scholarly journals P-Wave Reflection Approximation of a Thin Bed and Its Application

2020 ◽  
Vol 10 (22) ◽  
pp. 8061
Author(s):  
Chun Yang ◽  
Yun Wang ◽  
Shu Xiong ◽  
Zikun Li ◽  
Hewei Han
Keyword(s):  
Approximate Formula ◽  
Synthetic Data ◽  
Analytic Solutions ◽  
P Wave ◽  
Seismic Exploration ◽  
Inversion Method ◽  
Analytic Approximation ◽  
Zoeppritz Equations ◽  
Single Interface ◽  
Amplitude Versus

“Thin-bed” reservoirs have become important targets of seismic exploration and exploitation. However, traditional amplitude versus offset/amplitude versus angle (AVO/AVA) technologies, for example, those based on Zoeppritz equations and their approximations for a single interface, are not sufficiently accurate for thin-bed stratigraphy. Analytic solutions of thin-bed reflectivity may become practical for thin-bed AVO analysis and inversion. Therefore, a linear analytic approximation of thin-bed P-wave reflectivity is developed under small-incidence and thin-bed assumptions. Numerical simulations show that the amplitude approximation errors are usually smaller than 10% for incidence angles less than 20 degrees, and the thin-bed thicknesses are less than one-tenth of the P-wave wavelength. Based on the least-squares approach, the inversion strategy is proposed using the approximate formula. A synthetic data test shows that the proposed inversion method can produce more accurate thin-bed properties than that based on the Zoeppritz equations, which reveals the potential of the inversion method based on the linear analytic approximate formula in the fine characterization of thin reservoirs.

scholarly journals Seismic AVOA Inversion for Weak Anisotropy Parameters and Fracture Density in a Monoclinic Medium

2020 ◽  
Vol 10 (15) ◽  
pp. 5136 ◽  
Author(s):  
Zijian Ge ◽  
Shulin Pan ◽  
Jingye Li
Keyword(s):  
Fractured Rock ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
P Wave ◽  
Inversion Method ◽  
Fracture Density ◽  
Weak Anisotropy ◽  
Amplitude Versus Offset ◽  
Porosity And Permeability ◽  
Transverse Isotropic

In shale gas development, fracture density is an important lithologic parameter to properly characterize reservoir reconstruction, establish a fracturing scheme, and calculate porosity and permeability. The traditional methods usually assume that the fracture reservoir is one set of aligned vertical fractures, embedded in an isotropic background, and estimate some alternative parameters associated with fracture density. Thus, the low accuracy caused by this simplified model, and the intrinsic errors caused by the indirect substitution, affect the estimation of fracture density. In this paper, the fractured rock of monoclinic symmetry assumes two non-orthogonal vertical fracture sets, embedded in a transversely isotropic background. Firstly, assuming that the fracture radius, width, and orientation are known, a new form of P-wave reflection coefficient, in terms of weak anisotropy (WA) parameters and fracture density, was obtained by substituting the stiffness coefficients of vertical transverse isotropic (VTI) background, normal, and tangential fracture compliances. Then, a linear amplitude versus offset and azimuth (AVOA) inversion method, of WA parameters and fracture density, was constructed by using Bayesian theory. Tests on synthetic data showed that WA parameters, and fracture density, are stably estimated in the case of seismic data containing a moderate noise, which can provide a reliable tool in fracture prediction.

scholarly journals Relative moment tensors and deep Yakutat seismicity

2019 ◽  
Vol 219 (2) ◽  
pp. 1447-1462 ◽  
Author(s):  
Alexandre P Plourde ◽  
Michael G Bostock
Keyword(s):  
Principal Components ◽  
Moment Tensor ◽  
Synthetic Data ◽  
Principal Component ◽  
P Wave ◽  
Inversion Method ◽  
Low Velocity ◽  
Stress Regime ◽  
Moment Tensors ◽  
S Waves

SUMMARY We introduce a new relative moment tensor (MT) inversion method for clusters of nearby earthquakes. The method extends previous work by introducing constraints from S-waves that do not require modal decomposition and by employing principal component analysis to produce robust estimates of excitation. At each receiver, P and S waves from each event are independently aligned and decomposed into principal components. P-wave constraints on MTs are obtained from a ratio of coefficients corresponding to the first principal component, equivalent to a relative amplitude. For S waves we produce constraints on MTs involving three events, where one event is described as a linear combination of the other two, and coefficients are derived from the first two principal components. Nonlinear optimization is applied to efficiently find best-fitting tensile-earthquake and double-couple solutions for relative MT systems. Using synthetic data, we demonstrate the effectiveness of the P and S constraints both individually and in combination. We then apply the relative MT inversion to a set of 16 earthquakes from southern Alaska, at ∼125 km depth within the subducted Yakutat terrane. Most events are compatible with a stress tensor dominated by downdip tension, however, we observe several pairs of earthquakes with nearly antiparallel slip implying that the stress regime is heterogeneous and/or faults are extremely weak. The location of these events near the abrupt downdip termination of seismicity and the low-velocity zone suggest that they are caused by weakening via grain-size and volume reduction associated with eclogitization of the lower crustal gabbro layer.

scholarly journals High-Order AVO Inversion for Effective Pore-Fluid Bulk Modulus Based on Series Reversion and Bayesian Theory

Energies ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1313
Author(s):  
Lei Shi ◽  
Yuhang Sun ◽  
Yang Liu ◽  
David Cova ◽  
Junzhou Liu
Keyword(s):  
Bulk Modulus ◽  
Seismic Data ◽  
Pore Fluid ◽  
High Order ◽  
Bayesian Theory ◽  
P Wave ◽  
Seismic Exploration ◽  
Inversion Method ◽  
Fluid Identification ◽  
Avo Inversion

Pore-fluid identification is one of the key technologies in seismic exploration. Fluid indicators play important roles in pore-fluid identification. For sandstone reservoirs, the effective pore-fluid bulk modulus is more susceptible to pore-fluid than other fluid indicators. AVO (amplitude variation with offset) inversion is an effective way to obtain fluid indicators from seismic data directly. Nevertheless, current methods lack a high-order AVO equation for a direct, effective pore-fluid bulk modulus inversion. Therefore, based on the Zoeppritz equations and Biot–Gassmann theory, we derived a high-order P-wave AVO approximation for an effective pore-fluid bulk modulus. Series reversion and Bayesian theory were introduced to establish a direct non-linear P-wave AVO inversion method. By adopting this method, the effective pore-fluid bulk modulus, porosity, and density can be inverted directly from seismic data. Numerical simulation results demonstrate the precision of our proposed method. Model and field data evaluations show that our method is stable and feasible.

Frequency‐wavenumber elastic inversion of marine seismic data

Geophysics ◽  
1994 ◽  
Vol 59 (12) ◽  
pp. 1868-1881 ◽  
Author(s):  
Huasheng Zhao ◽  
Bjørn Ursin ◽  
Lasse Amundsen
Keyword(s):  
Wave Velocity ◽  
Reference Data ◽  
Jacobian Matrix ◽  
Synthetic Data ◽  
Velocity Model ◽  
P Wave ◽  
Stratified Medium ◽  
Inversion Method ◽  
S Wave ◽  
Time Space

We present an inversion method for determining the velocities, densities, and layer thicknesses of a horizontally stratified medium with an acoustic layer at the top and a stack of elastic layers below. The multioffset reflection response of the medium generated by a compressional point source is transformed from the time‐space domain into the frequency‐wavenumber domain where the inversion is performed by minimizing the difference between the reference data and the modeled data using a least‐squares technique. The forward modeling is based on the reflectivity method where the solution for each frequency‐wavenumber component is found by computing the generalized reflection and transmission matrices recursively. The gradient of the objective function is computed from analytical expressions of the Jacobian matrix derived directly from the recursive modeling equations. The partial derivatives of the reflection response of the stratified medium are then computed simultaneously with the reflection response by layer‐recursive formulas. The limited‐aperture and discretization effects in time and space of the reference data are included by applying a pair of frequency and wavenumber dependent filters to the predicted data and to the Jacobian matrix at each iteration. Numerical experiments performed with noise‐free synthetic data prove that the proposed inversion method satisfactorily reconstructs the elastic parameters of a stratified medium. The low‐frequency trends of the S‐wave velocity and density are found when the initial P‐wave velocity model gives approximately correct traveltimes. The convergence of the iterative minimization algorithm is fast.

scholarly journals A Low-Order Series Approximation of Thin-Bed PP-Wave Reflections

2019 ◽  
Vol 9 (4) ◽  
pp. 709 ◽  
Author(s):  
Chun Yang ◽  
Yun Wang ◽  
Jun Lu ◽  
Benchi Chen ◽  
Lei Shi
Keyword(s):  
Approximate Formula ◽  
Expansion Method ◽  
Wave Impedance ◽  
P Wave ◽  
Reflection Coefficients ◽  
Single Interface ◽  
Series Approximation ◽  
Amplitude Versus Offset ◽  
Small Incidence ◽  
Pp Wave

The study of thin-bed seismic phenomena is important in crustal, exploration and engineering seismology. Presently, seismic reflectivity theories based on single-interface assumption are widely used though they are only suitable for thick deposits. Thin-bed reflectivity theories are established on complex propagator matrices and are difficult to be applied to reveal thin-bed properties directly. Therefore, an approximation of thin-bed PP-wave reflection coefficients (RPP) is derived in this paper. First, the relationship between thin-bed RPP and incidence angles is analyzed through series expansion method. For PP-wave, its reflection coefficients are even power series functions of sine incidence angles. Then, for small incidence, RPP of the thin bed is further simplified into a second-order series approximation with respect to the sine incidence angles. Simulations and accuracy analyses of the approximate formula show that approximation errors are smaller than 5% as the incidence angles smaller than 20 degrees. Based on this approximate formula, an approach is given for estimating thin-bed properties including P-wave impedance ratios and thickness. The estimation approach is applied in properties estimation of a thin bed model. Perfect performances of the model example show the future potentiality of the approximate formula in thin-bed Amplitude-Versus-Offset (AVO) analysis and inversion.

An Adaptive Stratified Joint PP and PS AVA Inversion Using Accurate Jacobian Matrix

Geophysics ◽  
2021 ◽  
pp. 1-145
Author(s):  
Xiaobo Liu ◽  
Jingyi Chen ◽  
Jing Zeng ◽  
Fuping Liu ◽  
Handong Huang ◽  
...  
Keyword(s):  
Seismic Data ◽  
Jacobian Matrix ◽  
Incidence Angle ◽  
P Wave ◽  
Rock Properties ◽  
Inversion Method ◽  
S Wave ◽  
Zoeppritz Equations ◽  
Wave Velocities ◽  
Strong Contrast

Amplitude variation with incidence angle (AVA) analysis is an essential tool for discriminating lithology in the hydrocarbon reservoirs. Compared with the traditional AVA inversion using only P-wave information, joint AVA inversion using PP and PS seismic data provides better estimation of rock properties (e.g., density, P- and S-wave velocities). At present, the most used AVA inversions depend on the approximations of Zoeppritz equations (e.g., Shuey and Aki-Richards approximations), which are not suitable for formations with strong contrast interfaces and seismic data with large incidence angles. Based on the previous derivation of accurate Jacobian matrix, we find that the sign of each partial derivative of reflection coefficient with respect to P-, S-wave velocities and density changes across the interface, represents good indicator for the reflection interfaces. Accordingly, we propose an adaptive stratified joint PP and PS AVA inversion using the accurate Jacobian matrix that can automatically obtain the layer information and can be further used as a constraint in the inversion of in-layer rock properties (density, P- and S-wave velocities). Due to the use of the exact Zoeppritz equations and accurate Jacobian matrix, this proposed inversion method is more accurate than traditional AVA inversion methods, has higher computational efficiency and can be applied to seismic wide-angle reflection data or seismic data acquired for formations with strong contrast interfaces. The model study shows that this proposed inversion method works better than the classical Shuey and Aki-Richards approximations at estimating reflection interfaces and in-layer rock properties. It also works well in handling a part of the complex Marmousi 2 model and real seismic data.

scholarly journals S-wave experiments for the exploration of a deep geothermal carbonate reservoir in the German Molasse Basin

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Britta Wawerzinek ◽  
Hermann Buness ◽  
Hartwig von Hartmann ◽  
David C. Tanner
Keyword(s):  
Upper Jurassic ◽  
Carbonate Reservoir ◽  
P Wave ◽  
Seismic Survey ◽  
Seismic Exploration ◽  
Molasse Basin ◽  
S Wave ◽  
Induced Earthquakes ◽  
Conversion Point ◽  
Facies Classification

AbstractThere are many successful geothermal projects that exploit the Upper Jurassic aquifer at 2–3 km depth in the German Molasse Basin. However, up to now, only P-wave seismic exploration has been carried out. In an experiment in the Greater Munich area, we recorded S-waves that were generated by the conventional P-wave seismic survey, using 3C receivers. From this, we built a 3D volume of P- to S-converted (PS) waves using the asymptotic conversion point approach. By combining the P-volume and the resulting PS-seismic volume, we were able to derive the spatial distribution of the vp/vs ratio of both the Molasse overburden and the Upper Jurassic reservoir. We found that the vp/vs ratios for the Molasse units range from 2.0 to 2.3 with a median of 2.15, which is much higher than previously assumed. This raises the depth of hypocenters of induced earthquakes in surrounding geothermal wells. The vp/vs ratios found in the Upper Jurassic vary laterally between 1.5 and 2.2. Since no boreholes are available for verification, we test our results against an independently derived facies classification of the conventional 3D seismic volume and found it correlates well. Furthermore, we see that low vp/vs ratios correlate with high vp and vs velocities. We interpret the latter as dolomitized rocks, which are connected with enhanced permeability in the reservoir. We conclude that 3C registration of conventional P-wave surveys is worthwhile.

scholarly journals Methods for estimating uncertainty in factor analytic solutions

2014 ◽  
Vol 7 (3) ◽  
pp. 781-797 ◽  
Author(s):  
P. Paatero ◽  
S. Eberly ◽  
S. G. Brown ◽  
G. A. Norris
Keyword(s):  
Environmental Protection Agency ◽  
Synthetic Data ◽  
Analytic Solutions ◽  
Data Sets ◽  
Random Errors ◽  
Data Set ◽  
Factor Analytic ◽  
Uncertainty Estimates ◽  
Multilinear Engine ◽  
Analytic Models

Abstract. The EPA PMF (Environmental Protection Agency positive matrix factorization) version 5.0 and the underlying multilinear engine-executable ME-2 contain three methods for estimating uncertainty in factor analytic models: classical bootstrap (BS), displacement of factor elements (DISP), and bootstrap enhanced by displacement of factor elements (BS-DISP). The goal of these methods is to capture the uncertainty of PMF analyses due to random errors and rotational ambiguity. It is shown that the three methods complement each other: depending on characteristics of the data set, one method may provide better results than the other two. Results are presented using synthetic data sets, including interpretation of diagnostics, and recommendations are given for parameters to report when documenting uncertainty estimates from EPA PMF or ME-2 applications.

REAL-TIME 2.5D INVERSION OF LWD RESISTIVITY MEASUREMENTS USING DEEP LEARNING FOR GEOSTEERING APPLICATIONS ACROSS FAULTED FORMATIONS

2021 ◽  
Author(s):  
Kyubo Noh ◽  
◽  
Carlos Torres-Verdín ◽  
David Pardo ◽  
◽  
...  
Keyword(s):  
Deep Learning ◽  
Real Time ◽  
Fault Plane ◽  
Synthetic Data ◽  
Field Measurements ◽  
Geological Structure ◽  
Inversion Method ◽  
Adaptive Finite Element ◽  
Resistivity Measurements ◽  
Lwd Resistivity

We develop a Deep Learning (DL) inversion method for the interpretation of 2.5-dimensional (2.5D) borehole resistivity measurements that requires negligible online computational costs. The method is successfully verified with the inversion of triaxial LWD resistivity measurements acquired across faulted and anisotropic formations. Our DL inversion workflow employs four independent DL architectures. The first one identifies the type of geological structure among several predefined types. Subsequently, the second, third, and fourth architectures estimate the corresponding spatial resistivity distributions that are parameterized (1) without the crossings of bed boundaries or fault plane, (2) with the crossing of a bed boundary but without the crossing of a fault plane, and (3) with the crossing of the fault plane, respectively. Each DL architecture employs convolutional layers and is trained with synthetic data obtained from an accurate high-order, mesh-adaptive finite-element forward numerical simulator. Numerical results confirm the importance of using multi-component resistivity measurements -specifically cross-coupling resistivity components- for the successful reconstruction of 2.5D resistivity distributions adjacent to the well trajectory. The feasibility and effectiveness of the developed inversion workflow is assessed with two synthetic examples inspired by actual field measurements. Results confirm that the proposed DL method successfully reconstructs 2.5D resistivity distributions, location and dip angles of bed boundaries, and the location of the fault plane, and is therefore reliable for real-time well geosteering applications.

P-wave backazimuth anomalies observed by a small-aperture seismic array at Pinyon Flat, southern California: Implications for structure and source location

1996 ◽  
Vol 86 (2) ◽  
pp. 470-476 ◽  
Author(s):  
Cheng-Horng Lin ◽  
S. W. Roecker
Keyword(s):  
Southern California ◽  
Seismic Array ◽  
P Wave ◽  
Small Aperture ◽  
Data Set ◽  
Single Interface ◽  
Seismic Networks ◽  
Dense Seismic Array ◽  
Beamforming Technique

Abstract Seismograms of earthquakes and explosions recorded at local, regional, and teleseismic distances by a small-aperture, dense seismic array located on Pinyon Flat, in southern California, reveal large (±15°) backazimuth anomalies. We investigate the causes and implications of these anomalies by first comparing the effectiveness of estimating backazimuth with an array using three different techniques: the broadband frequency-wavenumber (BBFK) technique, the polarization technique, and the beamforming technique. While each technique provided nearly the same direction as a most likely estimate, the beamforming estimate was associated with the smallest uncertainties. Backazimuth anomalies were then calculated for the entire data set by comparing the results from beamforming with backazimuths derived from earthquake locations reported by the Anza and Caltech seismic networks and the Preliminary Determination of Epicenters (PDE) Bulletin. These backazimuth anomalies have a simple sinelike dependence on azimuth, with the largest anomalies observed from the southeast and northwest directions. Such a trend may be explained as the effect of one or more interfaces dipping to the northeast beneath the array. A best-fit model of a single interface has a dip and strike of 20° and 315°, respectively, and a velocity contrast of 0.82 km/sec. Application of corrections computed from this simple model to ray directions significantly improves locations at all distances and directions, suggesting that this is an upper crustal feature. We confirm that knowledge of local structure can be very important for earthquake location by an array but also show that corrections computed from simple models may not only be adequate but superior to those determined by raytracing through smoothed laterally varying models.

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