The effects of statics on tomographic velocity reconstructions

Geophysics ◽  
1992 ◽  
Vol 57 (2) ◽  
pp. 353-362 ◽  
Author(s):  
Livia J. Squires ◽  
Samuel N. Blakeslee ◽  
Paul L. Stoffa
Keyword(s):  
Tomographic Reconstruction ◽  
Lateral Velocity ◽  
Arrival Times ◽  
Surface Reflection ◽  
First Order ◽  
Velocity Error ◽  
Reflection Data ◽  
Model Study ◽  
First Arrival ◽  
First Order Correction

Seismic first arrival times from crosshole, VSP, and reversed VSP (RVSP) experiments are collectively inverted by least‐squares for the velocity distribution between two boreholes. The tomographic reconstruction exhibits a large lateral velocity contrast that is not supported by the surface reflection data from the same location. After examining the traveltime residuals from the three tomographic datasets separately, we conclude that the velocity contrast is due primarily to static delays in the RVSP first arrival times. When a first‐order correction is made for the statics, tomographic inversion results in a velocity reconstruction that is more consistent with the surface reflection data. To isolate the velocity errors produced by the RVSP statics, we compute a residual tomogram by subtracting the statics adjusted tomogram from the original. The residual tomogram shows that the statics introduce errors not only in the region sampled by the RVSP rays, but they indirectly contaminate other regions of the tomogram as well. We reproduce this velocity error distribution as part of a model study designed to simulate the effects of statics on tomographic velocity reconstructions. Results indicate that traveltime errors on the order of 2 percent can result in tomographic velocity errors of up to 7 percent.

Precision analysis of first‐break times in grid models

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 1062-1065 ◽  
Author(s):  
Thomas Gruber ◽  
Stewart A. Greenhalgh
Keyword(s):  
Numerical Models ◽  
Grid Point ◽  
Tomographic Reconstruction ◽  
Velocity Model ◽  
Model Parameters ◽  
Seismic Reflection Data ◽  
Arrival Times ◽  
Velocity Models ◽  
Reflection Data ◽  
Inversion Techniques

Rectangular grid velocity models and their derivatives are widely used in geophysical inversion techniques. Specifically, seismic tomographic reconstruction techniques, whether they be based on raypath methods (Bregman et al., 1989; Moser, 1991; Schneider et al., 1992; Cao and Greenhalgh, 1993; Zhou, 1993) or full wave equation methods (Vidale, 1990; Qin and Schuster, 1993; Cao and Greenhalgh, 1994) for calculating synthetic arrival times, involve propagation through a grid model. Likewise, migration of seismic reflection data, using asymptotic ray theory or finite difference/pseudospectral methods (Stolt and Benson, 1986; Zhe and Greenhalgh, 1997) involve assigning traveltimes to upward and downward propagating waves at every grid point in the model. The traveltimes in both cases depend on the grid specification. However, the precision level of such numerical models and their dependence on the model parameters is often unknown. In this paper, we describe a two‐dimensional velocity model and derive an error bound for first‐break times calculated with such a model. The analysis provides clear guidelines for grid specifications.

scholarly journals Machine Learning Enabled Traveltime Inversion Based on the Horizontal Source Location Perturbation

Geophysics ◽  
2021 ◽  
pp. 1-40
Author(s):  
Isa Eren Yildirim ◽  
Tariq Alkhalifah ◽  
Ertugrul Umut Yildirim
Keyword(s):  
Linear Optimization ◽  
Deep Convolutional Neural Networks ◽  
Lateral Velocity ◽  
Suggested Approach ◽  
Near Surface ◽  
Arrival Times ◽  
Velocity Models ◽  
Uniqueness Of The Solution ◽  
First Arrival ◽  
High Level

Gradient based traveltime tomography, which aims to minimize the difference between modeled and observed first arrival times, is a highly non-linear optimization problem. Stabilization of this inverse problem often requires employing regularization. While regularization helps avoid local minima solutions, it might cause low resolution tomograms because of its inherent smoothing property. On the other hand, although conventional ray-based tomography can be robust in terms of the uniqueness of the solution, it suffers from the limitations inherent in ray tracing, which limits its use in complex media. To mitigate the aforementioned drawbacks of gradient and ray-based tomography, we approach the problem in a completely novel way leveraging data-driven inversion techniques based on training deep convolutional neural networks (DCNN). Since DCNN often face challenges in detecting high level features from the relatively smooth traveltime data, we use this type of network to map horizontal changes in observed first arrival traveltimes caused by a source shift to lateral velocity variations. The relationship between them is explained by a linearized eikonal equation. Construction of the velocity models from this predicted lateral variation requires information from, for example, a vertical well-log in the area. This vertical profile is then used to build a tomogram from the output of the network. Both synthetic and field data results verify that the suggested approach estimates the velocity models reliably. Because of the limited depth penetration of first arrival traveltimes, the method is particularly favorable for near-surface applications.

Waveform tomography at a groundwater contamination site: Surface reflection data

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. G45-G55 ◽  
Author(s):  
Fuchun Gao ◽  
Alan Levander ◽  
R. Gerhard Pratt ◽  
Colin A. Zelt ◽  
Gian-Luigi Fradelizio
Keyword(s):  
Groundwater Contamination ◽  
Nonaqueous Phase Liquids ◽  
Seismic Profiles ◽  
Lateral Velocity ◽  
Data Set ◽  
Surface Reflection ◽  
Traveltime Tomography ◽  
Velocity Models ◽  
Reflection Data ◽  
Waveform Tomography

We have applied acoustic-waveform tomography to 45 2D seismic profiles to image the 3D geometry of a buried paleochannel at a groundwater-contamination site at Hill Air Force Base in Utah. The paleochannel, which is incised into an alluvium-covered clay aquitard, acts as a trap for dense nonaqueous-phase liquids (DNAPLs) that contaminate the shallowest groundwater system in the study area. The 2D profiles were extracted from a 3D surface reflection data set. First-arrival traveltime tomography provided initial velocity models for the waveform tomography. We inverted for six frequency components in the band [Formula: see text] of the direct and refracted waves to produce 45 2D velocity models. The flanks and bottom of a channel with a maximum depth of about [Formula: see text] were well modeled in most of the 45 parallel 2D slices, which allowed us to construct a 3D image of the channel by combining and interpolating between the 45 image slices. The 3D model of the channel will be useful for siting extraction wells within the site remediation program. The alluvium that fills the channel showed marked vertical and lateral velocity heterogeneity. Traveltime tomography and waveform tomography can be complementary approaches. Used together, they can provide high-resolution images of complicated shallow structures.

scholarly journals Interferometric identification of surface-related multiples

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. Q41-Q52 ◽  
Author(s):  
Boris Boullenger ◽  
Deyan Draganov
Keyword(s):  
Synthetic Data ◽  
Original Data ◽  
Data Set ◽  
Interferometric Method ◽  
Feedback Information ◽  
Arrival Times ◽  
Surface Reflection ◽  
Reflection Data ◽  
Multiple Prediction ◽  
Virtual Events

The theory of seismic interferometry predicts that crosscorrelations of recorded seismic responses at two receivers yield an estimate of the interreceiver seismic response. The interferometric process applied to surface-reflection data involves the summation, over sources, of crosscorrelated traces, and it allows retrieval of an estimate of the interreceiver reflection response. In particular, the crosscorrelations of the data with surface-related multiples in the data produce the retrieval of pseudophysical reflections (virtual events with the same kinematics as physical reflections in the original data). Thus, retrieved pseudophysical reflections can provide feedback information about the surface multiples. From this perspective, we have developed a data-driven interferometric method to detect and predict the arrival times of surface-related multiples in recorded reflection data using the retrieval of virtual data as diagnosis. The identification of the surface multiples is based on the estimation of source positions in the stationary-phase regions of the retrieved pseudophysical reflections, thus not necessarily requiring sources and receivers on the same grid. We have evaluated the method of interferometric identification with a two-layer acoustic example and tested it on a more complex synthetic data set. The results determined that we are able to identify the prominent surface multiples in a large range of the reflection data. Although missing near offsets proved to cause major problems in multiple-prediction schemes based on convolutions and inversions, missing near offsets does not impede our method from identifying surface multiples. Such interferometric diagnosis could be used to control the effectiveness of conventional multiple-removal schemes, such as adaptive subtraction of multiples predicted by convolution of the data.

Tomographic reconstruction of near‐borehole slowness using refracted borehole sonic arrivals

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1726-1738 ◽  
Author(s):  
Brian E. Hornby
Keyword(s):  
Field Data ◽  
Horizontal Well ◽  
Tomographic Reconstruction ◽  
Reconstruction Algorithm ◽  
Computer Models ◽  
Drilling Process ◽  
Arrival Times ◽  
Full Waveform ◽  
First Arrival ◽  
Full Waveforms

Two‐dimensional (2-D) reconstructions of the near‐borehole slowness field are computed using arrival times of refracted borehole sonic arrivals. First‐arrival traveltimes, derived from both computer simulations and field data from full‐waveform sonic tools, were inverted for the near‐borehole formation slowness both axially along the borehole and radially away from the borehole. The inversion is nonlinear; the solution is obtained by means of a series of linear inversions followed by provisional ray tracings. Each iteration involves the application of a tomographic reconstruction algorithm similar to those used in seismic crosswell tomography or medical imaging applications. The technique was demonstrated using ray‐theoretic examples to simulate radial variations in slowness. In addition, full‐waveforms were generated using two‐and‐a‐half‐dimensional (2.5-D) FDM computer models. The finite‐difference method (FDM) computer models were used to test the validity of the ray‐theoretic approximation used in the inversion scheme and to simulate the full‐waveform sonic tool response for both radial and axial changes in formation properties. Field data examples highlighted radial changes in formation slowness caused by two separate mechanisms: water take up by swelling shales and the mechanical breakdown of the near‐borehole rock resulting from stress relief caused by the drilling process. Finally, refracted sonic arrivals from near‐borehole bed boundaries were identified in a horizontal well setting. Using refractions arriving beyond the headwave, a 2-D map of formation slowness was computed in the reservoir away from the borehole. Interpretation of the slowness map resulted in an estimation of the stand‐off of the horizontal borehole from the reservoir boundary.

Strategies for imaging with Marchenko-retrieved Green’s functions

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. Q23-Q37 ◽  
Author(s):  
Satyan Singh ◽  
Roel Snieder
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Imaging Techniques ◽  
Imaging Condition ◽  
Surface Reflection ◽  
Reflection Data ◽  
First Arrival ◽  
The One

Recent papers show that imaging with the retrieved Green’s function constructed by the Marchenko equations, called Marchenko imaging, reduces artifacts from internal and free-surface multiples compared with standard imaging techniques. Even though artifacts are reduced, they can still be present in the image, depending on the imaging condition used. We have found that when imaging with the up- and downgoing Green’s functions, the multidimensional deconvolution (MDD) imaging condition yields better images than correlation and deconvolution. “Better” in this case means improved resolution, fewer artifacts, and a closer match with the true reflection coefficient of the model. We have determined that the MDD imaging condition only uses primaries to construct the image, whereas multiples are implicitly subtracted in the imaging step. Consequently, combining the first arrival of the downgoing Green’s function with the complete upgoing Green’s function produces superior (or at least equivalent) images than using the one-way Green’s functions because the first arrival of the downgoing Green’s function excludes all the downgoing multiply reflected waves. We also find that standard imaging algorithms which use the redatumed reflection response, constructed with the one-way Green’s functions, produce images with reduced artifacts from multiples compared with standard imaging conditions, which use surface reflection data. All imaging methods that rely on the Marchenko equations require the same inputs as standard imaging techniques: the reflection response at the surface and a smooth estimate of the subsurface velocities.

Robust refraction statics solution and near-surface velocity model building using feedback from reflection data

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. U63-U77
Author(s):  
Bernard K. Law ◽  
Daniel Trad
Keyword(s):  
Model Building ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Surface Velocity ◽  
Near Surface ◽  
Arrival Times ◽  
Reflection Data ◽  
Velocity Model Building ◽  
First Arrival ◽  
Refraction Data

An accurate near-surface velocity model is critical for weathering statics correction and initial model building for depth migration and full-waveform inversion. However, near-surface models from refraction inversion often suffer from errors in refraction data, insufficient sampling, and over-simplified assumptions used in refraction algorithms. Errors in refraction data can be caused by picking errors resulting from surface noise, attenuation, and dispersion of the first-arrival energy with offset. These errors are partially compensated later in the data flow by reflection residual statics. Therefore, surface-consistent residual statics contain information that can be used to improve the near-surface velocity model. We have developed a new dataflow to automatically include median and long-wavelength components of surface-consistent reflection residual statics. This technique can work with any model-based refraction solution, including grid-based tomography methods and layer-based methods. We modify the cost function of the refraction inversion by adding model and data weights computed from the smoothed surface-consistent residual statics. By using an iterative inversion, these weights allow us to update the near-surface velocity model and to reject first-arrival picks that do not fit the updated model. In this nonlinear optimization workflow, the refraction model is derived from maximizing the coherence of the reflection energy and minimizing the misfit between model arrival times and the recorded first-arrival times. This approach can alleviate inherent limitations in shallow refraction data by using coherent reflection data.

scholarly journals Superconformal boundaries in 4 − ϵ dimensions

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Aleix Gimenez-Grau ◽  
Pedro Liendo ◽  
Philine van Vliet
Keyword(s):  
Three Dimensional ◽  
Spacetime Dimension ◽  
Perfect Agreement ◽  
Bootstrap Analysis ◽  
First Order ◽  
Free Theory ◽  
First Order Correction ◽  
Free Parameters ◽  
Superconformal Theories ◽  
Zumino Model

Abstract Boundaries in three-dimensional $$ \mathcal{N} $$ N = 2 superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining 2d boundary algebra exhibits $$ \mathcal{N} $$ N = (0, 2) or $$ \mathcal{N} $$ N = (1) supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $$ \mathcal{N} $$ N = (1) supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the ϵ-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a super-symmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.

Sign in / Sign up

Export Citation Format

Share Document