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.

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.

scholarly journals Reconstructing the primary reflections in seismic data by Marchenko redatuming and convolutional interferometry

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. Q15-Q26 ◽  
Author(s):  
Giovanni Angelo Meles ◽  
Kees Wapenaar ◽  
Andrew Curtis
Keyword(s):  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Surface Reflection ◽  
Reflection Data ◽  
Reference Velocity ◽  
Time Migration ◽  
Recorded Data

State-of-the-art methods to image the earth’s subsurface using active-source seismic reflection data involve reverse time migration. This and other standard seismic processing methods such as velocity analysis provide best results only when all waves in the data set are primaries (waves reflected only once). A variety of methods are therefore deployed as processing to predict and remove multiples (waves reflected several times); however, accurate removal of those predicted multiples from the recorded data using adaptive subtraction techniques proves challenging, even in cases in which they can be predicted with reasonable accuracy. We present a new, alternative strategy to construct a parallel data set consisting only of primaries, which is calculated directly from recorded data. This obviates the need for multiple prediction and removal methods. Primaries are constructed by using convolutional interferometry to combine the first-arriving events of upgoing and direct-wave downgoing Green’s functions to virtual receivers in the subsurface. The required upgoing wavefields to virtual receivers are constructed by Marchenko redatuming. Crucially, this is possible without detailed models of the earth’s subsurface reflectivity structure: Similar to the most migration techniques, the method only requires surface reflection data and estimates of direct (nonreflected) arrivals between the virtual subsurface sources and the acquisition surface. We evaluate the method on a stratified synclinal model. It is shown to be particularly robust against errors in the reference velocity model used and to improve the migrated images substantially.

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.

Nonlinear inversion of seismic reflection data in a laterally invariant medium

Geophysics ◽  
1990 ◽  
Vol 55 (3) ◽  
pp. 284-292 ◽  
Author(s):  
A. Pica ◽  
J. P. Diet ◽  
A. Tarantola
Keyword(s):  
Conjugate Gradient ◽  
Velocity Model ◽  
Stratified Medium ◽  
Single Shot ◽  
Nonlinear Inversion ◽  
Reverse Time ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Seismic Waveforms ◽  
Reflection Data

Interpretation of seismic waveforms can be expressed as an optimization problem based on a non‐linear least‐squares criterion to find the model which best explains the data. An initial model is corrected iteratively using a gradient method (conjugate gradient). At each iteration, computation of the direction of the model perturbation requires the forward propagation of the actual sources and the reverse‐time propagation of the residuals (misfit between the data and the synthetics); the two wave fields thus obtained are then correlated. An extra forward propagation is required to compute the amplitude of the perturbation along the conjugate‐gradient direction. The number of propagations to be simulated numerically in each iteration equals three times the number of shots. Since a 2-D finite‐difference code is employed to solve forward‐ and backward‐propagation problems, the method is general and can handle arbitrary 2-D source‐receiver configurations and lateral heterogeneities. Using conventional velocity analysis to derive an initial velocity model, the method is implemented on a real marine data set. The data set which has been selected corresponds approximately to a horizontally stratified medium. Consequently, a single‐shot gather has been used for inversion. In spite of some simplifying assumptions used for wave‐field propagation (acoustic approximation, point source), and using synthetics generated by a nearby sonic log to calibrate amplitudes, our final synthetics match the input data very well and the inversion result has clear similarities to the log.

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).

Application of diffraction wavefront tomography to GPR data from a glacier

2020 ◽  
Author(s):  
Alexander Bauer ◽  
Benjamin Schwarz ◽  
Richard Delf ◽  
Dirk Gajewski
Keyword(s):  
Seismic Data ◽  
Velocity Model ◽  
High Amplitude ◽  
Small Scale ◽  
Coherence Analysis ◽  
Raw Data ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Passive Seismic ◽  
Zero Offset

<p>In the recent years, the diffracted wavefield has gained increasing attention in the field of applied seismics. While classical seismic imaging and inversion schemes mainly focus on high-amplitude reflected measurements, the faint and often masked diffracted wavefield is neglected or even treated as noise. In order to be able to extract depth-velocity models from seismic reflection data, sufficiently large source-receiver offsets are needed. However, the acquisition of such multi-channel seismic data is expensive and often only feasible for the hydrocarbon industry, while academia has to cope with low-fold or zero-offset data. The diffracted wavefield is the key for extracting depth velocities from such data, as the moveout of diffractions – in contrast to reflections – can be measured in the zero-offset domain. Recently, we have demonstrated on multi-channel, single-channel and passive seismic data that by means of wavefront tomography depth-velocity models can be retrieved solely based on diffractions or passive seismic events along with the localizations of these scatterers. The input for wavefront tomography are so-called wavefront attributes, which can be extracted from the data in an unsupervised fashion by means of coherence analysis. In order to obtain the required diffraction-only data, we use a recently proposed scheme that adaptively subtracts the high-amplitude reflected wavefield from the raw data. Due to their most common acquisition geometry, most ground-penetrating-radar (GPR) data inherently lack offsets. In addition, GPR data generally contain a rich diffracted wavefield, which in turn contains information about sought-after structures, as diffractions are caused by small-scale heterogeneities such as faults, tips or edges. In this work, we show an application of the suggested workflow – coherence analysis, diffraction separation and diffraction wavefront tomography – to GPR data acquired at a glacier, resulting in a depth-velocity model and the localizations of the scatterers, both obtained in a fully unsupervised fashion. While the resulting  velocity model may be used for depth migration of the raw data, the localizations of the scatterers may in addition provide important information on the inner structure of the glacier in order to, for instance, localize water intrusions or fractures.</p>

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.

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.

Migration velocity analysis from locally coherent events in 2‐D laterally heterogeneous media, Part I: Theoretical aspects

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1202-1212 ◽  
Author(s):  
Hervé Chauris ◽  
Mark S. Noble ◽  
Gilles Lambaré ◽  
Pascal Podvin
Keyword(s):  
Cost Function ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Paraxial Ray ◽  
The Cost

We present a new method based on migration velocity analysis (MVA) to estimate 2‐D velocity models from seismic reflection data with no assumption on reflector geometry or the background velocity field. Classical approaches using picking on common image gathers (CIGs) must consider continuous events over the whole panel. This interpretive step may be difficult—particularly for applications on real data sets. We propose to overcome the limiting factor by considering locally coherent events. A locally coherent event can be defined whenever the imaged reflectivity locally shows lateral coherency at some location in the image cube. In the prestack depth‐migrated volume obtained for an a priori velocity model, locally coherent events are picked automatically, without interpretation, and are characterized by their positions and slopes (tangent to the event). Even a single locally coherent event has information on the unknown velocity model, carried by the value of the slope measured in the CIG. The velocity is estimated by minimizing these slopes. We first introduce the cost function and explain its physical meaning. The theoretical developments lead to two equivalent expressions of the cost function: one formulated in the depth‐migrated domain on locally coherent events in CIGs and the other in the time domain. We thus establish direct links between different methods devoted to velocity estimation: migration velocity analysis using locally coherent events and slope tomography. We finally explain how to compute the gradient of the cost function using paraxial ray tracing to update the velocity model. Our method provides smooth, inverted velocity models consistent with Kirchhoff‐type migration schemes and requires neither the introduction of interfaces nor the interpretation of continuous events. As for most automatic velocity analysis methods, careful preprocessing must be applied to remove coherent noise such as multiples.

scholarly journals Study on the limitations of travel-time inversion applied to sub-basalt imaging

Solid Earth ◽  
2013 ◽  
Vol 4 (2) ◽  
pp. 543-554 ◽  
Author(s):  
I. Flecha ◽  
R. Carbonell ◽  
R. W. Hobbs
Keyword(s):  
Oil Industry ◽  
Velocity Model ◽  
Time Inversion ◽  
Wide Angle ◽  
Seismic Reflection Data ◽  
Additional Information ◽  
Velocity Models ◽  
Reflection Data ◽  
Travel Time Inversion ◽  
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. Stochastic tests based on Metropolis techniques support the need of additional information to properly resolve sub-basalt structures.

Sign in / Sign up

Export Citation Format

Share Document