Generalization of traveltime inversion

Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 9-14 ◽  
Author(s):  
Gérard C. Herman
Keyword(s):  
Time Windows ◽  
Velocity Model ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Error Norm ◽  
Arrival Times ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Use Of Data

A nonlinear inversion method is presented, especially suited for the determination of global velocity models. In a certain sense, it can be considered as a generalization of methods based on traveltimes of reflections, with the requirement of accurately having to determine traveltimes replaced by the (less stringent and less subjective) requirement of having to define time windows around main reflections (or composite reflections) of interest. It is based on an error norm, related to the phase of the wavefield, which is directly computed from wavefield measurements. Therefore, the cumbersome step of interpreting arrivals and measuring arrival times is avoided. The method is applied to the reconstruction of a depth‐dependent global velocity model from a set of plane‐wave responses and is compared to other methods. Despite the fact that the new error norm only makes use of data having a temporal bandwidth of a few Hz, its behavior is very similar to the behavior of the error norm used in traveltime inversion.

First-arrival traveltime inversion of seismic diving waves observed on undulant surface

2021 ◽  
Vol 225 (2) ◽  
pp. 1020-1031
Author(s):  
Huachen Yang ◽  
Jianzhong Zhang ◽  
Kai Ren ◽  
Changbo Wang
Keyword(s):  
Turning Points ◽  
Analytical Formula ◽  
Velocity Model ◽  
Western China ◽  
Inversion Method ◽  
Mountain Area ◽  
Traveltime Inversion ◽  
Static Correction ◽  
Velocity Models ◽  
First Arrival

SUMMARY A non-iterative first-arrival traveltime inversion method (NFTI) is proposed for building smooth velocity models using seismic diving waves observed on irregular surface. The new ray and traveltime equations of diving waves propagating in smooth media with undulant observation surface are deduced. According to the proposed ray and traveltime equations, an analytical formula for determining the location of the diving-wave turning points is then derived. Taking the influence of rough topography on first-arrival traveltimes into account, the new equations for calculating the velocities at turning points are established. Based on these equations, a method is proposed to construct subsurface velocity models from the observation surface downward to the bottom using the first-arrival traveltimes in common offset gathers. Tests on smooth velocity models with rugged topography verify the validity of the established equations, and the superiority of the proposed NFTI. The limitation of the proposed method is shown by an abruptly-varying velocity model example. Finally, the NFTI is applied to solve the static correction problem of the field seismic data acquired in a mountain area in the western China. The results confirm the effectivity of the proposed NFTI.

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.

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 Traveltime inversion for 2‐D anomaly structures

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1481-1487 ◽  
Author(s):  
Danilo R. Velis
Keyword(s):  
Optimization Problem ◽  
Inversion Method ◽  
Unknown Parameters ◽  
New Approach ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Highly Nonlinear ◽  
Small Set ◽  
A Cell ◽  
Parametric Functions

This work presents a traveltime inversion method that uses parametric functions to represent 2‐D anomaly structures. These functions are described by a small set of unknown parameters which in turn are obtained after solving a highly nonlinear optimization problem via simulated annealing (SA). The procedure favors neither smooth nor high contrasting anomalies and keeps the number of unknowns very small so as to make the problem tractable using SA. Yet the strategy allows one to accommodate a large class of velocity models. Results indicate that this new approach typically yields better images than a standard linearized inversion based on a cell parameterization scheme.

scholarly journals Study on the limitations of traveltime inversion in the presence of extreme velocity anomalies

2013 ◽  
Vol 5 (1) ◽  
pp. 189-226
Author(s):  
I. Flecha ◽  
R. Carbonell ◽  
R. W. Hobbs
Keyword(s):  
Oil Industry ◽  
Velocity Model ◽  
Wide Angle ◽  
Seismic Reflection Data ◽  
Traveltime Inversion ◽  
Additional Information ◽  
Velocity Models ◽  
Reflection Data ◽  
Velocity Anomalies ◽  
Tomographic Inversions

Abstract. The difficulties of seismic imaging beneath high velocity structures are widely recognised. In this setting, theoretical analysis of synthetic wide-angle seismic reflection data indicates that velocity models are not well constrained. A two-dimensional velocity model was built to simulate a simplified structural geometry given by a basaltic wedge placed within a sedimentary sequence. This model reproduces the geological setting in areas of special interest for the oil industry as the Faroe-Shetland Basin. A wide-angle synthetic dataset was calculated on this model using an elastic finite difference scheme. This dataset provided travel times for tomographic inversions. Results show that the original model can not be completely resolved without considering additional information. The resolution of nonlinear inversions lacks a functional mathematical relationship, therefore, statistical approaches are required. Stochastical tests based on Metropolis techniques support the need of additional information to properly resolve subbasalt structures.

scholarly journals Optimal coding of blended seismic sources for 2D full waveform inversion in time

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Katherine Flórez ◽  
Sergio Alberto Abreo Carrillo ◽  
Ana Beatriz Ramírez Silva
Keyword(s):  
Waveform Inversion ◽  
Velocity Model ◽  
Computational Time ◽  
Inversion Method ◽  
Single Shot ◽  
Full Waveform Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
Seismic Image ◽  
Blended Data

Full Waveform Inversion (FWI) schemes are gradually becoming more common in the oil and gas industry, as a new tool for studying complex geological zones, based on their reliability for estimating velocity models. FWI is a non-linear inversion method that iteratively estimates subsurface characteristics such as seismic velocity, starting from an initial velocity model and the preconditioned data acquired. Blended sources have been used in marine seismic acquisitions to reduce acquisition costs, reducing the number of times that the vessel needs to cross the exploration delineation trajectory. When blended or simultaneous without previous de-blending or separation, stage data are used in the reconstruction of the velocity model with the FWI method, and the computational time is reduced. However, blended data implies overlapping single shot-gathers, producing interference that affects the result of seismic approaches, such as FWI or seismic image migration. In this document, an encoding strategy is developed, which reduces the overlap areas within the blended data to improve the final velocity model with the FWI method.

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.

scholarly journals Relocation of earthquakes in the southern and eastern Alps (Austria, Italy) recorded by the dense, temporary SWATH-D network using a Markov chain Monte Carlo inversion

Solid Earth ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 1087-1109
Author(s):  
Azam Jozi Najafabadi ◽  
Christian Haberland ◽  
Trond Ryberg ◽  
Vincent F. Verwater ◽  
Eline Le Breton ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Velocity Model ◽  
Eastern Alps ◽  
Inversion Method ◽  
Parameter Uncertainties ◽  
Waveform Data ◽  
Velocity Models ◽  
Austroalpine Nappes

Abstract. In this study, we analyzed a large seismological dataset from temporary and permanent networks in the southern and eastern Alps to establish high-precision hypocenters and 1-D VP and VP/VS models. The waveform data of a subset of local earthquakes with magnitudes in the range of 1–4.2 ML were recorded by the dense, temporary SWATH-D network and selected stations of the AlpArray network between September 2017 and the end of 2018. The first arrival times of P and S waves of earthquakes are determined by a semi-automatic procedure. We applied a Markov chain Monte Carlo inversion method to simultaneously calculate robust hypocenters, a 1-D velocity model, and station corrections without prior assumptions, such as initial velocity models or earthquake locations. A further advantage of this method is the derivation of the model parameter uncertainties and noise levels of the data. The precision estimates of the localization procedure is checked by inverting a synthetic travel time dataset from a complex 3-D velocity model and by using the real stations and earthquakes geometry. The location accuracy is further investigated by a quarry blast test. The average uncertainties of the locations of the earthquakes are below 500 m in their epicenter and ∼ 1.7 km in depth. The earthquake distribution reveals seismicity in the upper crust (0–20 km), which is characterized by pronounced clusters along the Alpine frontal thrust, e.g., the Friuli-Venetia (FV) region, the Giudicarie–Lessini (GL) and Schio-Vicenza domains, the Austroalpine nappes, and the Inntal area. Some seismicity also occurs along the Periadriatic Fault. The general pattern of seismicity reflects head-on convergence of the Adriatic indenter with the Alpine orogenic crust. The seismicity in the FV and GL regions is deeper than the modeled frontal thrusts, which we interpret as indication for southward propagation of the southern Alpine deformation front (blind thrusts).

Joint wave-equation traveltime inversion of diving/direct and reflected waves for the P- and S-wave velocity macromodel building

Geophysics ◽  
2021 ◽  
pp. 1-145
Author(s):  
Zhiming Ren ◽  
Qianzong Bao ◽  
Bingluo Gu
Keyword(s):  
Wave Velocity ◽  
Velocity Model ◽  
S Wave ◽  
Direct Wave ◽  
Reflected Waves ◽  
Traveltime Inversion ◽  
Long Wavelength ◽  
Velocity Models ◽  
Reflected Wave ◽  
Background Models

Full waveform inversion (FWI) suffers from the local minima problem and requires a sufficiently accurate starting model to converge to the correct solution. Wave-equation traveltime inversion (WETI) is an effective tool to retrieve the long-wavelength components of the velocity model. We develop a joint diving/direct and reflected wave WETI (JDRWETI) method to build the P- and S-wave velocity macromodels. We estimate the traveltime shifts of seismic events (diving/direct waves, PP and PS reflections) through the dynamic warping scheme and construct a misfit function using both the time shifts of diving/direct and reflected waves. We derive the adjoint wave equations and the gradients with respect to the background models based on the joint misfit function. We apply the kernel decomposition scheme to extract the kernel of the diving/direct wave and the tomography kernels of PP and PS reflections. For an explosive source, the kernels of diving/direct wave and PP reflections and the kernel of PS reflections are used to compute the P- and S-wave gradients of the background models, respectively. We implement JDRWETI by a two-stage inversion workflow: first invert the P- and S-wave velocity models using the P-wave gradients and then improve the S-wave velocity model using the S-wave gradients. Numerical tests on synthetic and field datasets reveal that the JDRWETI method successfully recovers the long-wavelength components of P- and S-wave velocity models, which can be used for an initial model for the subsequent elastic FWI. Moreover, the proposed JDRWETI method prevails over the existing reflection WETI method and the cascaded diving/direct and reflected wave WETI method, especially when large velocity errors are present in the shallow part of the starting models. The JDRWETI method with the two-stage inversion workflow can give rise to reasonable inversion results even for the model with different P- and S-wave velocity structures.

Full-traveltime inversion

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. R261-R274 ◽  
Author(s):  
Yi Luo ◽  
Yue Ma ◽  
Yan Wu ◽  
Hongwei Liu ◽  
Lei Cao
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Low Frequency ◽  
Velocity Model ◽  
New Wave ◽  
Severe Problem ◽  
Reflected Waves ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Kinematic Information

Many previously published wave-equation-based methods, which attempt to automatically invert traveltime or kinematic information in seismic data or migrated gathers for smooth velocities, suffer a common and severe problem — the inversions are involuntarily and unconsciously hijacked by amplitude information. To overcome this problem, we have developed a new wave-equation-based traveltime inversion methodology, referred to as full-traveltime (i.e., fully dependent on traveltime) inversion (FTI), to automatically estimate a kinematically accurate velocity model from seismic data. The key idea of FTI is to make the inversion fully dependent on traveltime information, and thus prevent amplitude interference during inversion. Under the assumption that velocity perturbations cause only traveltime changes, we have derived the FTI method in the data and image domains, which are applicable to transmitted arrivals and reflected waves, respectively. FTI does not require an accurate initial velocity model or low-frequency seismic data. Synthetic and field data tests demonstrate that FTI produces satisfactory inversion results, even when using constant velocity models as initials.

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