Detection and measure of the shear‐wave birefringence from vertical seismic data: Theory and applications

Geophysics ◽  
1992 ◽  
Vol 57 (11) ◽  
pp. 1463-1481 ◽  
Author(s):  
Frédéric Lefeuvre ◽  
Laurence Nicoletis ◽  
Valérie Ansel ◽  
Christian Cliet
Keyword(s):  
Shear Wave ◽  
Least Squares Method ◽  
Synthetic Data ◽  
Real Data ◽  
Original Method ◽  
Depth Interval ◽  
Seismic Profiles ◽  
Data Set ◽  
Vertical Seismic Profiles ◽  
The Matrix

An original method is presented that allows us to measure the local shear‐wave birefringence properties over any depth interval. It requires the acquisition of two shear‐wave vertical seismic profiles (VSPs), each with different initial polarizations of the shear wave. The method is based on the estimation of a two by two matrix (called the propagator matrix) that represents a linear operator between two states of polarization. No information is required about layering above the zone of interest (in particular, about the weathering zone). If these two states of polarization correspond to the direct downgoing shear wave at two different depths [Formula: see text] and [Formula: see text], the operator represents the transmission properties between the two depths. Under the previous hypothesis, this operator is independent of the source polarization and can be accurately estimated by a least‐squares method in the frequency domain. Physically, this operator is a multicomponent deconvolution, whose column vectors represent the state of polarizations at a depth [Formula: see text] for two linear and mutually perpendicular polarizations at depth [Formula: see text]. This allows for the measurement of the birefringence properties in all azimuthal directions to determine the directions for which a linearly polarized shear‐wave propagates. In addition, the method can be applied to perform the deconvolution of the upgoing wavefield by the downgoing wavefield to obtain a reflection matrix. Then the matrix can be interpreted in terms of anisotropy below the receiver depths (particularly below the well bottom) and in terms of anisotropy of the reflector itself. The proposed method is validated on synthetic data and is applied to real data from the Paris basin. For this particular data set, the birefringence is located in two layers; the first layer consists of unproductive sands and clays while the second one corresponds to a carbonate oil reservoir from the Dogger formation. The natural directions in both layers are very close to the main directions known for the regional stress field. The presence of fractures in the reservoir layer can explain the strong birefringence ratio (>6 percent).

Traveltime inversion of offset vertical seismic profiles—A feasibility study

Geophysics ◽  
1984 ◽  
Vol 49 (3) ◽  
pp. 250-264 ◽  
Author(s):  
L. R. Lines ◽  
A. Bourgeois ◽  
J. D. Covey
Keyword(s):  
Inverse Method ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Profile ◽  
Inversion Method ◽  
Earth Model ◽  
Seismic Profiles ◽  
Traveltime Inversion ◽  
Vertical Seismic Profiles ◽  
Inversion Techniques

Traveltimes from an offset vertical seismic profile (VSP) are used to estimate subsurface two‐dimensional dip by applying an iterative least‐squares inverse method. Tests on synthetic data demonstrate that inversion techniques are capable of estimating dips in the vicinity of a wellbore by using the traveltimes of the direct arrivals and the primary reflections. The inversion method involves a “layer stripping” approach in which the dips of the shallow layers are estimated before proceeding to estimate deeper dips. Examples demonstrate that the primary reflections become essential whenever the ratio of source offset to layer depth becomes small. Traveltime inversion also requires careful estimation of layer velocities and proper statics corrections. Aside from these difficulties and the ubiquitous nonuniqueness problem, the VSP traveltime inversion was able to produce a valid earth model for tests on a real data case.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

scholarly journals Bayesian inversion of magnetotelluric data considering dimensionality discrepancies

2020 ◽  
Vol 223 (3) ◽  
pp. 1565-1583
Author(s):  
Hoël Seillé ◽  
Gerhard Visser
Keyword(s):  
Learning Algorithm ◽  
Synthetic Data ◽  
Real Data ◽  
Error Model ◽  
Bayesian Inversion ◽  
Magnetotelluric Data ◽  
Data Set ◽  
Likelihood Functions ◽  
Training Images ◽  
Phase Tensor

SUMMARY Bayesian inversion of magnetotelluric (MT) data is a powerful but computationally expensive approach to estimate the subsurface electrical conductivity distribution and associated uncertainty. Approximating the Earth subsurface with 1-D physics considerably speeds-up calculation of the forward problem, making the Bayesian approach tractable, but can lead to biased results when the assumption is violated. We propose a methodology to quantitatively compensate for the bias caused by the 1-D Earth assumption within a 1-D trans-dimensional Markov chain Monte Carlo sampler. Our approach determines site-specific likelihood functions which are calculated using a dimensionality discrepancy error model derived by a machine learning algorithm trained on a set of synthetic 3-D conductivity training images. This is achieved by exploiting known geometrical dimensional properties of the MT phase tensor. A complex synthetic model which mimics a sedimentary basin environment is used to illustrate the ability of our workflow to reliably estimate uncertainty in the inversion results, even in presence of strong 2-D and 3-D effects. Using this dimensionality discrepancy error model we demonstrate that on this synthetic data set the use of our workflow performs better in 80 per cent of the cases compared to the existing practice of using constant errors. Finally, our workflow is benchmarked against real data acquired in Queensland, Australia, and shows its ability to detect the depth to basement accurately.

scholarly journals Supervised Image Classification by Scattering Transform with Application to Weed Detection in Culture Crops of High Density

2019 ◽  
Vol 11 (3) ◽  
pp. 249 ◽  
Author(s):  
Pejman Rasti ◽  
Ali Ahmad ◽  
Salma Samiei ◽  
Etienne Belin ◽  
David Rousseau
Keyword(s):  
Texture Classification ◽  
Synthetic Data ◽  
Real Data ◽  
Local Binary Patterns ◽  
High Density ◽  
Weed Detection ◽  
Data Set ◽  
Scattering Transform ◽  
Supervised Image Classification ◽  
Occurrence Matrix

In this article, we assess the interest of the recently introduced multiscale scattering transform for texture classification applied for the first time in plant science. Scattering transform is shown to outperform monoscale approaches (gray-level co-occurrence matrix, local binary patterns) but also multiscale approaches (wavelet decomposition) which do not include combinatory steps. The regime in which scatter transform also outperforms a standard CNN architecture in terms of data-set size is evaluated ( 10 4 instances). An approach on how to optimally design the scatter transform based on energy contrast is provided. This is illustrated on the hard and open problem of weed detection in culture crops of high density from the top view in intensity images. An annotated synthetic data-set available under the form of a data challenge and a simulator are proposed for reproducible science (https://uabox.univ-angers.fr/index.php/s/iuj0knyzOUgsUV9). Scatter transform only trained on synthetic data shows an accuracy of 85 % when tested on real data.

Migration moveout analysis and depth focusing

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Claude F. Lafond ◽  
Alan R. Levander
Keyword(s):  
Heterogeneous Media ◽  
A Priori ◽  
Complex Structure ◽  
Tomographic Reconstruction ◽  
Synthetic Data ◽  
Real Data ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Data Set ◽  
Velocity Models

Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approach is more general than existing migration velocity analysis implementations, it is also much more computer intensive and is best used locally around a particularly complex structure. We demonstrate the technique using synthetic data from a model with strong velocity gradients and then apply it to a marine data set to improve the positioning of a major fault.

Vertical open fractures and shear‐wave velocities derived from VSPs, full waveform acoustic logs, and televiewer data

Geophysics ◽  
1993 ◽  
Vol 58 (6) ◽  
pp. 818-834 ◽  
Author(s):  
Frédéric Lefeuvre ◽  
Roger Turpening ◽  
Carol Caravana ◽  
Andrea Born ◽  
Laurence Nicoletis
Keyword(s):  
Shear Wave ◽  
Azimuthal Anisotropy ◽  
Stoneley Wave ◽  
Correlation Technique ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Full Waveform ◽  
Zero Offset

Fracture or stress‐related shear‐wave birefringence (or azimuthal anisotropy) from vertical seismic profiles (VSPs) is commonly observed today, but no attempt is made to fit the observations with observed in‐situ fractures and velocities. With data from a hard rock (limestones, dolomites, and anhydrites) region of Michigan, fast and slow shear‐wave velocities have been derived from a nine‐component zero offset VSP and compared to shear‐wave velocities from two full waveform acoustic logs. To represent the shear‐wave birefringence that affects the shear wave’s vertical propagation, a propagator matrix technique is used allowing a local measurement independent of the overburden layers. The picked times obtained by using a correlation technique have been corrected in the birefringent regions before we compute the fast and slow velocities. Although there are some differences between the three velocity sets, there is a good fit between the velocities from the shear‐wave VSP and those from the two logs. We suspect the formations showing birefringence to be vertically fractured. To support this, we examine the behavior of the Stoneley wave on the full waveform acoustic logs in the formations. In addition, we analyze the borehole televiewer data from a nearby well. There is a good fit between the fractures seen from the VSP data and those seen from the borehole.

scholarly journals Multidimensional scaling for the evaluation of a geostatistical seismic elastic inversion methodology

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. M1-M10 ◽  
Author(s):  
Leonardo Azevedo ◽  
Ruben Nunes ◽  
Pedro Correia ◽  
Amílcar Soares ◽  
Luis Guerreiro ◽  
...  
Keyword(s):  
Multidimensional Scaling ◽  
Metric Space ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Inversion ◽  
Inversion Algorithm ◽  
Data Set ◽  
The Real ◽  
Geostatistical Inversion ◽  
Impedance Models

Due to the nature of seismic inversion problems, there are multiple possible solutions that can equally fit the observed seismic data while diverging from the real subsurface model. Consequently, it is important to assess how inverse-impedance models are converging toward the real subsurface model. For this purpose, we evaluated a new methodology to combine the multidimensional scaling (MDS) technique with an iterative geostatistical elastic seismic inversion algorithm. The geostatistical inversion algorithm inverted partial angle stacks directly for acoustic and elastic impedance (AI and EI) models. It was based on a genetic algorithm in which the model perturbation at each iteration was performed recurring to stochastic sequential simulation. To assess the reliability and convergence of the inverted models at each step, the simulated models can be projected in a metric space computed by MDS. This projection allowed distinguishing similar from variable models and assessing the convergence of inverted models toward the real impedance ones. The geostatistical inversion results of a synthetic data set, in which the real AI and EI models are known, were plotted in this metric space along with the known impedance models. We applied the same principle to a real data set using a cross-validation technique. These examples revealed that the MDS is a valuable tool to evaluate the convergence of the inverse methodology and the impedance model variability among each iteration of the inversion process. Particularly for the geostatistical inversion algorithm we evaluated, it retrieves reliable impedance models while still producing a set of simulated models with considerable variability.

Measurements of attenuation from vertical seismic profiles by iterative modeling

Geophysics ◽  
1985 ◽  
Vol 50 (6) ◽  
pp. 931-949 ◽  
Author(s):  
Michel Dietrich ◽  
Michel Bouchon
Keyword(s):  
Velocity Dispersion ◽  
Synthetic Data ◽  
Layered Media ◽  
Spectral Ratio ◽  
Ratio Method ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
Anelastic Attenuation ◽  
Vsp Data ◽  
Intrinsic Dissipation

We present a numerical simulation of vertical seismic profiles (VSP) using the discrete horizontal wavenumber representation of seismic wave fields. The theoretical seismograms are computed in the acoustic case for flat layered media, and they include the effects of absorption and velocity dispersion. A study using the synthetic seismograms was conducted to investigate the accuracy and resolution of attenuation measurements from VSP data. It is shown that in finely layered media estimates of the anelastic attenuation obtained by use of the reduced spectral ratio method are usually inaccurate when the attenuation is measured over a small vertical extent. An iterative method is presented which improves the resolution of the measurements of intrinsic dissipation. This method allows determination for synthetic data of the quality factor over depth intervals of about one wavelength of the dominant seismic frequency.

Seismic‐controlled nonlinear extrapolation of well parameters using neural networks

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2035-2041 ◽  
Author(s):  
Zhengping Liu ◽  
Jiaqi Liu
Keyword(s):  
Neural Networks ◽  
Joint Inversion ◽  
Synthetic Data ◽  
Real Data ◽  
Wide Band ◽  
Seismic Section ◽  
Data Set ◽  
Multiple Parameters ◽  
Sonic Log ◽  
Well Data

We present a data‐driven method of joint inversion of well‐log and seismic data, based on the power of adaptive mapping of artificial neural networks (ANNs). We use the ANN technique to find and approximate the inversion operator guided by the data set consisting of well data and seismic recordings near the wells. Then we directly map seismic recordings to well parameters, trace by trace, to extrapolate the wide‐band profiles of these parameters using the approximation operator. Compared to traditional inversions, which are based on a few prior theoretical operators, our inversion is novel because (1) it inverts for multiple parameters and (2) it is nonlinear with a high degree of complexity. We first test our algorithm with synthetic data and analyze its sensitivity and robustness. We then invert real data to obtain two extrapolation profiles of sonic log (DT) and shale content (SH), the latter a unique parameter of the inversion and significant for the detailed evaluation of stratigraphic traps. The high‐frequency components of the two profiles are significantly richer than those of the original seismic section.

Sign in / Sign up

Export Citation Format

Share Document