Finite-frequency traveltime tomography using the Generalized Rytov approximation

2020 ◽  
Vol 221 (2) ◽  
pp. 1412-1426 ◽  
Author(s):  
B Feng ◽  
W Xu ◽  
R S Wu ◽  
X B Xie ◽  
H Wang
Keyword(s):  
Convergence Rate ◽  
Large Scale ◽  
Frequency Theory ◽  
Seismic Exploration ◽  
Finite Frequency ◽  
Traveltime Tomography ◽  
Sensitivity Kernel ◽  
Rytov Approximation ◽  
Weak Scattering ◽  
Small Phase

SUMMARY Wave-equation-based traveltime tomography has been extensively applied in both global tomography and seismic exploration. Typically, the traveltime Fréchet derivative is obtained using the first-order Born approximation, which is only satisfied for weak velocity perturbations and small phase shifts (i.e. the weak-scattering assumption). Although the small phase-shift restriction can be handled with the Rytov approximation, the weak velocity-perturbation assumption is still a major limitation. The recently developed generalized Rytov approximation (GRA) method can achieve an improved phase accuracy of the forward-scattered wavefield, in the presence of large-scale and strong velocity perturbations. In this paper, we combine GRA with the classical finite-frequency theory and propose a GRA-based traveltime sensitivity kernel (GRA-TSK), which overcomes the weak-scattering limitation of the conventional finite-frequency methods. Numerical examples demonstrate that the accumulated time delay of forward-scattered waves caused by large-scale smooth perturbations can be correctly handled by the GRA-TSK, regardless of the magnitude of the velocity perturbations. Then, we apply the new sensitivity kernel to solve the traveltime inverse problem, and we propose a matrix-free Gauss–Newton method that has a faster convergence rate compared with the gradient-based method. Numerical tests show that, compared with the conventional adjoint traveltime tomography, the proposed GRA-based traveltime tomography can obtain a more accurate model with a faster convergence rate, making it more suited for recovering the large-intermediate scale of the velocity model, even for strong-perturbation and complex subsurface structures.

Rytov-approximation-based wave-equation traveltime tomography

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R289-R297 ◽  
Author(s):  
Bo Feng ◽  
Wenjun Xu ◽  
Fei Luo ◽  
Huazhong Wang
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Born Approximation ◽  
Model Space ◽  
Finite Frequency ◽  
Space Vector ◽  
Traveltime Tomography ◽  
Sensitivity Kernel ◽  
Rytov Approximation ◽  
Matrix Free

Most finite-frequency traveltime tomography methods are based on the Born approximation, which requires that the scale of the velocity heterogeneity and the magnitude of the velocity perturbation should be small enough to satisfy the Born approximation. On the contrary, the Rytov approximation works well for large-scale velocity heterogeneity. Typically, the Rytov-approximation-based finite-frequency traveltime sensitivity kernel (Rytov-FFTSK) can be obtained by integrating the phase-delay sensitivity kernels with a normalized weighting function, in which the calculation of sensitivity kernels requires the numerical solution of Green’s function. However, solving the Green’s function explicitly is quite computationally demanding, especially for 3D problems. To avoid explicit calculation of the Green’s function, we show that the Rytov-FFTSK can be obtained by crosscorrelating a forward-propagated incident wavefield and reverse-propagated adjoint wavefield in the time domain. In addition, we find that the action of the Rytov-FFTSK on a model-space vector, e.g., the product of the sensitivity kernel and a vector, can be computed by calculating the inner product of two time-domain fields. Consequently, the Hessian-vector product can be computed in a matrix-free fashion (i.e., first calculate the product of the sensitivity kernel and a model-space vector and then calculate the product of the transposed sensitivity kernel and a data-space vector), without forming the Hessian matrix or the sensitivity kernels explicitly. We solve the traveltime inverse problem with the Gauss-Newton method, in which the Gauss-Newton equation is approximately solved by the conjugate gradient using our matrix-free Hessian-vector product method. An example with a perfect acquisition geometry found that our Rytov-approximation-based traveltime inversion method can produce a high-quality inversion result with a very fast convergence rate. An overthrust synthetic data test demonstrates that large- to intermediate-scale model perturbations can be recovered by diving waves if long-offset acquisition is available.

Cross-borehole tomography with correlation delay times

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. R1-R12 ◽  
Author(s):  
E. Diego Mercerat ◽  
Guust Nolet ◽  
Christophe Zaroli
Keyword(s):  
Time Window ◽  
Body Wave ◽  
Wave Dispersion ◽  
Spectral Element ◽  
Frequency Theory ◽  
P Wave ◽  
Checkerboard Pattern ◽  
Finite Frequency ◽  
Delay Times ◽  
Window Selection

We evaluated a comprehensive numerical experiment of finite-frequency tomography with ray-based (“banana-doughnut”) kernels that tested all aspects of this method, starting from the generation of seismograms in a 3D model, the window selection, and the crosscorrelation with seismograms predicted for a background model, to the final regularized inversion. In particular, we tested if the quasilinearity of crosscorrelation delays allowed us to forego multiple (linearized) iterations in the case of strong reverberations characterizing multiple scattering and the gain in resolution that can be obtained by observing body-wave dispersion. Contrary to onset times, traveltimes observed by crosscorrelation allowed us to exploit energy arriving later in the time window centered in the P-wave or any other indentifiable ray arrival, either scattered from, or diffracted around, lateral heterogeneities. We tested using seismograms calculated by the spectral element method in a cross-borehole experiment conducted in a 3D checkerboard cube. The use of multiple frequency bands allowed us to estimate body-wave dispersion caused by diffraction effects. The large velocity contrast (10%) and the regularity of the checkerboard pattern caused severe reverberations that arrived late in the crosscorrelation windows. Nevertheless, the model resulting from the inversion with a data fit with reduced [Formula: see text] resulted in an excellent correspondence with the input model and allowed for a complete validation of the linearizations that lay at the basis of the theory. The use of multiple frequencies led to a significant increase in resolution. Moreover, we evaluated a case in which the sign of the anomalies in the checkerboard was systematically reversed in the ray-theoretical solution, a clear demonstration of the reality of the “doughnut-hole” effect. The experiment validated finite-frequency theory and disqualified ray-theoretical inversions of crosscorrelation delay times.

Imaging the Nechako Basin, British Columbia, using ambient seismic noise1This article is one of a series of papers published in this Special Issue on the theme of New insights in Cordilleran Intermontane geoscience: reducing exploration risk in the mountain pine beetle-affected area, British Columbia.

2011 ◽  
Vol 48 (6) ◽  
pp. 1038-1049 ◽  
Author(s):  
O.A. Idowu ◽  
A.W. Frederiksen ◽  
J.F. Cassidy
Keyword(s):  
British Columbia ◽  
Surface Wave ◽  
Group Velocity ◽  
Large Scale ◽  
Green's Functions ◽  
Green’S Functions ◽  
Noise Analysis ◽  
Sedimentary Basins ◽  
Seismic Exploration ◽  
Velocity Models

The Nechako Basin in British Columbia, Canada is suspected to have hydrocarbon potential. However, it has been a difficult basin to explore because of the presence of Tertiary volcanic outcrop. The volcanic outcrop makes the use of conventional seismic exploration methods difficult owing to a strong velocity inversion at its base. An alternative is the passive source method known as ambient noise surface wave tomography. The method, which examines the high-frequency surface wave field that is obtained from noise analysis, is sensitive to large-scale crustal structure and has been successfully applied to measuring the depths of sedimentary basins. Station-to-station Green’s functions within the basin were estimated by cross-correlating the vertical components of the seismic noise data recorded by 12 POLARIS (Portable Observatories for Lithosphere Analysis and Research Investigating Seismicity) and CNSN (Canadian National Seismgraph Network) seismic stations between September 2006 and November 2007. The resulting Green’s functions were dominated by Rayleigh waves. The dispersion characteristics of the Rayleigh waveforms were measured within the microseismic band. Inversion of the dispersion curves produced 1-D and 2-D thickness models and 2-D group velocity models for the Nechako Basin and its surrounding region. The velocity models indicate two low group velocity structures within the basin that might represent sedimentary packages, and some pockets of high-velocity zones that show the presence of volcanic rocks within and on the basin. The thickness models indicated the presence of about six different velocity layers, in which the average thickness of the basin and the crust are ∼4.8 and 30–34 km, respectively.

The formation of new oceanic crust

1965 ◽  
Vol 258 (1088) ◽  
pp. 123-136 ◽  
Keyword(s):  
Oceanic Crust ◽  
Red Sea ◽  
Gulf Of California ◽  
Large Scale ◽  
Continental Drift ◽  
Active Regions ◽  
Seismic Exploration ◽  
Seismic Velocities ◽  
Crustal Structures ◽  
Rift Zones

Seismic exploration at sea has established that the oceanic crust is completely different from that of the continents. If we accept continental drift, it is therefore necessary to invoke a mechanism for the evolution of new oceanic crust. An attempt is made to locate regions where new oceanic crust may be forming and it is suggested that these regions are related to regions of uprising convection in the mantle. The crustal structures beneath the Red Sea and the Gulf of California are very similar and closer to oceanic than continental. As these are seismically active regions of extension, it seems reasonable to suppose that they represent areas where new oceanic crust is evolving in regions of continental break-up. These rift zones are in continuity with the seismically active oceanic rifts where similar seismic velocities (about 7 km/s) have been found and it is inferred that the oceanic rifts also represent regions where new oceanic crust is evolving. These are generally near the centres of the oceans. The tensional rift zones which are regions of shallow seismicity help to locate regions of rising convection currents in the mantle. It is further suggested that regions of deep and intermediate focus earthquakes locate regions of descending convection currents and maps of earthquake distributions are used to reveal a possible large-scale pattern of mantle convection. It is supposed that new oceanic crust evolves over the rising convection currents. A study is therefore made of the crustal sections for the Red Sea, Gulf of California and mid-oceanic rift regions and these are compared with typical continental and oceanic crusts. A possible mechanism for the evolution of new oceanic crust is given based on the isostatic equilibrium of oceans and continents.

GEOPHYSICAL RESEARCH AND PROGRESS IN EXPLORATION

Geophysics ◽  
1957 ◽  
Vol 22 (2) ◽  
pp. 412-433 ◽  
Author(s):  
Milton B. Dobrin ◽  
Henry F. Dunlap
Keyword(s):  
Large Scale ◽  
Gulf Coast ◽  
Academic Research ◽  
Geophysical Methods ◽  
Petroleum Exploration ◽  
Seismic Exploration ◽  
Annual Review ◽  
Neutron Generation ◽  
Geophysical Research ◽  
Research Activities

This paper, the SEG Research Committee’s second annual review of current developments in exploration geophysics, will emphasize research activities at universities and other non‐commercial institutions which relate closely to geophysical exploration. Industry developments worth noting in the seismic field include the considerable increase in use of magnetic recording, use of pressure‐sensitive geophones with preamplifiers in the bay and marsh areas of the Gulf Coast, use of fathometer‐type instruments to obtain near bottom layering in marine areas, and use of nonphotographic methods of reproducing seismic data. Considerable experimentation with weight dropping techniques, and with use of higher frequencies to get better resolution has continued during the past year. Use of models, particularly two dimensional models, is increasing. There have been significant innovations in logging techniques, particularly in the use of in‐hole accelerators for neutron generation, and in the development of in‐hole equipment for measuring gamma ray spectra. The use of continuous velocity logs is increasing. Academic research has been of two kinds. First, there are studies of basic physical principles underlying current or prospective exploration methods which could lead to improvements and new applications. Secondly, geophysical methods originally developed for petroleum exploration are being employed for large‐scale investigations of the earth’s crustal structure. These studies should contribute important information on the geology of such features as continental shelves, geosynclines, and mountain systems, information potentially useful to geologists for developing new concepts in exploration thinking. The two kinds of research illustrate the current interdependence between “pure” and “applied” geophysics. Important research projects on scattering, statistical improvement of signal‐to‐noise, explosionwave generation in the earth, and surface waves exemplify the activity going on in university laboratories today which may result in improved seismic exploration techniques tomorrow. Conversely, university‐sponsored seismic and gravity investigations of the deep oceans, the continental margins and various western mountain chains illustrate how geophysics is contributing basic geologic information on a regional to global scale.

Accelerate Convergence Rate of Distributed Consensus Algorithm with Optimized Topology

2014 ◽  
Vol 511-512 ◽  
pp. 950-953
Author(s):  
Huan Xin Peng ◽  
Wen Kai Wang ◽  
Bin Liu
Keyword(s):  
Convergence Rate ◽  
Large Scale ◽  
Nearest Neighbor ◽  
Consensus Algorithm ◽  
Algebraic Connectivity ◽  
Distributed Consensus ◽  
Consensus Algorithms ◽  
New Model ◽  
Accelerate Convergence ◽  
Topology Model

The convergence rate is very important in the distributed consensus problems, especially, for the distributed consensus algorithms based on large-scale complex networks. In order to accelerate the convergence rate of the distributed consensus algorithms, in the paper, we propose an optimized topology model by adding randomly a few shortcuts to the nearest neighbor coupling networks, and the shortcuts follow a normal distribution. By analyses and simulations, the results show that the algebraic connectivity of the new model is bigger than that of the NMW model, and the convergence rate of the distributed consensus based on the new model is higher than that based on the NMW model

Partitioned least-squares operator for large-scale geophysical inversion

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. R121-R128 ◽  
Author(s):  
Milton J. Porsani ◽  
Paul L. Stoffa ◽  
Mrinal K. Sen ◽  
Roustam K. Seif
Keyword(s):  
Least Squares ◽  
Large Scale ◽  
Velocity Estimation ◽  
Seismic Exploration ◽  
Wave Transformation ◽  
Normal Equation ◽  
Geophysical Inversion ◽  
The Earth ◽  
Toeplitz Systems ◽  
A New Technique

Least-squares (LS) problems are encountered in many geophysical estimation and data analysis problems where a large number of observations (data) are combined to determine a model (some aspect of the earth structure). Examples of least squares in seismic exploration include several data processing algorithms, theoretically accurate LS migration, inversion for reservoir parameters, and background velocity estimation. A frequently encountered problem is that the volume of data in 3D is so large that the matrices required for the LS solution cannot be stored within the memory of a single computer. A new technique is described for parallel computation of the LS operator that is based on a partitioned-matrix algorithm. The classical LS method for solution of block-Toeplitz systems of normal equation (NE) to the general case of block-Hermitian and non-Toeplitz systems of NE. is generalized. Specifically, a solution of a block-Hermitian system of NE is shown that may be obtained recursively by linearly combining the solutions of lesser order that are related to the forward and backward subsystems of equations. This results in an efficient parallel algorithm in which each partitioned system can be evaluated independently. The application of the algorithm to the problem of 3D plane wave transformation is demonstrated.

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