Single Velocity Model Research Articles

Elastic Transmitted Wave Reverse Time Migration for Imaging Earth’s Interior Discontinuities: A Numerical Study

ABSTRACT Seismic imaging is crucial in investigating Earth’s interior structures and understanding its tectonics and evolution. The reflected, converted, and scattered waves have attracted considerable attention in the previous studies, whereas the directly transmitted waves are less used in seismic imaging. In this study, we present a novel passive source elastic transmitted wave reverse time migration (T-RTM) method to characterize major discontinuities in Earth’s interior using transmitted P or S waveforms. By extrapolating and then cross correlating the wavefields from the sources with the transmitted wavefields from the receivers using flood velocity models, the velocity discontinuities can be clearly imaged. The advantages and potential applications of the proposed T-RTM method are demonstrated with three synthetic imaging experiments. First, with distributed acoustic sensing using submarine cables, we show that the proposed method can be used to image the Moho with teleseismic S waves recorded in a single axial component, which is difficult for other imaging methods. Second, using direct P waveforms with a single P-wave velocity model, we show that the proposed method can be used to image 3D Moho topography without relying on the VP/VS ratio like in the traditional receiver function imaging. Third, the proposed method can also be used to image a fault plane with a sharp velocity contrast using local earthquakes. We discuss the limitations of the proposed method and some potential issues in field-data applications with additional numerical experiments. The proposed T-RTM method could provide many new opportunities for utilizing transmitted waveforms in the study of oceanic and continental structures.

Deep Learning-Based P- and S-Wave Separation for Multicomponent Vertical Seismic Profiling

Vertical seismic profiling (VSP) helps to derive high-resolution images around the instrumented borehole and is a cost-effective technique for CO₂ storage monitoring. In routine VSP data processing, P- and S-wave separation is a crucial step to extract independent single-mode waves for accurate imaging and interpretation. Conventional wave mode separation involves tedious, subjective, and non-reproducible manual interventions, especially when dealing with complex geology. To better automate the process, we propose a data-driven deep learning-based P- and S-wave separation method. Our method adapts a fully convolutional neural network that simultaneously extracts P- and S-potential data from multicomponent VSP measurements. To reduce the enormous computational cost in wave simulation while constructing training datasets with sufficient kinematic and dynamic variations, we introduce virtual wellbores where synthetic VSP data sampling wide variations in seismic kinematics and dynamics are recorded using only a dozen elastic wave simulations on a single velocity model. We qualify the separation results both directly in data space and in image space after reverse time migration (RTM). Generalization tests on various synthetic models and their corresponding RTM images demonstrate that the proposed strategy provides sufficient sampling of the high-dimensional data space and essentially ensures successful applications of the trained neural network to similar yet different geological scenarios.

Microseismic Event Location by Considering the Influence of the Empty Area in an Excavated Tunnel

The velocity model is a key factor that affects the accuracy of microseismic event location around tunnels. In this paper, we consider the effect of the empty area on the microseismic event location and present a 3D heterogeneous velocity model for excavated tunnels. The grid-based heterogeneous velocity model can describe a 3D arbitrarily complex velocity model, where the microseismic monitoring areas are divided into many blocks. The residual between the theoretical arrival time calculated by the fast marching method (FMM) and the observed arrival time is used to identify the block with the smallest residual. Particle swarm optimization (PSO) is used to improve the location accuracy in this block. Synthetic tests show that the accuracy of the microseismic event location based on the heterogeneous velocity model was higher than that based on the single velocity model, independent of whether an arrival time error was considered. We used the heterogeneous velocity model to locate 7 blasting events and 44 microseismic events with a good waveform quality in the Qinling No. 4 tunnel of the Yinhanjiwei project from 6 June 2017 to 13 June 2017 and compared the location results of the heterogeneous-velocity model with those of the single-velocity model. The results of this case study show that the events located by the heterogeneous velocity model were concentrated around the working face, which matched the actual conditions of the project, while the events located by the single-velocity model were scattered and far from the working face.

The present-day seismicity of the White Sea region

A revised earthquake catalog has been compiled for the White Sea region for the period between 2005 and 2016. The earthquake parameters were revised using a single velocity model (BARENTS), a single methodological approach (Generalized Beamforming), and all available raw data and bulletins of Russian and foreign seismic stations. The location of two nuclear explosions detonated on July 18, 1985 and September 6, 1988 in northern European Russia for civilian purposes showed that the algorithm for calculating hypocenter parameters combined with the BARENTS velocity model is an effective tool. The resulting earthquake catalog enabled us to reveal the leading patterns in the distribution of recent seismicity in the White Sea region.

The present-day seismicity of the White Sea region

A revised earthquake catalog has been compiled for the White Sea region for the period between 2005 and 2016. The earthquake parameters were revised using a single velocity model (BARENTS), a single methodological approach (Generalized Beamforming), and all available raw data and bulletins of Russian and foreign seismic stations. The location of two nuclear explosions detonated on July 18, 1985 and September 6, 1988 in northern European Russia for civilian purposes showed that the algorithm for calculating hypocenter parameters combined with the BARENTS velocity model is an effective tool. The resulting earthquake catalog enabled us to reveal the leading patterns in the distribution of recent seismicity in the White Sea region.

A method for assessing earth model uncertainty in the Taranaki Basin, New Zealand

As exploration moves into areas of increasing geological complexity and limited legacy data, reservoir evaluation is often based on the interpretation of one seismic image. Building a suitable velocity model followed by pre-stack depth migration plays an important role in the creation of this image on which economic evaluations are often based. In many cases drilling commitments are planned long in advance. Geologists have a good idea about the geometry and size of a potential reservoir but require accurate interpretation and positioning in the depth domain. Typically, the amount of uncertainty associated with an image is poorly quantified. During a depth migration velocity model building project, such as shown here, we deliver a single final velocity model and its associated seismic products. The only quantitative measure of the reliability of the data would be through comparison with available auxiliary data or from analysis of volumetric residual move-out. This may provide an indication of how well the model converges to a solution which satisfies the observations on the data. The high non-linearity inherent within the tomography used to generate the model yield multiple solution realizations. These honour the constraining data and yield the same convergence criterion. In isolation such data provides little useful evidence of the reliability of any one individual model. We aim to rectify this by employing a workflow which assesses the uncertainty in our tomography process. This initially establishes both the resolution, and the degree to which the tomography fails to recover an implied perturbation. Using these criteria we generate a volume of models which equally conform to the observed data and derive confidence attributes assigned to the target model governing the image. Here we present data from Taranaki Basin, Offshore New Zealand, and show how a model uncertainty workflow could de-risk exploration and development decisions.

Simulating gas (vapor) outflow into a liquid

In this paper, an axisymmetric problem of gas outflow from a pipe end to an area of high density (two-phase mixture) is considered. Simulation of the two-phase coolant outflow without phase transition is carried out using a two-velocity model, solved by the LCPFCT software package [1]. Cross-verification is performed with the results of calculation obtained by the OpenFoam software [2] using the VOF method for the approximation of the single-velocity model of a two-phase compressible medium. Using various numerical programs and various physical models of a two-phase medium gives a more complete understanding of the occurring processes.

Single-Velocity Model of Two-Phase Liquids for Calculating Flows According to the First Principles’ Approach

A single velocity model of one-component media for calculating two-phase flows is presented. The model is based on conservation laws with minimal additional assumptions. The model and numerical method are intended for the direct numerical simulation (DNS) of complex two-phase flows with high-performance computing systems (exascale computing). The closed set of governing equations is written for nonaveraged parameters (so-called microparameters) and for a medium with a complex equation of state. It is assumed that each point of the flow is completely characterized by a single density, single velocity, and single internal energy. The diffused interface model is used for describing an interphase boundary. A method for generating the relationship between thermodynamic functions and all possible values of density and internal energy is presented. The real functions for the pure phases are used. The hydrodynamic basis of the model consists of Navier-Stokes equations or Euler equations that take heat conductivity processes into consideration. The reliability of the model is tested on a 1D problem for real water, in particular, on the Stefan problem and on the problem on the formation and coalescence of bubbles.

Nonmodal instability of a stratified plane-channel suspension flow with fine particles.

We consider the nonmodal instability and transient growth of small disturbances in a plane-channel suspension flow with a nonuniform concentration profile of fine noncolloidal particles accumulated in two localized layers, symmetric about the channel axis. A single-velocity model of an effective Newtonian fluid with a finite particle volume fraction is employed. It is established that fine particles distributed nonuniformly in the main flow significantly modify the growth rate of the first mode in a wide range of governing parameters. The most pronounced destabilizing effect is produced by the particles localized in the vicinity of the walls. A parametric study of the so-called optimal disturbances showed that they are streaks elongated in the flow direction, similar to the optimal disturbances in the flow devoid of particles. The transverse wave number of the optimal disturbances depends strongly on the location of the particle layers. Even when the particle mass concentration (averaged over the channel cross section) is small (of the order of a percent) and the particles are localized in the middle between the walls and the channel axis, the energy of the optimal disturbances is by several orders of magnitude larger than in dusty-gas and pure-fluid flows. When the particle layers are located in the vicinity of the walls or the channel axis, the nonmodal instability mechanism is less pronounced, as compared to the flow devoid of particles.

Двумерная односкоростная модель для расчета двухфазных течений реальной воды с учетом эффектов поверхностного натяжения

Двумерная односкоростная модель для расчета двухфазных течений реальной воды с учетом эффектов поверхностного натяжения

Assessing uncertainty in refraction seismic traveltime inversion using a global inversion strategy

ABSTRACTTo analyse and invert refraction seismic travel time data, different approaches and techniques have been proposed. One common approach is to invert first‐break travel times employing local optimization approaches. However, these approaches result in a single velocity model, and it is difficult to assess the quality and to quantify uncertainties and non‐uniqueness of the found solution. To address these problems, we propose an inversion strategy relying on a global optimization approach known as particle swarm optimization. With this approach we generate an ensemble of acceptable velocity models, i.e., models explaining our data equally well. We test and evaluate our approach using synthetic seismic travel times and field data collected across a creeping hillslope in the Austrian Alps. Our synthetic study mimics a layered near‐surface environment, including a sharp velocity increase with depth and complex refractor topography. Analysing the generated ensemble of acceptable solutions using different statistical measures demonstrates that our inversion strategy is able to reconstruct the input velocity model, including reasonable, quantitative estimates of uncertainty. Our field data set is inverted, employing the same strategy, and we further compare our results with the velocity model obtained by a standard local optimization approach and the information from a nearby borehole. This comparison shows that both inversion strategies result in geologically reasonable models (in agreement with the borehole information). However, analysing the model variability of the ensemble generated using our global approach indicates that the result of the local optimization approach is part of this model ensemble. Our results show the benefit of employing a global inversion strategy to generate near‐surface velocity models from refraction seismic data sets, especially in cases where no detailed a priori information regarding subsurface structures and velocity variations is available.

Thoughts and observations on interpreting depth-imaged data

Interpreting depth-imaged data requires attention to elements of uncertainty different from those associated with time-imaged data. In particular, an interpreter must visualize how the migration velocity model affects focusing and positioning of reflections in final images and, consequently, interpretation of the geology contained in those images. The availability of several versions of depth imaging based on a single velocity model but with different migration algorithms complicates interpretation in that the interpreter must decide which version provides the most accurate representation of the true geology.

Effective anisotropic velocity model from surface monitoring of microseismic events

ABSTRACTWe develop a methodology to obtain a consistent velocity model from calibration shots or microseismicity observed on a buried array. Using a layered 1D isotropic model derived from checkshots as an initial velocity model, we invert P‐wave arrival times to obtain effective anisotropic parameters with a vertical axis of symmetry (VTI). The nonlinear inversion uses iteration between linearized inversion for anisotropic parameters and origin times or depths, which is specific to microseismic monitoring. We apply this technique to multiple microseismic events from several treatments within a buried array. The joint inversion of selected events shows a largely reduced RMS error indicating that we can obtain robust estimates of anisotropic parameters, however we do not show improved source locations. For joint inversion of multiple microseismic events we obtained Thomsen anisotropic parameters ε of 0.15 and δ of 0.05, which are consistent with values observed in active seismic surveys. These values allow us to locate microseismic events from multiple hydraulic fracture treatments separated across thousands of metres with a single velocity model. As a result, we invert the effective anisotropy for the buried array region and are able to provide a more consistent microseismicity mapping for past and future hydraulic fracture stimulations.

A comparative study of various pressure relaxation closure models for one‐dimensional two‐material Lagrangian hydrodynamics

AbstractLagrangian hydrodynamics of strength‐free materials continues to present open issues, even in one dimension. We focus on the problem of closing a system of equations for a two‐material cell under the assumption of a single velocity model. There are several existing models and approaches, each possessing different levels of fidelity to the underlying physics and each exhibiting unique features in the computed solutions. We consider three models that take different approaches to breaking the assumption of instantaneous pressure equilibration in the mixed‐material cell. The first of these is the well‐known method of Tipton, in which a viscosity‐like pressure relaxation term is coupled with an otherwise isentropic pressure update to obtain closed‐form expressions for the materials' volume fractions and corresponding sub‐cell pressures. The second is the physics‐inspired, geometry‐based pressure relaxation model of Kamm and Shashkov, which is based on an optimization procedure that uses a local, exact Riemann problem. The third model is the unique aspect of this paper, inspired by the work of Delov and Sadchikov and Goncharov and Yanilkin. This sub‐scale dynamics approach is motivated by the linearized Riemann problem to initialize volume fraction changes, which are then modified, via the materials' SIEs, to drive the mixed cell toward pressure equilibrium. Each of these approaches is packaged in the framework of a two‐step time integration scheme. We compare these multi‐material pressure relaxation models, together with corresponding pure‐material calculations, on idealized, two‐material problems with either ideal‐gas or stiffened‐gas equations of state. Published in 2010 by John Wiley & Sons, Ltd.

A new pressure relaxation closure model for one-dimensional two-material Lagrangian hydrodynamics

We present a new model for closing a system of Lagrangian hydrodynamics equations for a two-material cell with a single velocity model. We describe a new approach that is motivated by earlier work of Delov and Sadchikov and of Goncharov and Yanilkin. Using a linearized Riemann problem to initialize volume fraction changes, we require that each material satisfy its own p dV equation, which breaks the overall energy balance in the mixed cell. To enforce this balance, we redistribute the energy discrepancy by assuming that the corresponding pressure change in each material is equal. This multiple-material model is packaged as part of a two-step time integration scheme. We compare results of our approach with other models and with corresponding pure-material calculations, on two-material test problems with ideal-gas or stiffened-gas equations of state.

A Pressure Relaxation Closure Model for One-Dimensional, Two-Material Lagrangian Hydrodynamics Based on the Riemann Problem

Despite decades of development, Lagrangian hydrodynamics of strengthfree materials presents numerous open issues, even in one dimension. We focus on the problem of closing a system of equations for a two-material cell under the assumption of a single velocity model. There are several existing models and approaches, each possessing different levels of fidelity to the underlying physics and each exhibiting unique features in the computed solutions. We consider the case in which the change in heat in the constituent materials in the mixed cell is assumed equal. An instantaneous pressure equilibration model for a mixed cell can be cast as four equations in four unknowns, comprised of the updated values of the specific internal energy and the specific volume for each of the two materials in the mixed cell. The unique contribution of our approach is a physics-inspired, geometry-based model in which the updated values of the sub-cell, relaxing-toward-equilibrium constituent pressures are related to a local Riemann problem through an optimization principle. This approach couples the modeling problem of assigning sub-cell pressures to the physics associated with the local, dynamic evolution. We package our approach in the framework of a standard predictor-corrector time integration scheme. We evaluate our model usingmore » idealized, two material problems using either ideal-gas or stiffened-gas equations of state and compare these results to those computed with the method of Tipton and with corresponding pure-material calculations.« less

Adaptation of the propagator for numerical acoustic holography of a wheel type object

Holography procedure of a vibrating object can be geometrically interpreted resulting in a guarantee of its identified vibratory velocity, the quality of which depends on the pressure measurement at an array of microphones and on the propagation model. In case of a wheel with the panel body, a plane array parallel to the visible side is the only one possible. The velocity is then accessible on the side concerned and needs a propagation model with adequate acoustic conditions over the whole plane with the visible side (source plane). Having in mind such a configuration, a theoretical work in the 3D space has shown the surrounding influence on the reconstructed velocity on the visible side. It has appeared that vibrations other than the ones of the front side and the rear acoustic load can be described with an admittance on the source plane. We present here an exhaustive search for the adequate admittance concerned leading to a correct propagator and a correct velocity identified. The success achieved in the procedure may rely on the single velocity and single model liable to radiate a given pressure on a sufficiently large antenna.

Plus�minus method to solve large�amplitude near�surface static corrections

ABSTRACTThe surface conditions in Saudi Arabia demonstrate significant variability ranging from flat gravel plains to sand�dunes, sabkhas (salt flats) and desert wadis (washouts). Saudi Aramco has used a single�layer velocity model from surface to datum for most of the prospective areas for both 2D and 3D seismic data. Source gathers have been interpreted by picking the first arrivals to obtain a linear fit for the direct and refractor arrivals using the intercept�time method. This creates depth and velocity control input for a multiple‐layer model of the near‐surface, from which static corrections to datum are calculated. On 2D lines with very large amplitude near‐surface anomalies, the plusminus technique has been applied to solve local areas. The implementation of the plus‐minus technique utilizes a variable near‐surface velocity derived from either upholes or the direct‐arrival velocity determined from source gathers. With this method, multiple source‐pairs build up effective spreads. Then by compiling high fold of delay‐times at a location, a statistical average is taken where the high fold reduces the significance of picking errors. The model is built utilizing multiple refraction layers and is referenced to the datum, thus tying it to the regional model.The example 2D seismic line has a static model calculated from the single‐layer velocity model. The intercept‐time method was applied locally over a near‐surface anomaly caused by unconsoli‐dated material at the foot of a cliff. Further analysis of the near‐surface involved the plus‐minus method to solve the high amplitude time shifts.

Using dual-azimuth data to image below salt domes

In complex geological areas, subsurface illumination is largely determined by the acquisition geometry. More recently, multi-azimuth and wide-azimuth surveys are increasingly being used to maximize subsurface coverage, but these can present new challenges; for example, how to combine the images from different azimuths into a single migrated image for use by the interpreter. Traditionally, the common practice is to ignore potential azimuthal velocity variations and build a single vertical velocity model, in some cases incorporating VTI anisotropy. Data from different azimuths are pre-stack migrated separately, but with a single velocity model usually derived from one azimuth, and then combined into a single image after application of residual move-out corrections. We present a case history of building a single velocity model for pre-stack depth migration of dual-azimuth data in the southern North Sea. The dual-azimuth data gave us enhanced illumination of the target zone, but somewhat to our surprise, it also showed strong azimuthal velocity variations in the overburden. We devised a methodology and built a single velocity model that incorporated these azimuthal velocity variations so that all events are migrated to their correct position. When the data sets are combined, primary events are reinforced while noise cancels out to give one optimal data set.

Integrated prestack depth migration of vertical seismic profile and surface seismic data from the Rocky Mountain Foothills of southern Alberta, Canada

We have developed an anisotropic prestack depth migration code that can migrate either vertical seismic profile (VSP) or surface seismic data. We use this migration code in a new method for integrated VSP and surface seismic depth imaging. Instead of splicing the VSP image into the section derived from surface seismic data, we use the same migration algorithm and a single velocity model to migrate both data sets to a common output grid. We then scale and sum the two images to yield one integrated depth‐migrated section. After testing this method on synthetic surface seismic and VSP data, we applied it to field data from a 2D surface seismic line and a multioffset VSP from the Rocky Mountain Foothills of southern Alberta, Canada. Our results show that the resulting integrated image exhibits significant improvement over that obtained from (a) the migration of either data set alone or (b) the conventional splicing approach. The integrated image uses the broader frequency bandwidth of the VSP data to provide higher vertical resolution than the migration of the surface seismic data. The integrated image also shows enhanced structural detail, since no part of the surface seismic section is eliminated, and good event continuity through the use of a single migration–velocity model, obtained by an integrated interpretation of borehole and surface seismic data. This enhanced migrated image enabled us to perform a more robust interpretation with good well ties.