Common‐angle migration: A strategy for imaging complex media

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1877-1894 ◽  
Author(s):  
Sheng Xu ◽  
Hervé Chauris ◽  
Gilles Lambaré ◽  
Mark Noble
Keyword(s):  
A Priori ◽  
Velocity Model ◽  
Complex Velocity ◽  
Data Set ◽  
Depth Imaging ◽  
Imaging Condition ◽  
Velocity Models ◽  
Inversion Operator ◽  
Single Fold ◽  
Lateral Variations

Complex velocity models characterized by strong lateral variations are certainly a great motivation, but also a great challenge, for depth imaging. In this context, some unexpected results can occur when using depth imaging algorithms. In general, after a common shot or common offset migration, the resulting depth images are sorted into common‐image gathers (CIG), for further processing such as migration‐based velocity analysis or amplitude‐variation‐with‐offset analysis. In this paper, we show that CIGs calculated by common‐shot or common‐offset migration can be strongly affected by artifacts, even when a correct velocity model is used for the migration. The CIGs are simply not flat, due to unexpected curved events (kinematic artifacts) and strong lateral variations of the amplitude (dynamic artifacts). Kinematic artifacts do not depend on the migration algorithm provided it can take into account lateral variations of the velocity model. This can be observed when migrating the 2‐D Marmousi dataset either with a wave‐equation migration or with a multivalued Kirchhoff migration/inversion. On the contrary, dynamic artifacts are specific to multi‐arrival ray‐based migration/inversion. This approach, which should provide a quantitative estimation of the reflectivity of the model, provides in this context dramatic results. In this paper, we propose an analysis of these artifacts through the study of the ray‐based migration/inversion operator. The artifacts appear when migrating a single‐fold subdata set with multivalued ray fields. They are due to the ambiguous focusing of individual reflected events at different locations in the image. No information is a priori available in the single‐fold data set for selecting the focusing position, while migration of multifold data would provide this information and remove the artifacts by the stack of the CIGs. Analysis of the migration/inversion operator provides a physical condition, the imaging condition, for insuring artifact free CIGs. The specific cases of common‐shot and common‐offset single‐fold gathers are studied. It appears clearly that the imaging condition generally breaks down in complex velocity models for both these configurations. For artifact free CIGs, we propose a novel strategy: compute CIGs versus the diffracting/reflecting angle. Working in the angle domain seems the natural way for unfolding multivalued ray fields, and it can be demonstrated theoretically and practically that common‐angle imaging satisfies the imaging condition in the great majority of cases. Practically, the sorting into angle gathers can not be done a priori over the data set, but is done in the inner depth migration loop. Depth‐migrated images are obtained for each angle range. A canonical example is used for illustrating the theoretical derivations. Finally, an application to the Marmousi model is presented, demonstrating the relevance of the approach.

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.

Fast and accurate dynamic raytracing in heterogeneous media

1990 ◽  
Vol 80 (5) ◽  
pp. 1284-1296
Author(s):  
Claude F. Lafond ◽  
Alan R. Levander
Keyword(s):  
Shooting Method ◽  
Heterogeneous Media ◽  
Velocity Model ◽  
Travel Times ◽  
Complex Velocity ◽  
Geometrical Spreading ◽  
Imaging Condition ◽  
Depth Migration ◽  
Velocity Models ◽  
Complex Velocity Model

Abstract We have developed a fast and accurate dynamic raytracing method for 2.5-D heterogeneous media based on the kinematic algorithm proposed by Langan et al. (1985). This algorithm divides the model into cells of constant slowness gradient, and the positions, directions, and travel times of the rays are expressed as polynomials of the travel path length, accurate to the second other in the gradient. This method is efficient because of the use of simple polynomials at each raytracing step. We derived similar polynomial expressions for the dynamic raytracing quantities by integrating the raytracing system and expanding the solutions to the second order in the gradient. This new algorithm efficiently computes the geometrical spreading, amplitude, and wavefront curvature on individual rays. The two-point raytracing problem is solved by the shooting method using the geometrical spreading. Paraxial corrections based on the wavefront curvature improve the accuracy of the travel time and amplitude at a given receiver. The computational results for two simple velocity models are compared with those obtained with the SEIS83 seismic modeling package (Cerveny and Psencik, 1984); this new method is accurate for both travel times and amplitudes while being significantly faster. We present a complex velocity model that shows that the algorithm allows for realistic models and easily computes rays in structures that pose difficulties for conventional methods. The method can be extended to raytracing in 3-D heterogeneous media and can be used as a support for a Gaussian beam algorithm. It is also suitable for computing the Green's function and imaging condition needed for prestack depth migration.

Interferometric imaging condition for wave-equation migration

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. S47-S61 ◽  
Author(s):  
Paul Sava ◽  
Oleg Poliannikov
Keyword(s):  
Large Scale ◽  
Wigner Distribution ◽  
Random Noise ◽  
Velocity Model ◽  
Distribution Functions ◽  
Small Scale ◽  
Interferometric Imaging ◽  
Imaging Data ◽  
Imaging Condition ◽  
Velocity Models

The fidelity of depth seismic imaging depends on the accuracy of the velocity models used for wavefield reconstruction. Models can be decomposed in two components, corresponding to large-scale and small-scale variations. In practice, the large-scale velocity model component can be estimated with high accuracy using repeated migration/tomography cycles, but the small-scale component cannot. When the earth has significant small-scale velocity components, wavefield reconstruction does not completely describe the recorded data, and migrated images are perturbed by artifacts. There are two possible ways to address this problem: (1) improve wavefield reconstruction by estimating more accurate velocity models and image using conventional techniques (e.g., wavefield crosscorrelation) or (2) reconstruct wavefields with conventional methods using the known background velocity model but improve the imaging condition to alleviate the artifacts caused by the imprecise reconstruction. Wedescribe the unknown component of the velocity model as a random function with local spatial correlations. Imaging data perturbed by such random variations is characterized by statistical instability, i.e., various wavefield components image at wrong locations that depend on the actual realization of the random model. Statistical stability can be achieved by preprocessing the reconstructed wavefields prior to the imaging condition. We use Wigner distribution functions to attenuate the random noise present in the reconstructed wavefields, parameterized as a function of image coordinates. Wavefield filtering using Wigner distribution functions and conventional imaging can be lumped together into a new form of imaging condition that we call an interferometric imaging condition because of its similarity to concepts from recent work on interferometry. The interferometric imaging condition can be formulated both for zero-offset and for multioffset data, leading to robust, efficient imaging procedures that effectively attenuate imaging artifacts caused by unknown velocity models.

Nonlinear velocity inversion by a two‐step Monte Carlo method.

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 577-590 ◽  
Author(s):  
Side Jin ◽  
Raul Madariaga
Keyword(s):  
Monte Carlo ◽  
Velocity Model ◽  
Small Scale ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Ray Theory ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Reference Velocity

Seismic reflection data contain information on small‐scale impedance variations and a smooth reference velocity model. Given a reference velocity model, the reflectors can be obtained by linearized migration‐inversion. If the reference velocity is incorrect, the reflectors obtained by inverting different subsets of the data will be incoherent. We propose to use the coherency of these images to invert for the background velocity distribution. We have developed a two‐step iterative inversion method in which we separate the retrieval of small‐scale variations of the seismic velocity from the longer‐period reference velocity model. Given an initial background velocity model, we use a waveform misfit‐functional for the inversion of small‐scale velocity variations. For this linear step we use the linearized migration‐inversion method based on ray theory that we have recently developed with Lambaré and Virieux. The reference velocity model is then updated by a Monte Carlo inversion method. For the nonlinear inversion of the velocity background, we introduce an objective functional that measures the coherency of the short wavelength components obtained by inverting different common shot gathers at the same locations. The nonlinear functional is calculated directly in migrated data space to avoid expensive numerical forward modeling by finite differences or ray theory. Our method is somewhat similar to an iterative migration velocity analysis, but we do an automatic search for relatively large‐scale 1-D reference velocity models. We apply the nonlinear inversion method to a marine data set from the North Sea and also show that nonlinear inversion can be applied to realistic scale data sets to obtain a laterally heterogeneous velocity model with a reasonable amount of computer time.

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.

Inversion of seismic refraction and reflection data for building long-wavelength velocity models

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. R81-R93 ◽  
Author(s):  
Haiyang Wang ◽  
Satish C. Singh ◽  
Francois Audebert ◽  
Henri Calandra
Keyword(s):  
Wave Equation ◽  
Short Wavelength ◽  
Velocity Model ◽  
Density Model ◽  
Data Set ◽  
Reflected Waves ◽  
Long Wavelength ◽  
Velocity Models ◽  
Computation Efficiency ◽  
Refracted Waves

Long-wavelength velocity model building is a nonlinear process. It has traditionally been achieved without appealing to wave-equation-based approaches for combined refracted and reflected waves. We developed a cascaded wave-equation tomography method in the data domain, taking advantage of the information contained in the reflected and refracted waves. The objective function was the traveltime residual that maximized the crosscorrelation function between real and synthetic data. To alleviate the nonlinearity of the inversion problem, refracted waves were initially used to provide vertical constraints on the velocity model, and reflected waves were then included to provide lateral constraints. The use of reflected waves required scale separation. We separated the long- and short-wavelength subsurface structures into velocity and density models, respectively. The velocity model update was restricted to long wavelengths during the wave-equation tomography, whereas the density model was used to absorb all the short-wavelength impedance contrasts. To improve the computation efficiency, the density model was converted into the zero-offset traveltime domain, where it was invariant to changes of the long-wavelength velocity model. After the wave-equation tomography has derived an optimized long-wavelength velocity model, full-waveform inversion was used to invert all the data to retrieve the short-wavelength velocity structures. We developed our method in two synthetic tests and then applied it to a marine field data set. We evaluated the results of the use of refracted and reflected waves, which was critical for accurately building the long-wavelength velocity model. We showed that our wave-equation tomography strategy was robust for the real data application.

Upper crustal structure at the KTB drilling site from ambient noise tomography

2020 ◽  
Author(s):  
Ehsan Qorbani ◽  
Irene Bianchi ◽  
Petr Kolínský ◽  
Dimitri Zigone ◽  
Götz Bokelmann
Keyword(s):  
Ambient Noise ◽  
Velocity Model ◽  
Ambient Noise Tomography ◽  
Data Set ◽  
Crustal Rocks ◽  
Velocity Models ◽  
Path Coverage ◽  
Passive Seismic ◽  
Cross Correlations ◽  
Drilling Site

<p>In this study, we show results from ambient noise tomography at the KTB drilling site, Germany. The Continental Deep Drilling Project, or ‘Kontinentales Tiefbohrprogramm der Bundesrepublik Deutschland’ (KTB) is at the northwestern edge of the Bohemian Massif and is located on the Variscan belt of Europe. During the KTB project crustal rocks have been drilled down to 9 km depth and several active seismic studies have been performed in the surrounding. The KTB area therefore presents an ideal test area for testing and verifying the potential resolution of passive seismic techniques. The aim of this study is to present a new shear-wave velocity model of the area while comparing the results to the previous velocity models and hints for anisotropy depicted by former passive and active seismological studies. We use a unique data set composed of two years of continuous data recorded at nine 3-component temporary stations installed from July 2012 to July 2014 located on top and vicinity of the drilling site. Moreover, we included a number of permanent stations in the region in order to improve the path coverage and density. Cross correlations of ambient noise are computed between the station pairs using all possible combination of three-component data. Dispersion curves of surface waves are extracted and are then inverted to obtain group velocity maps. We present here a new velocity model of the upper crust of the area, which shows velocity variations at short scales that correlate well with geology in the region.</p>

High-resolution depth imaging of long-offset 2D data using full-waveform inversion: The Malvinas Basin, Argentina

2019 ◽  
Vol 38 (3) ◽  
pp. 220-225
Author(s):  
Laurence Letki ◽  
Mike Saunders ◽  
Monica Hoppe ◽  
Milos Cvetkovic ◽  
Lewis Goss ◽  
...  
Keyword(s):  
High Resolution ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Depth Imaging ◽  
Additional Information ◽  
Full Waveform ◽  
Seismic Image ◽  
2D Data

The Argentina Austral Malvinas survey comprises 13,784 km of 2D data extending from the shelf to the border with the Falkland Islands. The survey was acquired using a 12,000 m streamer and continuous recording technology and was processed through a comprehensive broadband prestack depth migration workflow focused on producing a high-resolution, high-fidelity data set. Source- and receiver-side deghosting to maximize the bandwidth of the data was an essential ingredient in the preprocessing. Following the broadband processing sequence, a depth-imaging workflow was implemented, with the initial model built using a time tomography approach. Several passes of anisotropic reflection tomography provided a significant improvement in the velocity model prior to full-waveform inversion (FWI). Using long offsets, FWI made use of additional information contained in the recorded wavefield, including the refracted and diving wave energy. FWI resolved more detailed velocity variations both in the shallow and deeper section and culminated in an improved seismic image.

PS Energy Imaging Condition for Microseismic Data - Part 1: Theory and Applications in 3D Isotropic Media

Geophysics ◽  
2020 ◽  
pp. 1-79
Author(s):  
Can Oren ◽  
Jeffrey Shragge
Keyword(s):  
Wave Velocity ◽  
Model Building ◽  
Velocity Model ◽  
Microseismic Monitoring ◽  
Elastic Model ◽  
S Wave ◽  
Imaging Condition ◽  
Velocity Models ◽  
Monitoring Programs ◽  
Imaging Conditions

Accurately estimating event locations is of significant importance in microseismic investigations because this information greatly contributes to the overall success of hydraulic fracturing monitoring programs. Full-wavefield time-reverse imaging (TRI) using one or more wave-equation imaging conditions offers an effective methodology for locating surface-recorded microseismic events. To be most beneficial in microseismic monitoring programs, though, the TRI procedure requires using accurate subsurface models that account for elastic media effects. We develop a novel microseismic (extended) PS energy imaging condition that explicitly incorporates the stiffness tensor and exhibits heightened sensitivity to isotropic elastic model perturbations compared to existing imaging conditions. Numerical experiments demonstrate the sensitivity of microseismic TRI results to perturbations in P- and S-wave velocity models. Zero-lag and extended microseismic source images computed at selected subsurface locations yields useful information about 3D P- and S-wave velocity model accuracy. Thus, we assert that these image volumes potentially can serve as the input into microseismic elastic velocity model building algorithms.

Velocity model estimation with data‐derived wavefront attributes

Geophysics ◽  
2004 ◽  
Vol 69 (1) ◽  
pp. 265-274 ◽  
Author(s):  
Eric Duveneck
Keyword(s):  
Velocity Model ◽  
Inversion Method ◽  
Data Set ◽  
Velocity Models ◽  
Common Reflection Surface ◽  
Data Points ◽  
Inversion Procedure ◽  
Optimum Model ◽  
Zero Offset ◽  
Kinematic Information

Kinematic information for constructing velocity models can be extracted in a robust way from seismic prestack data with the common‐reflection‐surface (CRS) stack. This data‐driven process results, in addition to a simulated zero‐offset section, in a number of wavefront attributes—wavefront curvatures and normal ray emergence angles—associated with each simulated zero‐offset sample. A tomographic inversion method is presented that uses this kinematic information to determine smooth, laterally heterogeneous, isotropic subsurface velocity models for depth imaging. The input for the inversion consists of wavefront attributes picked at a number of locations in the simulated zero‐offset section. The smooth velocity model is described by B‐splines. An optimum model is found iteratively by minimizing the misfit between the picked data and the corresponding modeled values. The required forward‐modeled quantities are obtained during each iteration by dynamic ray tracing along normal rays pertaining to the input data points. Fréchet derivatives for the tomographic matrix are calculated by ray perturbation theory. The inversion procedure is demonstrated on a 2D synthetic prestack data set.

Sign in / Sign up

Export Citation Format

Share Document