SINS attitude algorithm based on moving-window overdetermined polynomial fitting of gyro outputs

2021 ◽  
Author(s):  
huai fang ◽  
Guobin Chang ◽  
zhi bao ◽  
Kai Chen ◽  
xiannan han
Keyword(s):  
Differential Equation ◽  
Angular Velocity ◽  
Measurement Errors ◽  
Order Approximation ◽  
Direction Cosine ◽  
Velocity Model ◽  
Moving Window ◽  
Polynomial Fitting ◽  
Integration Algorithm ◽  
Velocity Models

Abstract The attitude algorithm is the most important part of the whole strapdown inertial navigation (SINS) processing. It calculates the attitude of certain parameterization by integrating the gyro outputs or measurements in a specifically tailored way according to the attitude kinematic differential equation. The measurements or some angular velocity models obtained by fitting these measurements are often assumed free of errors in order to assess the numerical errors only. However, the gyro outputs and hence the models from them are by no means free of measurement errors. It is more often than not that the measurement errors dominate the numerical ones in practice. In this study, with coping with the measurement errors as the focus, we aim to improve the angular velocity model which is used as input in an attitude integration algorithm. This is achieved by exploiting the potential of overdetermined least-squares polynomial fitting. In order to avoid reducing the update rate by incorporating more measurements, the moving window trick is employed to re-use measurements in the previous update interval. The conventional attitude algorithm with second-order approximation in solving the differential equation of the equivalent rotation vector is employed as an example; however, the proposed method can be readily applied to other parameterizations such as direction cosine matrix, quaternion or Rodrigues parameters, and other high order approximations in solving the differential equation widely studied recently.

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.

scholarly journals Earthquake location in tectonic structures of the Alpine Chain: the case of the Constance Lake (Central Europe) seismic sequence

2021 ◽  
Author(s):  
Francesca D’Ajello Caracciolo ◽  
Rodolfo Console
Keyword(s):  
Central Europe ◽  
Velocity Model ◽  
Moho Depth ◽  
Seismic Sequence ◽  
Tectonic Structures ◽  
Study Region ◽  
Waveform Data ◽  
Seismic Stations ◽  
Velocity Models ◽  
Master Event

AbstractA set of four magnitude Ml ≥ 3.0 earthquakes including the magnitude Ml = 3.7 mainshock of the seismic sequence hitting the Lake Constance, Southern Germany, area in July–August 2019 was studied by means of bulletin and waveform data collected from 86 seismic stations of the Central Europe-Alpine region. The first single-event locations obtained using a uniform 1-D velocity model, and both fixed and free depths, showed residuals of the order of up ± 2.0 s, systematically affecting stations located in different areas of the study region. Namely, German stations to the northeast of the epicenters and French stations to the west exhibit negative residuals, while Italian stations located to the southeast are characterized by similarly large positive residuals. As a consequence, the epicentral coordinates were affected by a significant bias of the order of 4–5 km to the NNE. The locations were repeated applying a method that uses different velocity models for three groups of stations situated in different geological environments, obtaining more accurate locations. Moreover, the application of two methods of relative locations and joint hypocentral determination, without improving the absolute location of the master event, has shown that the sources of the four considered events are separated by distances of the order of one km both in horizontal coordinates and in depths. A particular attention has been paid to the geographical positions of the seismic stations used in the locations and their relationship with the known crustal features, such as the Moho depth and velocity anomalies in the studied region. Significant correlations between the observed travel time residuals and the crustal structure were obtained.

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.

Kinematic interpretation in the prestack depth‐migrated domain

Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1226-1237 ◽  
Author(s):  
Irina Apostoiu‐Marin ◽  
Andreas Ehinger
Keyword(s):  
Signal To Noise Ratio ◽  
Velocity Model ◽  
Point Of View ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Velocity Models ◽  
Time Domain Data ◽  
And Migration ◽  
Point To Point ◽  
Homogeneous Media

Prestack depth migration can be used in the velocity model estimation process if one succeeds in interpreting depth events obtained with erroneous velocity models. The interpretational difficulty arises from the fact that migration with erroneous velocity does not yield the geologically correct reflector geometries and that individual migrated images suffer from poor signal‐to‐noise ratio. Moreover, migrated events may be of considerable complexity and thus hard to identify. In this paper, we examine the influence of wrong velocity models on the output of prestack depth migration in the case of straight reflector and point diffractor data in homogeneous media. To avoid obscuring migration results by artifacts (“smiles”), we use a geometrical technique for modeling and migration yielding a point‐to‐point map from time‐domain data to depth‐domain data. We discover that strong deformation of migrated events may occur even in situations of simple structures and small velocity errors. From a kinematical point of view, we compare the results of common‐shot and common‐offset migration. and we find that common‐offset migration with erroneous velocity models yields less severe image distortion than common‐shot migration. However, for any kind of migration, it is important to use the entire cube of migrated data to consistently interpret in the prestack depth‐migrated domain.

Kirchhoff migration using eikonal-based computation of traveltime source derivatives

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. S211-S219 ◽  
Author(s):  
Siwei Li ◽  
Sergey Fomel
Keyword(s):  
Differential Equation ◽  
Eikonal Equation ◽  
Order Partial Differential Equation ◽  
Fast Marching ◽  
First Order ◽  
Velocity Models ◽  
Kirchhoff Migration ◽  
Input Source ◽  
First Arrival ◽  
Synthetic Models

The computational efficiency of Kirchhoff-type migration can be enhanced by using accurate traveltime interpolation algorithms. We addressed the problem of interpolating between a sparse source sampling by using the derivative of traveltime with respect to the source location. We adopted a first-order partial differential equation that originates from differentiating the eikonal equation to compute the traveltime source derivatives efficiently and conveniently. Unlike methods that rely on finite-difference estimations, the accuracy of the eikonal-based derivative did not depend on input source sampling. For smooth velocity models, the first-order traveltime source derivatives enabled a cubic Hermite traveltime interpolation that took into consideration the curvatures of local wavefronts and can be straightforwardly incorporated into Kirchhoff antialiasing schemes. We provided an implementation of the proposed method to first-arrival traveltimes by modifying the fast-marching eikonal solver. Several simple synthetic models and a semirecursive Kirchhoff migration of the Marmousi model demonstrated the applicability of the proposed method.

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.

Migration velocity analysis based on focusing diffractions generated using the CRS wavefront attributes: Application to real land data

Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
German Garabito ◽  
José Silas dos Santos Silva ◽  
Williams Lima
Keyword(s):  
Time Domain ◽  
Real Data ◽  
Normal Incidence ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
The Time Domain

In land seismic data processing, the prestack time migration (PSTM) image remains the standard imaging output, but a reliable migrated image of the subsurface depends on the accuracy of the migration velocity model. We have adopted two new algorithms for time-domain migration velocity analysis based on wavefield attributes of the common-reflection-surface (CRS) stack method. These attributes, extracted from multicoverage data, were successfully applied to build the velocity model in the depth domain through tomographic inversion of the normal-incidence-point (NIP) wave. However, there is no practical and reliable method for determining an accurate and geologically consistent time-migration velocity model from these CRS attributes. We introduce an interactive method to determine the migration velocity model in the time domain based on the application of NIP wave attributes and the CRS stacking operator for diffractions, to generate synthetic diffractions on the reflection events of the zero-offset (ZO) CRS stacked section. In the ZO data with diffractions, the poststack time migration (post-STM) is applied with a set of constant velocities, and the migration velocities are then selected through a focusing analysis of the simulated diffractions. We also introduce an algorithm to automatically calculate the migration velocity model from the CRS attributes picked for the main reflection events in the ZO data. We determine the precision of our diffraction focusing velocity analysis and the automatic velocity calculation algorithms using two synthetic models. We also applied them to real 2D land data with low quality and low fold to estimate the time-domain migration velocity model. The velocity models obtained through our methods were validated by applying them in the Kirchhoff PSTM of real data, in which the velocity model from the diffraction focusing analysis provided significant improvements in the quality of the migrated image compared to the legacy image and to the migrated image obtained using the automatically calculated velocity model.

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.

Practical approaches for subsalt velocity model building

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE183-VE194 ◽  
Author(s):  
Junru Jiao ◽  
David R. Lowrey ◽  
John F. Willis ◽  
Ruben D. Martínez
Keyword(s):  
Software Package ◽  
Model Building ◽  
Velocity Model ◽  
Fine Tuning ◽  
Inherent Difficulty ◽  
Velocity Models ◽  
First Approximation ◽  
Velocity Model Building ◽  
Trade Offs ◽  
Efficient Performance

Imaging sediments below salt bodies is challenging because of the inherent difficulty of estimating accurate velocity models. These models can be estimated in a variety of ways with varying degrees of expense and effectiveness. Two methods are commercially viable trade-offs. In the first method, residual-moveout analysis is performed in a layer-stripping mode. The models produced with this method can be used as a first approximation of the subsalt velocity field. A wave-equation migration scanning technique is more suitable for fine-tuning the velocity model below the salt. Both methods can be run as part of a sophisticated interactive velocity interpretation software package that makes velocity interpretation efficient. Performance of these methods has been tested on synthetic and field data examples.

Full-waveform inversion for full-wavefield imaging: Decades in the making

2021 ◽  
Vol 40 (5) ◽  
pp. 324-334
Author(s):  
Rongxin Huang ◽  
Zhigang Zhang ◽  
Zedong Wu ◽  
Zhiyuan Wei ◽  
Jiawei Mei ◽  
...  
Keyword(s):  
Model Building ◽  
Seismic Imaging ◽  
Structural Information ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Data Sets ◽  
Full Waveform Inversion ◽  
Data Types ◽  
Velocity Models ◽  
Full Waveform

Seismic imaging using full-wavefield data that includes primary reflections, transmitted waves, and their multiples has been the holy grail for generations of geophysicists. To be able to use the full-wavefield data effectively requires a forward-modeling process to generate full-wavefield data, an inversion scheme to minimize the difference between modeled and recorded data, and, more importantly, an accurate velocity model to correctly propagate and collapse energy of different wave modes. All of these elements have been embedded in the framework of full-waveform inversion (FWI) since it was proposed three decades ago. However, for a long time, the application of FWI did not find its way into the domain of full-wavefield imaging, mostly owing to the lack of data sets with good constraints to ensure the convergence of inversion, the required compute power to handle large data sets and extend the inversion frequency to the bandwidth needed for imaging, and, most significantly, stable FWI algorithms that could work with different data types in different geologic settings. Recently, with the advancement of high-performance computing and progress in FWI algorithms at tackling issues such as cycle skipping and amplitude mismatch, FWI has found success using different data types in a variety of geologic settings, providing some of the most accurate velocity models for generating significantly improved migration images. Here, we take a step further to modify the FWI workflow to output the subsurface image or reflectivity directly, potentially eliminating the need to go through the time-consuming conventional seismic imaging process that involves preprocessing, velocity model building, and migration. Compared with a conventional migration image, the reflectivity image directly output from FWI often provides additional structural information with better illumination and higher signal-to-noise ratio naturally as a result of many iterations of least-squares fitting of the full-wavefield data.

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