Moveout analysis of wave-equation extended images

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. S151-S161 ◽  
Author(s):  
Tongning Yang ◽  
Paul Sava
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Time Lag ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Estimation Methods ◽  
Future Application ◽  
Time Lags ◽  
Imaging Condition ◽  
Space And Time

Conventional velocity analysis applied to images produced by wave-equation migration with a crosscorrelation imaging condition uses moveout information from space lags or focusing information from time lag. However, more robust velocity-estimation methods can be designed to simultaneously take advantage of the semblance and focusing information provided by migrated images. Such a velocity estimation requires characterization of the moveout surfaces defined jointly for space- and time-lags extended images. The analytic solutions to the moveout surfaces can be derived by solving the system of equations representing the shifted source and receiver wavefields. The superposition of the surfaces from many experiments (shots) is equivalent to the envelope for the family of the individual surface. The envelopeforms a shape that can be characterized as a cone in the extended space of depth, space lag, and time lag. When imaged with the correct velocity, the apex of the cone is located at the correct reflection depth and at zero space and time lags. When imaged with the incorrect velocity, the apex of the cone shifts in the depth direction and along the time-lag axis. The characteristics of the cones are directly related to the quality of the velocity model. Thus, their analysis provides a rich source of information for velocity model-building. Synthetic examples verify the derived formulas characterizing the moveout surfaces. The analytic formulas match the numeric experiments well, demonstrating the accuracy of the formulas. Based on information provided by the extended imaging condition, future application for velocity updates can benefit from the robustness of the depth-focusing analysis and of the high resolution of the semblance analysis.

scholarly journals Seismic velocity estimation: A deep recurrent neural-network approach

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. U21-U29
Author(s):  
Gabriel Fabien-Ouellet ◽  
Rahul Sarkar
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Model Building ◽  
Seismic Velocity ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Interval Velocity ◽  
Velocity Model Building ◽  
3D Velocity Model

Applying deep learning to 3D velocity model building remains a challenge due to the sheer volume of data required to train large-scale artificial neural networks. Moreover, little is known about what types of network architectures are appropriate for such a complex task. To ease the development of a deep-learning approach for seismic velocity estimation, we have evaluated a simplified surrogate problem — the estimation of the root-mean-square (rms) and interval velocity in time from common-midpoint gathers — for 1D layered velocity models. We have developed a deep neural network, whose design was inspired by the information flow found in semblance analysis. The network replaces semblance estimation by a representation built with a deep convolutional neural network, and then it performs velocity estimation automatically with recurrent neural networks. The network is trained with synthetic data to identify primary reflection events, rms velocity, and interval velocity. For a synthetic test set containing 1D layered models, we find that rms and interval velocity are accurately estimated, with an error of less than [Formula: see text] for the rms velocity. We apply the neural network to a real 2D marine survey and obtain accurate rms velocity predictions leading to a coherent stacked section, in addition to an estimation of the interval velocity that reproduces the main structures in the stacked section. Our results provide strong evidence that neural networks can estimate velocity from seismic data and that good performance can be achieved on real data even if the training is based on synthetics. The findings for the 1D problem suggest that deep convolutional encoders and recurrent neural networks are promising components of more complex networks that can perform 2D and 3D velocity model building.

Redatuming through a salt canopy and target-oriented salt-flank imaging

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. S63-S71 ◽  
Author(s):  
Rongrong Lu ◽  
Mark Willis ◽  
Xander Campman ◽  
Jonathan Ajo-Franklin ◽  
M. Nafi Toksöz
Keyword(s):  
Velocity Gradient ◽  
Model Building ◽  
Velocity Structure ◽  
Velocity Model ◽  
Seismic Profile ◽  
Velocity Estimation ◽  
Reverse Time ◽  
Estimation Model ◽  
Depth Migration ◽  
Prestack Migration

We describe a new shortcut strategy for imaging the sediments and salt edge around a salt flank through an overburden salt canopy. We tested its performance and capabilities on 2D synthetic acoustic seismic data from a Gulf of Mexico style model. We first redatumed surface shots, using seismic interferometry, from a walkaway vertical seismic profile survey as if the source and receiver pairs had been located in the borehole at the positions of the receivers. This process creates effective downhole shot gathers by completely moving surface shots through the salt canopy, without any knowledge of overburden velocity structure. After redatuming, we can apply multiple passes of prestack migration from the reference datum of the bore-hole. In our example, first-pass migration, using only a simple vertical velocity gradient model, reveals the outline of the salt edge. A second pass of reverse-time, prestack depth migration using full two-way wave equation was performed with an updated velocity model that consisted of the velocity gradient and salt dome. The second-pass migration brings out dipping sediments abutting the salt flank because these reflectors were illuminated by energy that bounced off the salt flank, forming prismatic reflections. In this target-oriented strategy, the computationally fast redatuming process eliminates the need for the traditional complex process of velocity estimation, model building, and iterative depth migration to remove effects of the salt canopy and surrounding overburden. This might allow this strategy to be used in the field in near real time.

Velocity-estimation improvements and migration/demigration using the common-reflection surface with continuing deconvolution in the time domain

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. S229-S238 ◽  
Author(s):  
Martina Glöckner ◽  
Sergius Dell ◽  
Benjamin Schwarz ◽  
Claudia Vanelle ◽  
Dirk Gajewski
Keyword(s):  
Model Building ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Initial Time ◽  
Model Errors ◽  
Imaging Methods ◽  
Time Migration ◽  
Common Reflection Surface ◽  
The Common ◽  
And Migration

To obtain an image of the earth’s subsurface, time-imaging methods can be applied because they are reasonably fast, are less sensitive to velocity model errors than depth-imaging methods, and are usually easy to parallelize. A powerful tool for time imaging consists of a series of prestack time migrations and demigrations. We have applied multiparameter stacking techniques to obtain an initial time-migration velocity model. The velocity model building proposed here is based on the kinematic wavefield attributes of the common-reflection surface (CRS) method. A subsequent refinement of the velocities uses a coherence filter that is based on a predetermined threshold, followed by an interpolation and smoothing. Then, we perform a migration deconvolution to obtain the final time-migrated image. The migration deconvolution consists of one iteration of least-squares migration with an estimated Hessian. We estimate the Hessian by nonstationary matching filters, i.e., in a data-driven fashion. The model building uses the framework of the CRS, and the migration deconvolution is fully automated. Therefore, minimal user interaction is required to carry out the velocity model refinement and the image update. We apply the velocity refinement and migration deconvolution approaches to complex synthetic and field data.

Depth migration by the Gaussian beam summation method

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. S81-S93 ◽  
Author(s):  
Mikhail M. Popov ◽  
Nikolay M. Semtchenok ◽  
Peter M. Popov ◽  
Arie R. Verdel
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Velocity Structure ◽  
Velocity Model ◽  
Summation Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Depth Migration ◽  
Time Migration ◽  
Ray Methods

Seismic depth migration aims to produce an image of seismic reflection interfaces. Ray methods are suitable for subsurface target-oriented imaging and are less costly compared to two-way wave-equation-based migration, but break down in cases when a complex velocity structure gives rise to the appearance of caustics. Ray methods also have difficulties in correctly handling the different branches of the wavefront that result from wave propagation through a caustic. On the other hand, migration methods based on the two-way wave equation, referred to as reverse-time migration, are known to be capable of dealing with these problems. However, they are very expensive, especially in the 3D case. It can be prohibitive if many iterations are needed, such as for velocity-model building. Our method relies on the calculation of the Green functions for the classical wave equation by per-forming a summation of Gaussian beams for the direct and back-propagated wavefields. The subsurface image is obtained by cal-culating the coherence between the direct and backpropagated wavefields. To a large extent, our method combines the advantages of the high computational speed of ray-based migration with the high accuracy of reverse-time wave-equation migration because it can overcome problems with caustics, handle all arrivals, yield good images of steep flanks, and is readily extendible to target-oriented implementation. We have demonstrated the quality of our method with several state-of-the-art benchmark subsurface models, which have velocity variations up to a high degree of complexity. Our algorithm is especially suited for efficient imaging of selected subsurface subdomains, which is a large advantage particularly for 3D imaging and velocity-model refinement applications such as subsalt velocity-model improvement. Because our method is also capable of providing highly accurate migration results in structurally complex subsurface settings, we have also included the concept of true-amplitude imaging in our migration technique.

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.

Reverse time migration for microseismic sources using the geometric mean as an imaging condition

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. KS51-KS60 ◽  
Author(s):  
Nori Nakata ◽  
Gregory C. Beroza
Keyword(s):  
Time Reversal ◽  
Geometric Mean ◽  
Time Lag ◽  
Computational Cost ◽  
Velocity Model ◽  
Seismic Sources ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration

Time reversal is a powerful tool used to image directly the location and mechanism of passive seismic sources. This technique assumes seismic velocities in the medium and propagates time-reversed observations of ground motion at each receiver location. Assuming an accurate velocity model and adequate array aperture, the waves will focus at the source location. Because we do not know the location and the origin time a priori, we need to scan the entire 4D image (3D in space and 1D in time) to localize the source, which makes time-reversal imaging computationally demanding. We have developed a new approach of time-reversal imaging that reduces the computational cost and the scanning dimensions from 4D to 3D (no time) and increases the spatial resolution of the source image. We first individually extrapolate wavefields at each receiver, and then we crosscorrelate these wavefields (the product in the frequency domain: geometric mean). This crosscorrelation creates another imaging condition, and focusing of the seismic wavefields occurs at the zero time lag of the correlation provided the velocity model is sufficiently accurate. Due to the analogy to the active-shot reverse time migration (RTM), we refer to this technique as the geometric-mean RTM or GmRTM. In addition to reducing the dimension from 4D to 3D compared with conventional time-reversal imaging, the crosscorrelation effectively suppresses the side lobes and yields a spatially high-resolution image of seismic sources. The GmRTM is robust for random and coherent noise because crosscorrelation enhances signal and suppresses noise. An added benefit is that, in contrast to conventional time-reversal imaging, GmRTM has the potential to be used to retrieve velocity information by analyzing time and/or space lags of crosscorrelation, which is similar to what is done in active-source imaging.

scholarly journals Common-image gathers using the excitation amplitude imaging condition

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S261-S269 ◽  
Author(s):  
Mahesh Kalita ◽  
Tariq Alkhalifah
Keyword(s):  
Computational Cost ◽  
Velocity Model ◽  
Excitation Amplitude ◽  
Time Lags ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Disk Storage ◽  
Time Migration ◽  
Migration Velocity Analysis

Common-image gathers (CIGs) are extensively used in migration velocity analysis. Any defocused events in the subsurface offset domain or equivalently nonflat events in angle-domain CIGs are accounted for revising the migration velocities. However, CIGs from wave-equation methods such as reverse time migration are often expensive to compute, especially in 3D. Using the excitation amplitude imaging condition that simplifies the forward-propagated source wavefield, we have managed to extract extended images for space and time lags in conjunction with prestack reverse time migration. The extended images tend to be cleaner, and the memory cost/disk storage is extensively reduced because we do not need to store the source wavefield. In addition, by avoiding the crosscorrelation calculation, we reduce the computational cost. These features are demonstrated on a linear [Formula: see text] model, a two-layer velocity model, and the Marmousi model.

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