Fast acoustic velocity tomography of focusing operators

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. R121-R131 ◽  
Author(s):  
Hu Jin ◽  
George A. McMechan
Keyword(s):  
Constant Velocity ◽  
Null Space ◽  
Focal Point ◽  
Grid Point ◽  
Synthetic Data ◽  
Velocity Model ◽  
The Stability ◽  
Starting Model ◽  
Velocity Tomography ◽  
Focus Point

A 2D velocity model was estimated by tomographic imaging of overlapping focusing operators that contain one-way traveltimes, from common-focus points to receivers in an aperture along the earth’s surface. The stability and efficiency of convergence and the quality of the resulting models were improved by a sequence of ideas. We used a hybrid parameterization that has an underlying grid, upon which is superimposed a flexible, pseudolayer model. We first solved for the low-wavenumber parts of the model (approximating it as constant-velocity pseudo layers), then we allowed intermediate wavenumbers (allowing the layers to have linear velocity gradients), and finally did unconstrained iterations to add the highest wavenumber details. Layer boundaries were implicitly defined by focus points that align along virtual marker (reflector) horizons. Each focus point sampled an area bounded by the first and last rays in the data aperture at the surface; this reduced the amount of computation and the size of the effective null space of the solution. Model updates were performed simultaneously for the velocities and the local focus point positions in two steps; local estimates were performed independently by amplitude semblance for each focusing operator within its area of dependence, followed by a tomographic weighting of the local estimates into a global solution for each grid point, subject to the constraints of the parameterization used at that iteration. The system of tomographic equations was solved by simultaneous iterative reconstruction, which is equivalent to a least-squares solution, but it does not involve a matrix inversion. The algorithm was successfully applied to synthetic data for a salt dome model using a constant-velocity starting model; after a total of 25 iterations, the velocity error was [Formula: see text] and the final mean focal point position error was [Formula: see text] wavelength.

scholarly journals Rapid estimation of earthquake locations using waveform traveltimes

2019 ◽  
Vol 217 (3) ◽  
pp. 1727-1741 ◽  
Author(s):  
D W Vasco ◽  
Seiji Nakagawa ◽  
Petr Petrov ◽  
Greg Newman
Keyword(s):  
Standard Error ◽  
Random Noise ◽  
Grid Point ◽  
Synthetic Data ◽  
Velocity Model ◽  
Source Location ◽  
Model Errors ◽  
Average Deviation ◽  
Origin Time ◽  
Data Set

SUMMARY We introduce a new approach for locating earthquakes using arrival times derived from waveforms. The most costly computational step of the algorithm scales as the number of stations in the active seismographic network. In this approach, a variation on existing grid search methods, a series of full waveform simulations are conducted for all receiver locations, with sources positioned successively at each station. The traveltime field over the region of interest is calculated by applying a phase picking algorithm to the numerical wavefields produced from each simulation. An event is located by subtracting the stored traveltime field from the arrival time at each station. This provides a shifted and time-reversed traveltime field for each station. The shifted and time-reversed fields all approach the origin time of the event at the source location. The mean or median value at the source location thus approximates the event origin time. Measures of dispersion about this mean or median time at each grid point, such as the sample standard error and the average deviation, are minimized at the correct source position. Uncertainty in the event position is provided by the contours of standard error defined over the grid. An application of this technique to a synthetic data set indicates that the approach provides stable locations even when the traveltimes are contaminated by additive random noise containing a significant number of outliers and velocity model errors. It is found that the waveform-based method out-performs one based upon the eikonal equation for a velocity model with rapid spatial variations in properties due to layering. A comparison with conventional location algorithms in both a laboratory and field setting demonstrates that the technique performs at least as well as existing techniques.

Tomographic inversion by matrix transformation

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE35-VE38 ◽  
Author(s):  
Jonathan Liu ◽  
Lorie Bear ◽  
Jerry Krebs ◽  
Raffaella Montelli ◽  
Gopal Palacharla
Keyword(s):  
Linear System ◽  
Seismic Velocity ◽  
Synthetic Data ◽  
Velocity Model ◽  
Matrix Transformation ◽  
Uniform Grid ◽  
Complex Structures ◽  
Tomographic Inversion ◽  
Velocity Models ◽  
The Stability

We have developed a new method to build seismic velocity models for complex structures. In our approach, we use a spatially nonuniform parameterization of the velocity model in tomography and a uniform grid representation of the same velocity model in ray tracing to generate the linear system of tomographic equations. Subsequently, a matrix transformation is applied to the system of equations to produce a new linear system of tomographic equations using nonuniform parameterization. In this way, we improved the stability of tomographic inversion without adding computing costs. We tested the effectiveness of our process on a 3D synthetic data example.

Postmap migration of crosswell reflection seismic data

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 135-146 ◽  
Author(s):  
Joongmoo Byun ◽  
James W. Rector III ◽  
Tamas Nemeth
Keyword(s):  
Constant Velocity ◽  
Guided Waves ◽  
Synthetic Data ◽  
Velocity Model ◽  
Lateral Resolution ◽  
Velocity Variation ◽  
Coherent Noise ◽  
Image Domain ◽  
Seismic Reflection Data ◽  
Specific Implementation

Vertical seismic profiling/common depth point (VSP‐CDP) mapping is often preferred to crosswell migration when imaging crosswell seismic reflection data. The principal advantage of VSP‐CDP mapping is that it can be configured as a one‐to‐one operation between data in the acquisition domain and data in the image domain and therefore does not smear coherent noise such as tube waves, guided waves, and converted waves as crosswell migration could. However, unlike crosswell migration, VSP‐CDP mapping cannot collapse diffractions; therefore, the lateral resolution of reflection events suffers. We present a migration algorithm that is applied to the crosswell data after they have been mapped. By performing crosswell migration in two distinct steps—mapping followed by diffraction stacking—noise events can be identified and filtered in the mapped domain without smearing effects commonly associated with conventional crosswell migration operators. Tests on noise‐free synthetic crosswell data indicate that the two‐step migration yields results nearly identical with conventional crosswell migration. Our specific implementation of the two‐step migration algorithm maps the data using an estimate of the interwell velocity field and then performs diffraction stacking using a constant‐velocity assumption. The migrated results are confined to the mapped region to reduce edge effects commonly associated with conventional crosswell migration. Results from synthetic data indicate that the constant‐velocity assumption used for diffraction stacking is remarkably robust, even for models with large vertical velocity variation. It is, however, important that the data are mapped with the correct interwell velocity model. After applying postmap migration to two field data sets mapped by VSP‐CDP mapping, better fault resolution was achieved and the lateral resolution was improved significantly.

Estimating a starting model for full-waveform inversion using a global optimization method

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. R211-R223 ◽  
Author(s):  
Debanjan Datta ◽  
Mrinal K. Sen
Keyword(s):  
Global Optimization ◽  
Local Minimum ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Optimization Method ◽  
Full Waveform Inversion ◽  
Global Optimization Method ◽  
Full Waveform ◽  
Starting Model

Full-waveform inversion (FWI) has become a popular method to estimate elastic earth properties from seismograms. It is formulated as a data-fitting least-squares minimization problem that iteratively updates an initial velocity model with the scaled gradient of the misfit until a satisfactory match between the real and synthetic data is obtained. However, such a local optimization approach can converge to a local minimum if the starting model used is not close enough to an optimal model. We have developed a two-step process in which we first estimate a starting model using a global optimization method. Unlike local optimization methods, a global optimization method starts with a random starting model and is not generally susceptible to be trapped in a local minimum. The starting model for FWI that we aim to estimate is sparsely parameterized and contains a set of interfaces and velocities that are used to represent the entire velocity model. We have obtained the depth of the interfaces and the velocities by minimizing the data misfit in the least-squares sense using a global optimization method called very fast simulated annealing (VFSA). Once the sparse velocity model was obtained from VFSA, we used that as a starting model in a conventional gradient-based FWI to obtain the final model. We have applied the proposed method to one synthetic data set and two field data sets from offshore India. The proposed method was able to estimate a velocity model that was not cycle skipped for realistic frequency bands. We have demonstrated that with the proper choice of model parameterization and optimization parameters, the global and gradient optimization algorithms converge in a finite number of iterations. We have determined that the resulting algorithm is computationally feasible in two dimensions and accurate for practical implementation of FWI.

scholarly journals Adaptive waveform inversion: Theory

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. R429-R445 ◽  
Author(s):  
Michael Warner ◽  
Lluís Guasch
Keyword(s):  
Waveform Inversion ◽  
Computational Cost ◽  
Synthetic Data ◽  
Velocity Model ◽  
Seismic Inversion ◽  
New Method ◽  
Low Frequencies ◽  
Full Waveform ◽  
True Model ◽  
Starting Model

Conventional full-waveform seismic inversion attempts to find a model of the subsurface that is able to predict observed seismic waveforms exactly; it proceeds by minimizing the difference between the observed and predicted data directly, iterating in a series of linearized steps from an assumed starting model. If this starting model is too far removed from the true model, then this approach leads to a spurious model in which the predicted data are cycle skipped with respect to the observed data. Adaptive waveform inversion (AWI) provides a new form of full-waveform inversion (FWI) that appears to be immune to the problems otherwise generated by cycle skipping. In this method, least-squares convolutional filters are designed that transform the predicted data into the observed data. The inversion problem is formulated such that the subsurface model is iteratively updated to force these Wiener filters toward zero-lag delta functions. As that is achieved, the predicted data evolve toward the observed data and the assumed model evolves toward the true model. This new method is able to invert synthetic data successfully, beginning from starting models and under conditions for which conventional FWI fails entirely. AWI has a similar computational cost to conventional FWI per iteration, and it appears to converge at a similar rate. The principal advantages of this new method are that it allows waveform inversion to begin from less-accurate starting models, does not require the presence of low frequencies in the field data, and appears to provide a better balance between the influence of refracted and reflected arrivals upon the final-velocity model. The AWI is also able to invert successfully when the assumed source wavelet is severely in error.

Pushing the limits of seismic imaging, Part I: Prestack migration in terms of double dynamic focusing

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 937-953 ◽  
Author(s):  
A. J. Berkhout
Keyword(s):  
Error Analysis ◽  
Evaluation Method ◽  
Structural Information ◽  
Grid Point ◽  
Velocity Model ◽  
Migration Process ◽  
Prestack Migration ◽  
Post Evaluation ◽  
Focused Beams ◽  
Focus Point

In this paper, the author proposes to extend the synthesis of areal sources (controlled emission) to the synthesis of areal detectors (controlled detection) such that the concept of numerical focusing can be formulated as a special version of target‐oriented synthesis. As a consequence, the insight in the complex prestack migration process can be improved significantly by making use of the concepts “focusing in emission” and “focusing in detection.” Focusing in emission transforms shot records into so‐called common focus‐point (CFP) gathers. Focusing in detection transforms CFP gathers into the prestack migration result. If structural information is sought, the focus point in emission is chosen equal to the focus point in detection: confocal version of CFP migration. If rock and pore information is required as well, the focus point in emission is chosen different from the focus point in detection: bifocal version of CFP migration. Errors in the underlying macro velocity model can be better analysed than before by using CFP gathers as an intermediate migration output. The error analysis involves a comparison between each CFP gather and its related focusing operator. The quality (amplitude accuracy, noise content, resolution) of prestack migration results can be evaluated effectively at each subsurface grid point by analysing the two focused beams involved (pre‐evaluation) and by analyzing the so‐called grid‐point gather (post‐evaluation). The proposed pre‐evaluation method may lead to an improved way of coping with “acquisition footprints” of relatively sparse source and receiver coverage.

Pushing the limits of seismic imaging, Part II: Integration of prestack migration, velocity estimation, and AVO analysis

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 954-969 ◽  
Author(s):  
A. J. Berkhout
Keyword(s):  
Grid Point ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Migration Process ◽  
Inversion Process ◽  
Prestack Migration ◽  
Grid Points ◽  
Updating Procedure ◽  
Amplitude Versus ◽  
Focus Point

The author proposes an operator‐driven prestack migration scheme that is based on the synthesis of common focus‐point (CFP) gathers. Each CFP gather represents the response of a synthesized source array that aims at the illumination of one subsurface gridpoint (focus point). The involved synthesis operator is referred to as the focusing operator. If the time‐reversed focusing operator and its related focus‐point response have equal traveltimes, then the underlying macro velocity model is correct and the focus‐point response in the CFP gather is stacked by weighted addition along the common traveltime curve (CFP‐stacking), yielding the prestack migration result at the subsurface grid point under consideration. If the time‐reversed focusing operator and its related focus‐point response have different traveltimes, then the underlying macro velocity model is incorrect and the correct focusing operator can be derived from the two traveltime curves. A simple updating procedure is proposed. The total CFP migration process of synthesis, updating, and stacking is repeated for all subsurface grid points of interest, leading to the prestack migration result in one‐way image time together with a distribution of updated focusing operators. In a postprocessing step, all operator traveltime information can be used to derive a velocity model for the time‐to‐depth conversion process. Hence, in the presented “CFP technology” the author proposes to estimate the velocity model from the correct focusing operators by a global inversion process after the migration process has been carried out (“beyond depth migration”). For each subsurface grid point, the amplitudes along the pairs of updated traveltime curves provide amplitude‐versus‐offset (AVO) information. In addition, by introducing the grid‐point gather with the aid of an extension of the second focusing process, the author shows that this gather leads to the extraction of pre‐ and postcritical amplitude‐versus‐ray parameter (AVP) information at each grid point. Finally, just as a velocity model can be estimated from all grid‐point‐oriented traveltime information, a lithology model can be estimated from all grid‐point—oriented amplitude information by a postimaging global inversion process.

TITIK FOKUS ILOKUSI ARTIKEL PEMENANG PERTAMA LOMBA PENULISAN OPINI TINGKAT SLTA SEKALIMANTAN SELATAN

Jurnal KATA ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 371
Author(s):  
Rissari Yayuk
Keyword(s):  
High School ◽  
Data Analysis ◽  
Focal Point ◽  
Senior High School ◽  
School Level ◽  
High School Level ◽  
Purposive Sampling ◽  
Collection Data ◽  
Focus Point ◽  
Opinion Writing

<p><em>This study examines the focal point of illustration of the first winner of the contest for writing opinion of the senior high school level in South Kalimantan. This study aims to describe 1) the focus point of illustration of the title of the first winner of the contest writing opinion of the senior high school level in South Kalimantan? 2) the focal point of information information of the first winner of writing contest for high school level opinion in South Kalimantan; 3) the focal point of illocution of the moral message of the first winner of the high school opinion writing contest in South Kalimantan. The study was conducted in October 2016 at Balai Bahasa Balai. The method used is qualitative deskreptif. The technique used in this paper is the sampling purposive sampling. The sample used as data is the first winner of the contest for writing the opinion of the senior high school level in South Kalimantan, in South Kalimantan Language Hall, in 2016. This first winner is named Norhidayah, a student of SMAN 4 Banjarbaru, with the title of Language Role in Introducing Children of Nation. Data analysis is done by steps, data collection, data identification, classification, selection and interpretation. The results of data analysis are presented in ordinary words with technical terminology. Based on the results of the study of the focal point of the article, the first winner of the South Kalimantan high school opinion writing contest includes the focus point of the title illusion, the focus point of information illocution, and the focus point of the illustration of the moral mandate. The focus of the title illustration can be seen in the meaning of its ilokusinya, language, and suitability of the theme in the title. The focus point of the information illumination of the article can be seen in its meaning of ilokusinya, its language style, and the type of discourse. The focus point of the illustration of its moral mandate can be seen in the author's expectations contained in the title, the focus of the information, and on the final paragraph of the paper</em></p><p><em><br /></em></p><p>Masalah yang dibahasa mengenai titik fokus ilokusi  artikel pemenang pertama  lomba penulisan opini tingkat SLTA se-Kalimantan Selatan. Penelitian ini bertujuan mendeskripsikan 1) titik fokus ilokusi judul artikel pemenang pertama  lomba penulisan opini tingkat SLTA se-Kalimantan Selatan? 2) titik fokus ilokusi informasi artikel pemenang pertama  lomba penulisan opini tingkat SLTA se-Kalimantan Selatan; 3) titik fokus ilokusi amanat moral  artikel pemenang pertama  lomba penulisan opini tingkat SLTA se-Kalimantan Selatan. Penelitian ini dilaksanakan pada bulan Oktober 2016 di Balai Bahasa Kalimantan Selatan. Metode yang digunakan adalah deskreptif kualitatif. Teknik yang digunakan dalam tulisan ini adalah pengambilan sampel purposive sampling. Sampel yang dijadikan data adalah artikel pemenang pertama lomba penulisan opini tingkat SLTA se-Kalimantan Selatan, di Balai Bahasa Kalimantan Selatan, tahun 2016. Pemenang pertama ini bernama Norhidayah, siswa SMAN 4 Banjarbaru, dengan judul Peran Bahasa dalam Mencerdaskan Anak Bangsa. Analisis data dilakukan dengan  langkah-langkah, pengumpulan data, indentifikasi data, klasifikasi, seleksi dan  interpretasi. Hasil analisis data disajikan dengan kata-kata biasa dengan terminologi yang teknis sifatnya. Berdasarkan hasil kajian titik fokus ilokusi artikel pemenang pertama  lomba penulisan opini tingkat SLTA se-Kalimantan Selatan  meliputi titik fokus ilokusi judul, titik fokus ilokusi  informasi , dan  titik fokus ilokusi amanat moral.Titik fokus ilokusi judul dapat dilihat pada makna ilokusinya, gaya bahasanya, daya bahasa, dan kesesuaian tema pada judul. Titik fokus ilokusi informasi artikel dapat dilihat pada makna ilokusinya, gaya bahasanya, dan jenis wacananya.Titik fokus ilokusi amanat moralnya dapat dilihat pada harapan penulis yang terdapat pada judul, fokus informasi, dan pada paragrap akhir karya tulis</p>

OPTIMAL VELOCITY MODEL WITH RELATIVE VELOCITY

2006 ◽  
Vol 17 (01) ◽  
pp. 65-73 ◽  
Author(s):  
SHIRO SAWADA
Keyword(s):  
Nonlinear Analysis ◽  
Relative Velocity ◽  
Velocity Model ◽  
Fundamental Diagram ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Optimal Velocity Model ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Good Agreement

The optimal velocity model which depends not only on the headway but also on the relative velocity is analyzed in detail. We investigate the effect of considering the relative velocity based on the linear and nonlinear analysis of the model. The linear stability analysis shows that the improvement in the stability of the traffic flow is obtained by taking into account the relative velocity. From the nonlinear analysis, the relative velocity dependence of the propagating kink solution for traffic jam is obtained. The relation between the headway and the velocity and the fundamental diagram are examined by numerical simulation. We find that the results by the linear and nonlinear analysis of the model are in good agreement with the numerical results.

Marchenko multiple elimination and full wavefield migration in a resonant pinch-out model

Geophysics ◽  
2021 ◽  
pp. 1-59
Author(s):  
Evert Slob ◽  
Lele Zhang ◽  
Eric Verschuur
Keyword(s):  
Constant Velocity ◽  
Local Minimum ◽  
Velocity Model ◽  
Dominant Frequency ◽  
Data Sampling ◽  
Multiple Reflections ◽  
Linear Inversion ◽  
Acoustic Reflection ◽  
Reflection Data ◽  
Multiple Elimination

Marchenko multiple elimination schemes are able to attenuate all internal multiple reflections in acoustic reflection data. These can be implemented with and without compensation for two-way transmission effects in the resulting primary reflection dataset. The methods are fully automated and run without human intervention, but require the data to be properly sampled and pre-processed. Even when several primary reflections are invisible in the data because they are masked by overlapping primaries, such as in the resonant wedge model, all missing primary reflections are restored and recovered with the proper amplitudes. Investigating the amplitudes in the primary reflections after multiple elimination with and without compensation for transmission effects shows that transmission effects are properly accounted for in a constant velocity model. When the layer thickness is one quarter of the wavelength at the dominant frequency of the source wavelet, the methods cease to work properly. Full wavefield migration relies on a velocity model and runs a non-linear inversion to obtain a reflectivity model which results in the migration image. The primary reflections that are masked by interference with multiples in the resonant wedge model, are not recovered. In this case, minimizing the data misfit function leads to the incorrect reflector model even though the data fit is optimal. This method has much lower demands on data sampling than the multiple elimination schemes, but is prone to get stuck in a local minimum even when the correct velocity model is available. A hybrid method that exploits the strengths of each of these methods could be worth investigating.

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