accurate imaging for well placement: The image from the final isotropic model indicates that the well trajectory is on the intended side of the fault, while the well results showed the trajectory had crossed the fault and needed to be sidetracked. The subsequently built tilted transverse isotropic (TTI) model reveals that the trajectory has indeed crossed the fault. This example stresses the importance of detailed and accurate anisotropic model building.

Regularized Laplace–Fourier-Domain Full Waveform Inversion Using a Weighted l 2 Objective Function

Full waveform inversion (FWI) can be applied to obtain an accurate velocity model that contains important geophysical and geological information. FWI suffers from the local minimum problem when the starting model is not sufficiently close to the true model. Therefore, an accurate macroscale velocity model is essential for successful FWI, and Laplace–Fourier-domain FWI is appropriate for obtaining such a velocity model. However, conventional Laplace–Fourier-domain FWI remains an ill-posed and ill-conditioned problem, meaning that small errors in the data can result in large differences in the inverted model. This approach also suffers from certain limitations related to the logarithmic objective function. To overcome the limitations of conventional Laplace–Fourier-domain FWI, we introduce a weighted l 2 objective function, instead of the logarithmic objective function, as the data-domain objective function, and we also introduce two different model-domain regularizations: first-order Tikhonov regularization and prior model regularization. The weighting matrix for the data-domain objective function is constructed to suitably enhance the far-offset information. Tikhonov regularization smoothes the gradient, and prior model regularization allows reliable prior information to be taken into account. Two hyperparameters are obtained through trial and error and used to control the trade-off and achieve an appropriate balance between the data-domain and model-domain gradients. The application of the proposed regularizations facilitates finding a unique solution via FWI, and the weighted l 2 objective function ensures a more reasonable residual, thereby improving the stability of the gradient calculation. Numerical tests performed using the Marmousi synthetic dataset show that the use of the weighted l 2 objective function and the model-domain regularizations significantly improves the Laplace–Fourier-domain FWI. Because the Laplace–Fourier-domain FWI is improved, the frequency-domain FWI, in which the Laplace–Fourier-domain FWI result is used as the starting model, yields inversion result much closer to the true velocity.

Full-traveltime inversion

Many previously published wave-equation-based methods, which attempt to automatically invert traveltime or kinematic information in seismic data or migrated gathers for smooth velocities, suffer a common and severe problem — the inversions are involuntarily and unconsciously hijacked by amplitude information. To overcome this problem, we have developed a new wave-equation-based traveltime inversion methodology, referred to as full-traveltime (i.e., fully dependent on traveltime) inversion (FTI), to automatically estimate a kinematically accurate velocity model from seismic data. The key idea of FTI is to make the inversion fully dependent on traveltime information, and thus prevent amplitude interference during inversion. Under the assumption that velocity perturbations cause only traveltime changes, we have derived the FTI method in the data and image domains, which are applicable to transmitted arrivals and reflected waves, respectively. FTI does not require an accurate initial velocity model or low-frequency seismic data. Synthetic and field data tests demonstrate that FTI produces satisfactory inversion results, even when using constant velocity models as initials.

FLAC/SPECFEM2D coupled numerical simulation of wavefields near excavation boundaries in underground mines

A nonlinear velocity model that considers the influence of confinement and rock mass failure on wave velocity is developed. A numerical method, which couples FLAC and SPECFEM2D, is developed for ground motion modeling near excavation boundaries in underground mines. The motivation of developing the FLAC/SPECFEM2D coupled approach is to take merits of each code, such as the stress analysis capability in FLAC and the powerful wave propagation analysis capability in SPECFEM2D. Because stress redistribution and failure of the rock mass around an excavation are considered, realistic non-uniform velocity fields for the SPECFEM2D model can be obtained, and this is a notable feature of this study. Very large differences in wavefields and ground motion are observed between the results from the non-uniform and the uniform velocity models. If the non-uniform velocity model is used, the ground motion around a stope can be amplified up to five times larger than that given by the design scaling law. If a uniform velocity model is used, the amplification factor is only about three. Using the FLAC/SPECFEM2D coupled modeling approach, accurate velocity models can be constructed and this in turn will assist in predicting ground motions accurately around underground excavations.

Wave equation based microseismic source location and velocity inversion

The microseismic event locations and velocity information can be used to infer the stress field and guide hydraulic fracturing process, as well as to image the subsurface structures. How to get accurate microseismic event locations and velocity model is the principal problem in reservoir monitoring. For most location methods, the velocity model has significant relation with the accuracy of the location results. The velocity obtained from log data is usually too rough to be used for location directly. It is necessary to discuss how to combine the location and velocity inversion. Among the main techniques for locating microseismic events, time reversal imaging (TRI) based on wave equation avoids traveltime picking and offers high-resolution locations. Frequency dependent wave equation traveltime inversion (FWT) is an inversion method that can invert velocity model with source uncertainty at certain frequency band. Thus we combine TRI with FWT to produce improved event locations and velocity model. In the proposed approach, the location and model information are interactively used and updated. Through the proposed workflow, the inverted model is better resolved and the event locations are more accurate. We test this method on synthetic borehole data and filed data of a hydraulic fracturing experiment. The results verify the effectiveness of the method and prove it has potential for real-time microseismic monitoring.

Multiples: Signal or noise?

Migration and migration inversion are the seismic processing methods for structural determination and subsequent amplitude analysis, respectively. To date, the most well-founded and physically interpretable migration method is based on predicting a coincident source and receiver experiment at depth at time equals zero. We have extended that migration method for heterogeneous media and to accommodate two-way propagation in a local sense at every point from the source to the target reflector and back from the reflector to the receiver and in a global sense, separately for each of the two legs from the source to the reflector and from the reflector to the receiver. That provides the first migration method that avoids high-frequency assumptions in the imaging principle and how it is implemented, and hence, it is equally effective at all frequencies at the target or reservoir. This advance for two-way wave propagation migration then provides a tool to quantitatively, unambiguously, and definitively define the role of primaries and multiples in migration. Our conclusion was that with data consisting of primaries and multiples, for an accurate discontinuous velocity model, only primaries contribute to migration with the same image and inversion results independent of whether multiples are kept or removed. However, for a smooth and continuous velocity model (i.e., generally assumed in practice), every multiple will result in a false, misleading, and potentially injurious subsurface image and hence must be removed before migration. In practice, we migrate with a smooth velocity model, and hence multiples must be removed. When the collection of primaries is incomplete, a multiple can be used to provide an approximate image of an unrecorded primary. However, it is always the migration of primaries that provides subsurface structure and amplitude information.

Accelerating extended least-squares migration with weighted conjugate gradient iteration

Least-squares migration (LSM) iteratively achieves a mean-square best fit to seismic reflection data, provided that a kinematically accurate velocity model is available. The subsurface offset extension adds extra degrees of freedom to the model, thereby allowing LSM to fit the data even in the event of significant velocity error. This type of extension also implies additional computational expense per iteration from crosscorrelating source and receiver wavefields over the subsurface offset, and therefore places a premium on rapid convergence. We have accelerated the convergence of extended least-squares migration by combining the conjugate gradient algorithm with weighted norms in range (data) and domain (model) spaces that render the extended Born modeling operator approximately unitary. We have developed numerical examples that demonstrate that the proposed algorithm dramatically reduces the number of iterations required to achieve a given level of fit or gradient reduction compared with conjugate gradient iteration with Euclidean (unweighted) norms.

Joint optimization of vertical component gravity and P-wave first arrivals by simulated annealing

Joint seismic and gravity analyses of the San Emidio geothermal field in the northwest Basin and Range province of Nevada demonstrate that joint optimization changes interpretation outcomes. The prior 0.3–0.5 km deep basin interpretation gives way to a deeper than 1.3 km basin model. Kirchoff prestack depth migrations reveal that joint optimization ameliorates shallow velocity artifacts, flattening antiformal reflectors that could have been interpreted as folds. Furthermore, joint optimization provides a clearer picture of the rangefront fault by increasing the depth of constrained velocities, which improves reflector coherency at depth. This technique provides new insight when applied to existing data sets and could replace the existing strategy of forward modeling to match gravity data. We have achieved stable joint optimization through simulated annealing, a global optimization algorithm that does not require an accurate initial model. Balancing the combined seismic-gravity objective function is accomplished by a new approach based on analysis of Pareto charts. Gravity modeling uses an efficient convolution model, and the basis of seismic modeling is the highly efficient Vidale eikonal equation traveltime generation technique. Synthetic tests found that joint optimization improves velocity model accuracy and provides velocity control below the deepest headwave raypath. Restricted offset-range migration analysis provides insights into precritical and gradient reflections in the data set.

Full-waveform inversion as a game changer: Are we there yet?

Full-waveform inversion (FWI) has the potential to be a game changer for the seismic industry since it produces accurate velocity models at a resolution that cannot be matched by conventional traveltime tomography, with the additional advantage that it runs on basically raw data. Today, these two features should be better exploited to maximize the business value that FWI can deliver to an oil and gas operator. Provided that we acquire adequate data sets, FWI can be run starting from a smooth velocity model so that traveltime tomography is completely bypassed. As very little processing is required, FWI can be executed in parallel with the main preprocessing efforts, with the results of shortening considerably the overall project turnaround. For imaging purposes, FWI can be limited to the low-frequency range (∼ 10 Hz) but if run in the high-frequency range (∼ 30 Hz), FWI velocities have such a resolution that they can be used directly for interpretation. In particular, applications in the field of pore-pressure prediction and shallow hazard have great potential. In the current implementation, the main limitations are linked to data quality and computational power, but both these issues can be adequately addressed.

Near-surface fault detection by migrating back-scattered surface waves with and without velocity profiles

We demonstrate that diffraction stack migration can be used to discover the distribution of near-surface faults. The methodology is based on the assumption that near-surface faults generate detectable back-scattered surface waves from impinging surface waves. We first isolate the back-scattered surface waves by muting or FK filtering, and then migrate them by diffraction migration using the surface wave velocity as the migration velocity. Instead of summing events along trial quasi-hyperbolas, surface wave migration sums events along trial quasi-linear trajectories that correspond to the moveout of back-scattered surface waves. We have also proposed a natural migration method that utilizes the intrinsic traveltime property of the direct and the back-scattered waves at faults. For the synthetic data sets and the land data collected in Aqaba, where surface wave velocity has unexpected perturbations, we migrate the back-scattered surface waves with both predicted velocity profiles and natural Green's function without velocity information. Because the latter approach avoids the need for an accurate velocity model in event summation, both the prestack and stacked migration images show competitive quality. Results with both synthetic data and field records validate the feasibility of this method. We believe applying this method to global or passive seismic data can open new opportunities in unveiling tectonic features.

Velocity calibration for microseismic event location using surface data

Because surface-based monitoring of hydraulic fracturing is not restricted by borehole geometry or the difficulties in maintaining subsurface equipment, it is becoming an increasingly common part of microseismic monitoring. The ability to determine an accurate velocity model for the monitored area directly affects the accuracy of microseismic event locations. However, velocity model calibration for location with surface instruments is difficult for several reasons: well log measurements are often inaccurate or incomplete, yielding intractable models; origin times of perforation shots are not always accurate; and the non-uniqueness of velocity models obtained by inversion becomes especially problematic when only perforation shots are used. In this paper, we propose a new approach to overcome these limitations. We establish an initial velocity model from well logging data, and then use the root mean square (RMS) error of double-difference arrival times as a proxy measure for the misfit between the well log velocity model and the true velocity structure of the medium. Double-difference RMS errors are reduced by using a very fast simulated annealing for model perturbance, and a sample set of double-difference RMS errors is then selected to determine an empirical threshold. This threshold value is set near the minimum RMS of the selected samples, and an appropriate number of travel times within the threshold range are chosen. The corresponding velocity models are then used to relocate the perforation-shot. We use the velocity model with the smallest relative location errors as the basis for microseismic location. Numerical analysis with exact input velocity models shows that although large differences exist between the calculated and true velocity models, perforation shots can still be located to their actual positions with the proposed technique; the location inaccuracy of the perforation is <2 m. Further tests on field data demonstrate the validity of this technique.

Joint interpretation of high-resolution velocity and resistivity models from the Barents Sea

To realize the full potential of a geophysical data set, and resolve interpretation ambiguities, the data must be integrated with other geological and complementary geophysical data. Seismic velocity and electrical resistivity are rock properties that both depend on lithology and fluid content: we show that valuable insight can be gained by integrated interpretation of high-resolution velocity and resistivity models produced by inversion and imaging of broadband dual-sensor (GeoStreamer) and Towed Streamer EM data respectively. Broadband dual-sensor seismic data enables high-resolution velocity model building and depth imaging using reflections, refractions and sea-surface multiples. As a result of advances in algorithms, workflows and high performance computing it is fast becoming routine to produce high resolution and accurate velocity models for large-scale 3D broadband dual-sensor data-sets as part of the depth imaging workflow. Thus seismic velocity is a rock property that can now be determined with sufficient resolution and precision to be of use to an interpreter in an exploration setting, before more detailed quantitative interpretation studies are undertaken. Marine Controlled Source EM (CSEM) data has been used extensively to improve the chance of success in the search for hydrocarbons given that accumulations of oil and gas can be characterized by increased resistivity. CSEM data have been used mostly to de-risk prospects. By using a Towed Streamer EM system it is possible to acquire CSEM data efficiently to determine the sub-surface resistivity reliably at both regional and prospect scales.

Reverse time migration for microseismic sources using the geometric mean as an imaging condition

Time reversal is a powerful tool used to image directly the location and mechanism of passive seismic sources. This technique assumes seismic velocities in the medium and propagates time-reversed observations of ground motion at each receiver location. Assuming an accurate velocity model and adequate array aperture, the waves will focus at the source location. Because we do not know the location and the origin time a priori, we need to scan the entire 4D image (3D in space and 1D in time) to localize the source, which makes time-reversal imaging computationally demanding. We have developed a new approach of time-reversal imaging that reduces the computational cost and the scanning dimensions from 4D to 3D (no time) and increases the spatial resolution of the source image. We first individually extrapolate wavefields at each receiver, and then we crosscorrelate these wavefields (the product in the frequency domain: geometric mean). This crosscorrelation creates another imaging condition, and focusing of the seismic wavefields occurs at the zero time lag of the correlation provided the velocity model is sufficiently accurate. Due to the analogy to the active-shot reverse time migration (RTM), we refer to this technique as the geometric-mean RTM or GmRTM. In addition to reducing the dimension from 4D to 3D compared with conventional time-reversal imaging, the crosscorrelation effectively suppresses the side lobes and yields a spatially high-resolution image of seismic sources. The GmRTM is robust for random and coherent noise because crosscorrelation enhances signal and suppresses noise. An added benefit is that, in contrast to conventional time-reversal imaging, GmRTM has the potential to be used to retrieve velocity information by analyzing time and/or space lags of crosscorrelation, which is similar to what is done in active-source imaging.

Velocity model estimation by full waveform inversion of time-lapse 4D passive seismic array data

SUMMARY In passive-source monitoring, an accurate velocity model is important to precisely estimate microseismic source locations, and to understand changes in reservoir properties. In this study, we employ frequency-domain full waveform inversion in order to obtain a high- resolution velocity model by exploiting full wavefields. We demonstrate the feasibility of the method for a surface geophone array by inverting for time-lapse 4D velocity changes in a realistic subsurface model. Our method successfully estimates the small velocity changes of a few percent within layers of 10s of meters, even for a single passive seismic source event. The analysis of wavepaths and gradients suggests that keys for the successful inversion are the use of full wavefields (both first and scattered arrivals), the vicinity of velocity changes to the source, and the wide-aperture surface array.

Imaging through shallow gas: Integrating broadband acquisition, processing and high-end model building for improved imaging of deeper targets

SUMMARY We present a case study offshore Malaysia, shallow gas features in the overburden distort the seismic imaging at the target level. While a multifaceted approach involving a combination of seismic acquisition and processing strategies were used to improve the bandwidth of the seismic data, particularly for the low-frequency content of the seismic image, several distortions still existed at the target level. The prominent structural sag evident at the reservoir level is a typical indication that the overlying shallow gas velocity model needed to be resolved and incorporated into a depth migration algorithm. To resolve the transversally and laterally variant velocity features in the shallow gas areas, a solution that consisted of full waveform inversion (FWI) and high-resolution reflection traveltime tomography was utilized to produce an accurate compressional velocity model. To further resolve the amplitude and phase distortions at the reservoir level due to shallow gas effects, Q tomography was incorporated into the model building phase to derive a space-variant 1/Qmodel and Q compensation was integrated within depth migration. The integrated approach of broadband receiver acquisition, data processing strategies and high-end Earth model building has cumulatively improved the imaging of the reservoir below the shallow gas anomalies.

Extended imaging conditions for passive seismic data

Seismic monitoring at injection sites (e.g., CO2 sequestration, hydraulic fracturing) has become an increasingly common tool amongst oil and gas producers. The information obtained from these data is often limited to seismic event properties (e.g., location, initiation time, moment tensor), the accuracy of which greatly depends on the assumed or estimated elastic velocity models. However, estimating accurate 3D velocity models from passive array data remains a challenging problem. Extended imaging conditions (eICs) for passive wave-equation imaging algorithms represent a key step towards generating – and verifying – elastic velocity models. By extending imaging conditions away from zero-lag in time and space we can better evaluate the focusing of a given event based on the principle that waves focus at zero lag only when the velocity models are correct. We demonstrate that given an elastic medium and multi-component recordings, we can propagate and correlate microseismic P- and S-wavefield modes to compute eICs for P- and S- velocity perturbations. We observe that the maximum correlation deviates from the zero-lag in time and space for a P/S cross-correlation imaging condition when using an incorrect P- and/or S-wave velocity, and thus there is sensitivity to velocity error not observable when using individual wavefield components.

High-density point-receiver seismic survey of a deep carbonate cave reservoir system: a case study from the Tarim Basin, Western China

In the northern rim of the Tarim Basin, western China, oil is being produced from an extensive system of interconnected caves, faults and fractures in Ordovician carbonates buried about 6000 to 7000 m below the surface. Although onshore, drilling costs are high due to the depth of the field, so, to produce the field economically, wells must be accurately located within the cavernous features to access as large a drainage area as possible. However, imaging fine details of the reservoir structures presents challenges due to a complex overburden. While the surface terrain and near-surface geology are relatively benign for land seismic operations, the subsurface exhibits large lateral velocity changes related to widely distributed Permian volcanic formations around 1000 and 1200 m above the target zone. These formations are considered to have led to errors in the imaging of the target layers in legacy datasets due to incorrect velocity modelling of the overburden. Improved imaging of detailed features of the deep cavernous carbonate reservoir beneath the complex overburden would require an accurate velocity model in addition to seismic data with both high temporal and spatial resolution. To determine whether new land seismic acquisition and processing technologies could provide a significant uplift in imaging quality, in 2013 PetroChina Tarim Oil Company (TOC) acquired a high-density full-azimuth 3D seismic survey using a point-source and point-receiver geometry. The dataset was recorded using an advanced high-channel count acquisition system and processed with high-end processing techniques designed to address the various challenges presented in the area. Three approaches were used over different depth ranges to develop an accurate velocity model for prestack depth migration (PSDM). Model velocities were constrained using available well data, providing confidence in the accuracy of the resulting image. Relative amplitude preserving (RAP) methods were used for noise attenuation and signal processing to maximise the reliability of subsequent inversion and interpretation work.

Vertical seismic profile migration velocity analysis via residual moveout in receiver domain common image gathers

The success of imaging vertical seismic profile (VSP) data critically depends upon obtaining and using an accurate subsurface velocity model. First-arrival-time tomography can be used to derive velocities above the receivers. Reflection time tomography can be used to derive velocities below the receivers, but it requires reflection time picking and association with appropriate horizons. We described an alternative, faster way to perform velocity analysis by assessing the residual moveout after migrating walk-away VSP data. We have derived residual moveout equations for migrated common receiver gathers assuming a constant velocity model with a single horizontal reflector. The observed residual moveout in common image gathers in the receiver domain will be aligned and flat if the migration velocity is correct. If the residual moveout is not flat, by digitizing the extreme point on the unstacked, migrated traces in each common receiver gather, we could invert for the velocity of the target layer using our new residual moveout equations. We then extended this method to handle depth and laterally varying layer geometries using an iterative root-mean-square velocity scheme and a layer-stripping strategy. We combined the power of a prestack VSP depth migration using complicated velocity structures with straightforward velocity updating equations. For a range of synthetic cases and geometries, the estimated velocities were within 3% of the actual value.