VSP traveltime inversion for linear inhomogeneity and elliptical anisotropy

Geophysics ◽  
2004 ◽  
Vol 69 (2) ◽  
pp. 373-377 ◽  
Author(s):  
Michael A. Slawinski ◽  
Chad J. Wheaton ◽  
Miro Powojowski
Keyword(s):  
Statistical Analysis ◽  
Least Squares ◽  
Field Data ◽  
Velocity Model ◽  
Western Canada ◽  
Velocity Dependence ◽  
Traveltime Inversion ◽  
Seismic Profiling ◽  
Vertical Seismic Profiling ◽  
Good Agreement

To account for measured vertical seismic profiling (VSP) traveltimes, we study a velocity model described by three parameters. We assume that the velocity increases linearly with depth and is given in terms of parameters a and b, whereas the anisotropy is the result of elliptical velocity dependence and is given in terms of parameter χ. Using this model, we formulate an analytical expression for traveltime between a given source and a given receiver. This traveltime expression contains the three parameters that are present in the velocity model. To obtain the values of a, b, and χ, we use least‐squares fitting of this traveltime expression, with respect to measured traveltimes. This process of obtaining the parameters is exemplified by a study of traveltime data acquired with a two‐offset VSP in the Western Canada Basin. Having obtained a, b, and χ, we perform a statistical analysis, which shows good agreement between the field data and the modeled data. Furthermore, it shows that the elliptical velocity dependence, although small, is statistically significant.

scholarly journals Mitigation of defocusing by statics and near-surface velocity errors by interferometric least-squares migration with a reference datum

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S195-S206 ◽  
Author(s):  
Mrinal Sinha ◽  
Gerard T. Schuster
Keyword(s):  
Least Squares ◽  
Prior Knowledge ◽  
Seismic Data ◽  
Field Data ◽  
Velocity Model ◽  
Well Logs ◽  
Surface Velocity ◽  
Near Surface ◽  
Reference Layer ◽  
Least Squares Migration

Imaging seismic data with an erroneous migration velocity can lead to defocused migration images. To mitigate this problem, we first choose a reference reflector whose topography is well-known from the well logs, for example. Reflections from this reference layer are correlated with the traces associated with reflections from deeper interfaces to get crosscorrelograms. Interferometric least-squares migration (ILSM) is then used to get the migration image that maximizes the crosscorrelation between the observed and the predicted crosscorrelograms. Deeper reference reflectors are used to image deeper parts of the subsurface with a greater accuracy. Results on synthetic and field data show that defocusing caused by velocity errors is largely suppressed by ILSM. We have also determined that ILSM can be used for 4D surveys in which environmental conditions and acquisition parameters are significantly different from one survey to the next. The limitations of ILSM are that it requires prior knowledge of a reference reflector in the subsurface and the velocity model below the reference reflector should be accurate.

Least‐squares migration of incomplete reflection data

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 208-221 ◽  
Author(s):  
Tamas Nemeth ◽  
Chengjun Wu ◽  
Gerard T. Schuster
Keyword(s):  
Least Squares ◽  
Frequency Distribution ◽  
Field Data ◽  
Radar Data ◽  
Data Set ◽  
Frequency Distributions ◽  
Vertical Seismic Profiling ◽  
Reflection Data ◽  
Ground Penetrating ◽  
Least Squares Migration

A least‐squares migration algorithm is presented that reduces the migration artifacts (i.e., recording footprint noise) arising from incomplete data. Instead of migrating data with the adjoint of the forward modeling operator, the normal equations are inverted by using a preconditioned linear conjugate gradient scheme that employs regularization. The modeling operator is constructed from an asymptotic acoustic integral equation, and its adjoint is the Kirchhoff migration operator. We tested the performance of the least‐squares migration on synthetic and field data in the cases of limited recording aperture, coarse sampling, and acquisition gaps in the data. Numerical results show that the least‐squares migrated sections are typically more focused than are the corresponding Kirchhoff migrated sections and their reflectivity frequency distributions are closer to those of the true model frequency distribution. Regularization helps attenuate migration artifacts and provides a sharper, better frequency distribution of estimated reflectivity. The least‐squares migrated sections can be used to predict the missing data traces and interpolate and extrapolate them according to the governing modeling equations. Several field data examples are presented. A ground‐penetrating radar data example demonstrates the suppression of the recording footprint noise due to a limited aperture, a large gap, and an undersampled receiver line. In addition, better fault resolution was achieved after applying least‐squares migration to a poststack marine data set. And a reverse vertical seismic profiling example shows that the recording footprint noise due to a coarse receiver interval can be suppressed by least‐squares migration.

Least-squares migration in the presence of velocity errors

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. S153-S161 ◽  
Author(s):  
Simon Luo ◽  
Dave Hale
Keyword(s):  
Wave Propagation ◽  
Least Squares ◽  
Field Data ◽  
Velocity Model ◽  
Forward Modeling ◽  
Background Model ◽  
Seismic Migration ◽  
Least Squares Migration

Seismic migration requires an accurate background velocity model that correctly predicts the kinematics of wave propagation in the true subsurface. Least-squares migration, which seeks the inverse rather than the adjoint of a forward modeling operator, is especially sensitive to errors in this background model. This can result in traveltime differences between predicted and observed data that lead to incoherent and defocused migration images. We have developed an alternative misfit function for use in least-squares migration that measures amplitude differences between predicted and observed data, i.e., differences after correcting for nonzero traveltime shifts between predicted and observed data. We demonstrated on synthetic and field data that, when the background velocity model is incorrect, the use of this misfit function results in better focused migration images. Results suggest that our method best enhances image focusing when differences between predicted and observed data can be explained by traveltime shifts.

scholarly journals Adaptive traveltime inversion

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. U13-U29 ◽  
Author(s):  
Bingbing Sun ◽  
Tariq Alkhalifah
Keyword(s):  
Least Squares ◽  
Penalty Function ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Second Order ◽  
P Wave ◽  
Order Moment ◽  
Traveltime Inversion ◽  
First Order ◽  
Matching Filter

We have developed a method to obtain a misfit function for robust waveform inversion. In this method, called adaptive traveltime inversion (ATI), a matching filter that matches predicted data to measured data is computed. If the velocity model is relatively accurate, the resulting matching filter is close to a Dirac delta function. Its traveltime shift, which characterizes the defocusing of the matching filter, is computed by minimization of the crosscorrelation between a penalty function such as [Formula: see text] and the matching filter. ATI is constructed by minimization of the least-squares errors of the calculated traveltime shift. Further analysis indicates that the resulting traveltime shift corresponds to a first-order moment, the mean value of the resulting matching filter distribution. We extend ATI to a more general misfit function formula by computing different order moment of the resulting matching filter distribution. Choosing the penalty function in adaptive waveform inversion (AWI) as [Formula: see text], the misfit function of AWI is the second-order moment, the variance of the resulting matching filter distribution with zero mean. Because our ATI method is based on a global comparison using deconvolution, such as AWI, it can resolve the “cycle skipping” issue. We evaluate our ATI misfit function and compare it with state-of-the-art options such as least-squares inversion (L2 norm), wave-equation traveltime inversion, and AWI using schematic examples before moving to more complex examples, such as the Marmousi model. For the Marmousi model, starting with a 1D [Formula: see text] model, with data without low frequencies (no energy below 3 Hz), a meaningful estimation of the P-wave velocity model is recovered. Our ATI misfit function (first-order moment) indicates comparable performance with the AWI misfit function (the second-order moment). We also include a real data example from the Gulf of Mexico to demonstrate the effectiveness of our method.

Local vertical seismic profiling (VSP) elastic reverse-time migration and migration resolution: Salt-flank imaging with transmitted P-to-S waves

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. S35-S49 ◽  
Author(s):  
Xiang Xiao ◽  
W. Scott Leaney
Keyword(s):  
Velocity Model ◽  
Staggered Grid ◽  
Image Point ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Seismic Profiling ◽  
Vertical Seismic Profiling ◽  
Time Migration

To avoid the defocusing effects of propagating waves through salt and overburden with an inaccurate overburden velocity model, we introduce a vertical seismic profiling (VSP) local elastic reverse-time-migration (RTM) method for salt-flank imaging by transmitted P-to-S waves. This method back-projects the transmitted PS waves using a local velocity model around the well until they are in phase with the back-projected PP waves at the salt boundaries. The merits of this method are that it does not require the complex overburden and salt-body velocities and it automatically accounts for source-side statics. In addition, the method accounts for kinematic and dynamic effects, including anisotropy, absorption, and all other unknown rock effects outside of this lo-cal subsalt velocity model. Numerical tests on an elastic salt model and offset 2D VSP data in the Gulf of Mexico, using a finite-difference time-domain staggered-grid RTM scheme, partly demonstrate the effectiveness of this method over interferometry PS-PP transmission migration and local acoustic RTM. Our method separates elastic wavefields to vector P- and S-wave velocity components at the trial image point and achieves better resolution than local acoustic RTM and interferometric transmission migration. The analytical formulas of migration resolution for local acoustic and elastic RTM show that the migration illumination is limited by data frequency and receiver aperture, and the spatial resolution is lower than standard poststack and prestack migration. This new method can image salt flanks as well as subsalt reflectors.

Rapid VSP-CDP mapping of 3-D VSP data

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1631-1640 ◽  
Author(s):  
Genmeng Chen ◽  
Janusz Peron ◽  
Luis Canales
Keyword(s):  
Ray Tracing ◽  
Velocity Model ◽  
Mapping Method ◽  
Computation Method ◽  
Layered Model ◽  
Seismic Profiling ◽  
Vertical Seismic Profiling ◽  
Kirchhoff Migration ◽  
Vsp Data ◽  
Image Volume

Vertical seismic profiling‐common depth point (VSPCDP) mapping with rapid ray tracing in a horizontally layered velocity model is used to create 3-D image volumes using Blackfoot and Oseberg 3-D vertical seismic profiling (VSP) data. The ray‐tracing algorithm uses Fermat’s principle and is specially programmed for the layered model. The algorithm is about ten times faster than either a 3-D VSP-CDP mapping program with an eikonal traveltime computation method or a 3-D VSP Kirchhoff migration program. The mapping method automatically separates the image zone from the nonimage zone within the 3-D image volume. The Oseberg data example shows that the lateral extent of the image zone created by the 3D VSP-CDP mapping is larger than that created by 3-D VSP Kirchhoff migration. The same sample result also provides high‐frequency events at target zones. We include an analysis of the imaging error induced from using a horizontally layered model for the Oseberg data, indicating that the method is reliable in the presence of gently dipping structure.

Positioning drill-bit and look-ahead events using seismic traveltime data

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. F79-F90 ◽  
Author(s):  
Jo Eidsvik ◽  
Ketil Hokstad
Keyword(s):  
Velocity Model ◽  
Drill Bit ◽  
Surface Sampling ◽  
Data Set ◽  
Norwegian Sea ◽  
Seismic Profiling ◽  
Vertical Seismic Profiling ◽  
Look Ahead ◽  
Sampling Locations ◽  
Dense Sampling

We study seismic traveltime measurements acquired in the borehole, including vertical seismic profiling, seismic measurements while drilling, and drill-bit noise generated data. These traveltime data are used to assess informative parameters, including drill-bit position, distance to drilling target, and parameters of the velocity model. First, we analyze seismic traveltime data using a simple hyperbolic traveltime equation for rays between surface sampling locations and the drill bit. Second, we describe a model for estimating both the position of the drill bit and the relative distance to geologic interfaces ahead of the bit. Finally, we present a dynamic Bayesian strategy for real-time prediction of drill-bit positions, velocity parameters, and distances to geologic markers. Walk-away vertical seismic profiling data from the Norwegian Sea are used to demonstrate our methods. For this data set, we pick five key reflectors ahead of the drill bit. The deepest reflector is estimated to be [Formula: see text] ahead of the drill bit, using seismic traveltime data alone. The effects of aperture and surface sampling locations are large on our estimates and their associated uncertainties, and we observe that large offset is preferable to dense sampling in terms of positioning accuracy.

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

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