Narrow-angle representations of the phase and group velocities and their applications in anisotropic velocity-model building for microseismic monitoring

Geophysics ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. WC127-WC142 ◽  
Author(s):  
Vladimir Grechka ◽  
Anton A. Duchkov
Keyword(s):  
Seismic Anisotropy ◽  
Model Building ◽  
Elastic Stiffness ◽  
Coordinate Frame ◽  
Gas Field ◽  
Angular Aperture ◽  
Data Set ◽  
Velocity Models ◽  
Phase And Group Velocities ◽  
Group Velocities

It is usually believed that angular aperture of seismic data should be at least 20° to allow estimation of the subsurface anisotropy. Although this is certainly true for reflection data, for which anisotropy parameters are inverted from the stacking velocities or the nonhyperbolic moveout, traveltimes of direct P- and S-waves recorded in typical downhole microseismic geometries make it possible to infer seismic anisotropy in angular apertures as narrow as about 10°. To ensure the uniqueness of such an inversion, it has to be performed in a local coordinate frame tailored to a particular data set. Because any narrow fan of vectors is naturally characterized by its average direction, we choose the axes of the local frame to coincide with the polarization vectors of three plane waves corresponding to such a direction. This choice results in a significant simplification of the conventional equations for the phase and group velocities in anisotropic media and makes it possible to predict which elements of the elastic stiffness tensor are constrained by the available data. We illustrate our approach on traveltime synthetics and then apply it to perforation-shot data recorded in a shale-gas field. Our case study indicates that isotropic velocity models are inadequate and accounting for seismic anisotropy is a prerequisite for building a physically sound model that explains the recorded traveltimes.

Deep learning-driven velocity model building workflow

2019 ◽  
Vol 38 (11) ◽  
pp. 872a1-872a9 ◽  
Author(s):  
Mauricio Araya-Polo ◽  
Stuart Farris ◽  
Manuel Florez
Keyword(s):  
Deep Learning ◽  
Seismic Data ◽  
Model Building ◽  
Ground Truth ◽  
Velocity Model ◽  
Training Data ◽  
Quality Data ◽  
Generative Adversarial Network ◽  
Data Set ◽  
Velocity Models

Exploration seismic data are heavily manipulated before human interpreters are able to extract meaningful information regarding subsurface structures. This manipulation adds modeling and human biases and is limited by methodological shortcomings. Alternatively, using seismic data directly is becoming possible thanks to deep learning (DL) techniques. A DL-based workflow is introduced that uses analog velocity models and realistic raw seismic waveforms as input and produces subsurface velocity models as output. When insufficient data are used for training, DL algorithms tend to overfit or fail. Gathering large amounts of labeled and standardized seismic data sets is not straightforward. This shortage of quality data is addressed by building a generative adversarial network (GAN) to augment the original training data set, which is then used by DL-driven seismic tomography as input. The DL tomographic operator predicts velocity models with high statistical and structural accuracy after being trained with GAN-generated velocity models. Beyond the field of exploration geophysics, the use of machine learning in earth science is challenged by the lack of labeled data or properly interpreted ground truth, since we seldom know what truly exists beneath the earth's surface. The unsupervised approach (using GANs to generate labeled data)illustrates a way to mitigate this problem and opens geology, geophysics, and planetary sciences to more DL applications.

Estimation of elastic stiffness coefficients of an orthorhombic physical model using group velocity analysis on transmission data

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. R27-R39 ◽  
Author(s):  
Faranak Mahmoudian ◽  
G. F. Margrave ◽  
P. F. Daley ◽  
J. Wong ◽  
D. C. Henley
Keyword(s):  
Physical Model ◽  
Group Velocity ◽  
Body Wave ◽  
Elastic Stiffness ◽  
Laboratory Model ◽  
Theoretical Dependence ◽  
Stiffness Coefficients ◽  
Phase Velocities ◽  
Phase And Group Velocities ◽  
Group Velocities

We acquired 3C ultrasonic transmission seismograms, measured group velocities associated with the three quasi-body wave types, and determined density-normalized stiffness coefficients ([Formula: see text]) over an orthorhombic physical (laboratory) model. The estimation of [Formula: see text] is based on an approximate relationship between the nine orthorhombic [Formula: see text] and group velocities. Estimation of the anisotropic [Formula: see text] is usually done using phase velocities with well-known formulas expressing their theoretical dependence on [Formula: see text]. However, on time-domain seismograms, arrivals are observed traveling with group velocities. Group velocity measurements are found to be straightforward, reasonably accurate, and independent of the size of the transducers used. In contrast, the accuracy of phase velocities derived from the [Formula: see text] transform analysis was found to be very sensitive to small differences in picked arrival times and to transducer size. Theoretical phase and group velocities, calculated in a forward manner from the [Formula: see text] estimates, agreed with the originally measured phase and group velocities, respectively. This agreement confirms that it is valid to use easily measured group velocities with their approximate theoretical relationship to the [Formula: see text] to determine the full stiffness matrix. Compared to the phase-velocity procedure, the technique involving group velocities is much less prone to error due to time-picking uncertainties, and therefore is more suitable for analyzing physical model seismic data.

Velocity model building in a crosswell acquisition geometry with image-trained artificial neural networks

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. U31-U46
Author(s):  
Wenlong Wang ◽  
Jianwei Ma
Keyword(s):  
Wave Equations ◽  
Model Building ◽  
Velocity Model ◽  
P Wave ◽  
Common Source ◽  
Data Set ◽  
Velocity Models ◽  
Velocity Model Building ◽  
Artificial Neural ◽  
The Cost

We have developed an artificial neural network to estimate P-wave velocity models directly from prestack common-source gathers. Our network is composed of a fully connected layer set and a modified fully convolutional layer set. The parameters in the network are tuned through supervised learning to map multishot common-source gathers to velocity models. To boost the generalization ability, the network is trained on a massive data set in which the velocity models are modified from natural images that are collected from an online repository. Multishot seismic traces are simulated from those models with acoustic wave equations in a crosswell acquisition geometry. Shot gathers from different source positions are transformed as channels in the network to increase data redundancy. The training process is expensive, but it only occurs once up front. The cost for predicting velocity models is negligible once the training is complete. Different variations of the network are trained and analyzed. The trained networks indicate encouraging results for predicting velocity models from prestack seismic data that are acquired with the same geometry as in the training set.

Localized anisotropic tomography with well information in VTI media

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. D37-D45 ◽  
Author(s):  
Andrey Bakulin ◽  
Marta Woodward ◽  
Dave Nichols ◽  
Konstantin Osypov ◽  
Olga Zdraveva
Keyword(s):  
Vertical Velocity ◽  
Seismic Data ◽  
Model Building ◽  
Synthetic Data ◽  
Resolution Limit ◽  
Data Set ◽  
Anisotropic Models ◽  
Velocity Models ◽  
First Case ◽  
Well Data

We develop a concept of localized seismic grid tomography constrained by well information and apply it to building vertically transversely isotropic (VTI) velocity models in depth. The goal is to use a highly automated migration velocity analysis to build anisotropic models that combine optimal image focusing with accurate depth positioning in one step. We localize tomography to a limited volume around the well and jointly invert the surface seismic and well data. Well information is propagated into the local volume by using the method of preconditioning, whereby model updates are shaped to follow geologic layers with spatial smoothing constraints. We analyze our concept with a synthetic data example of anisotropic tomography applied to a 1D VTI model. We demonstrate four cases of introducing additionalinformation. In the first case, vertical velocity is assumed to be known, and the tomography inverts only for Thomsen’s [Formula: see text] and [Formula: see text] profiles using surface seismic data alone. In the second case, tomography simultaneously inverts for all three VTI parameters, including vertical velocity, using a joint data set that consists of surface seismic data and vertical check-shot traveltimes. In the third and fourth cases, sparse depth markers and walkaway vertical seismic profiling (VSP) are used, respectively, to supplement the seismic data. For all four examples, tomography reliably recovers the anisotropic velocity field up to a vertical resolution comparable to that of the well data. Even though walkaway VSP has the additional dimension of angle or offset, it offers no further increase in this resolution limit. Anisotropic tomography with well constraints has multiple advantages over other approaches and deserves a place in the portfolio of model-building tools.

Shear-wave group-velocity surfaces in low-symmetry anisotropic media

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. C1-C7 ◽  
Author(s):  
Vladimir Grechka
Keyword(s):  
Group Velocity ◽  
Body Wave ◽  
Transverse Isotropy ◽  
Shear Waves ◽  
Anisotropic Media ◽  
The Body ◽  
Velocity Models ◽  
Phase And Group Velocities ◽  
Low Symmetry ◽  
Group Velocities

Shear waves excited by natural sources constitute a significant part of useful energy recorded in downhole microseismic surveys. In rocks, such as fractured shales, exhibiting symmetries lower than transverse isotropy (TI), the shear wavefronts are always multivalued in certain directions, potentially complicating the data processing and analysis. This paper discusses a basic tool — the computation of the phase and group velocities of all waves propagating along a given ray — that intends to facilitate the understanding of geometries of the shear wavefronts in homogeneous anisotropic media. With this tool, arbitrarily complex group-velocity surfaces can be conveniently analyzed, providing insights into possible challenges to be faced when processing shear waves in anisotropic velocity models that have symmetries lower than TI. Among those challenges are complicated multipathing and the presence of cones of directions, known as internal refraction cones, in which no fast shear waves propagate and the entire shear portion of the body-wave seismic data consists of several branches of the slow shear wavefronts.

Simultaneous inversion for microseismic event location and velocity model in Vaca Muerta Formation

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. KS23-KS34 ◽  
Author(s):  
Zhishuai Zhang ◽  
Jing Du ◽  
Fuchun Gao
Keyword(s):  
Model Building ◽  
Velocity Model ◽  
S Wave ◽  
Reservoir Properties ◽  
Data Set ◽  
Simultaneous Inversion ◽  
Velocity Models ◽  
Vaca Muerta ◽  
Vaca Muerta Formation ◽  
Microseismic Event

Velocity models play a key role in locating microseismic events; however, it is usually challenging to construct them reliably. Traditional model-building strategies depend on the availability of well logs or perforation shots. We simultaneously invert for microseismic event locations and a velocity model under the Bayesian inference framework, and we apply it in a field data set acquired in the Vaca Muerta Formation at Neuquén, Argentina. This methodology enables uncertainty and posterior covariance analysis. By matching the moveouts of the P- and S-wave arrival times, we were able to estimate a 1D velocity model to achieve improved event locations. Various analyses indicate the superiority of this model over a model built with the traditional strategy. With this algorithm, we can perform microseismic monitoring to fracturing treatments in which no perforation data are available. In addition, we can also apply it for long-term passive seismicity reservoir monitoring in which changes of reservoir properties are expected.

scholarly journals GCT-73. EXPRESSION PROFILING OF INTRACRANIAL GERM CELL TUMORS REVEALS UPREGULATION OF RAS THROUGH mRNA-microRNA SIGNALING PATHWAY

2020 ◽  
Vol 22 (Supplement_3) ◽  
pp. iii343-iii343
Author(s):  
Aaron M Taylor ◽  
Jianhe Shen ◽  
Lingzhao Ren ◽  
Keita Terashima ◽  
Lei Huang ◽  
...  
Keyword(s):  
Gene Expression ◽  
Germ Cell ◽  
Expression Profiling ◽  
Model Building ◽  
Rna Binding ◽  
Molecular Subtype ◽  
Germ Cell Tumors ◽  
Cell Renewal ◽  
Data Set ◽  
Intracranial Germ Cell Tumors

Abstract Intracranial germ cell tumors (IGCTs) account for 3% of CNS tumors in children in the U.S. and 11% in Japan and East Asian countries. IGCTs are separated into two distinct subtypes based on histology: germinomas and non-germinomatous germ cell tumors (NGGCTs). The deep central location of IGCTs makes surgical resection and therefore molecular subtype classification difficult, and previous gene expression studies are limited. We performed mRNA expression profiling (Human Genome U133 Plus 2.0) and microRNA expression profiling (ABI TaqMan) with 36 and 49 IGCTs, respectively. Sample stratification using non-negative matrix factorization clustering of gene expression revealed two distinct subgroups that delineated germinomas from NGGCTs. Employing stepwise model building in each data set separately, we were able to separate these groups using only mRNA probes for the LIN28B and L1TD1 genes, and two microRNA, microRNA-26a and microRNA-373. MicroRNA26a suppresses the LIN28B gene and is down-regulated in germinoma. LIN28B directly binds and suppresses the let-7 microRNA family, which suppress the KRAS oncogene, previously found to be mutated in ~19% of IGCTs. L1TD1 is required for human stem cell renewal and directly interacts with LIN28B for its RNA binding function. LIN28B and L1TD1 are both known to be upregulated in other systemic germ cell tumors, but this has not yet been documented in IGCTs. In conclusion, these results show that intracranial germinomas have similar gene expression compared to systemic seminoma, and suggest a mechanism by which activation of LIN28B and L1TD1 downregulates the let-7 microRNA and subsequently upregulates KRAS.

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

2021 ◽  
pp. 108128652110238
Author(s):  
Barış Erbaş ◽  
Julius Kaplunov ◽  
Isaac Elishakoff
Keyword(s):  
Ad Hoc ◽  
Moving Load ◽  
Low Frequency ◽  
Elastic Beam ◽  
Winkler Foundation ◽  
One Dimensional ◽  
Beam Equations ◽  
Dimensional Equation ◽  
Phase And Group Velocities ◽  
Group Velocities

A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.

Compressional‐wave velocities in attenuating media: A laboratory physical model study

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1162-1167 ◽  
Author(s):  
Joseph B. Molyneux ◽  
Douglas R. Schmitt
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Propagation Distance ◽  
Compressional Wave ◽  
Arrival Times ◽  
Wave Velocities ◽  
Amplitude Maximum ◽  
Phase And Group Velocities ◽  
Group Velocities

Elastic‐wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material’s intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol‐saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high‐frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self‐consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.

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