Traveltime inversion using transmitted waves of offset VSP data

Geophysics ◽  
1990 ◽  
Vol 55 (8) ◽  
pp. 1089-1097 ◽  
Author(s):  
Myung W. Lee
Keyword(s):  
Seismic Profile ◽  
Inversion Method ◽  
Earth Model ◽  
Computationally Efficient ◽  
Arrival Times ◽  
Traveltime Inversion ◽  
Interval Velocity ◽  
Vsp Data ◽  
First Arrival ◽  
Interval Velocities

Estimation of layer parameters such as interval velocity, reflector depth, and dip can be formulated as a generalized linear inverse problem using observed arrival times. Based on a 2-D earth model, a computationally efficient and accurate formula is derived for traveltime inversion. This inversion method is applied to offset vertical seismic profile (VSP) data for estimating layer parameters using only transmitted first‐arrival times. As opposed to a layer‐stripping method, this method estimates all layer parameters simultaneously, thus reducing the cumulative error resulting from the errors in the upper layers. This investigation indicates (1) at least two source locations are required to estimate layer parameters properly, and (2) accurate arrival times are essential for computing the dip of a layer reliably. Bulk time shifts, such as static shifts, do not affect the parameter estimation significantly if the amount of shift is not too large. The result of real and modeled VSP data inversions indicates that traveltime inversion using transmitted first‐arrival times from at least two source locations is a viable method for estimating interval velocities, reflector depths, and reflector dips.

Traveltime inversion of offset vertical seismic profiles—A feasibility study

Geophysics ◽  
1984 ◽  
Vol 49 (3) ◽  
pp. 250-264 ◽  
Author(s):  
L. R. Lines ◽  
A. Bourgeois ◽  
J. D. Covey
Keyword(s):  
Inverse Method ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Profile ◽  
Inversion Method ◽  
Earth Model ◽  
Seismic Profiles ◽  
Traveltime Inversion ◽  
Vertical Seismic Profiles ◽  
Inversion Techniques

Traveltimes from an offset vertical seismic profile (VSP) are used to estimate subsurface two‐dimensional dip by applying an iterative least‐squares inverse method. Tests on synthetic data demonstrate that inversion techniques are capable of estimating dips in the vicinity of a wellbore by using the traveltimes of the direct arrivals and the primary reflections. The inversion method involves a “layer stripping” approach in which the dips of the shallow layers are estimated before proceeding to estimate deeper dips. Examples demonstrate that the primary reflections become essential whenever the ratio of source offset to layer depth becomes small. Traveltime inversion also requires careful estimation of layer velocities and proper statics corrections. Aside from these difficulties and the ubiquitous nonuniqueness problem, the VSP traveltime inversion was able to produce a valid earth model for tests on a real data case.

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.

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.

3-D interpretation of reflected arrival times by finite‐difference techniques

Geophysics ◽  
1994 ◽  
Vol 59 (5) ◽  
pp. 844-849 ◽  
Author(s):  
M. Ali Riahi ◽  
Christopher Juhlin
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Real Data ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Computationally Efficient ◽  
Reflected Waves ◽  
Arrival Times ◽  
First Arrival ◽  
Difference Methods

Finite‐difference methods have generally been used to solve dynamic wave propagation problems over the last 25 years (Alterman and Karal, 1968; Boore, 1972; Kelly et al., 1976; and Levander, 1988). Recently, finite‐difference methods have been applied to the eikonal equation to calculate the kinematic solution to the wave equation (Vidale, 1988 and 1990; Podvin and Lecomte, 1991; Van Trier and Symes, 1991; Qin et al., 1992). The calculation of the first‐arrival times using this method has proven to be considerably faster than using classical ray tracing, and problems such as shadow zones, multipathing, and barrier penetration are easily handled. Podvin and Lecomte (1991) and Matsuoka and Ezaka (1992) extended and expanded upon Vidale’s (1988) algorithm to calculate traveltimes for reflected waves in two dimensions. Based on finite‐difference calculations for first‐arrival times, Hole et al. (1992) devised a scheme for inverting synthetic and real data to estimate the depth to refractors in the crust in three dimensions. The method of Hole et al. (1992) for inversion is computationally efficient since it avoids the matrix inversion of many of the published schemes for refraction and reflection traveltime data (Gjøystdal and Ursin, 1981).

Two methods for determining geophone orientations from VSP data

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. V87-V97 ◽  
Author(s):  
Xiaoxian Zeng ◽  
George A. McMechan
Keyword(s):  
A Priori ◽  
Polarization Plane ◽  
Seismic Profile ◽  
P Wave ◽  
Earth Model ◽  
S Wave ◽  
Coherent Signals ◽  
Plane Method ◽  
Wave Separation ◽  
Vsp Data

Vertical seismic profile (VSP) data are usually acquired with three-component geophones of unknown azimuthal orientation. The geophone orientation must be estimated from the recorded data as a prerequisite to processing such as P- and S-wave separation, calculation of wave-incident directions, and 3D migration. We compare and combine two methods for estimating azimuthal orientation by least-squares fitting over a large number of shots. Combining the two methods can be done in an automated manner, which provides more accurate estimates of the geophone orientations than previous methods. In the polarization-plane method, we calculate the polarization plane of the first P-wave arrival. Then we subtract the source azimuth to determine the geophone orientation, independently for each geophone, with an angular uncertainty of [Formula: see text], and with no accumulated errors. In the relative-angle method, we obtain relative angles between adjacent geophone pairs using trace crosscorrelations, and operate on all coherent signals (even noise). Swapped geophone components can be detected automatically using the polarization-plane method. The main limitation of these (and all other known) methods is that uncertainties associated with path refraction are not estimated, unless some geophones have a priori known orientations, or we have a known earth model to correct for refraction.

1-D seismic inversion of dual wavefield data: Part I, Nonuniqueness and stability

Geophysics ◽  
1994 ◽  
Vol 59 (5) ◽  
pp. 782-788 ◽  
Author(s):  
Steve T. Hildebrand ◽  
George A. McMechan
Keyword(s):  
Seismic Inversion ◽  
Inversion Method ◽  
Velocity Analysis ◽  
Dominant Wavelength ◽  
Parameter Estimator ◽  
Interval Velocity ◽  
Problem Resolution ◽  
Impedance Response ◽  
Variance Estimate ◽  
Interval Velocities

The inversion problem for determining seismic impedance is nonunique and nonstable because of limited recording aperture, data bandwidth, and data noise. For large reflection angles, small errors in the reflection coefficients give rise to arbitrarily large errors in the seismic impedance estimates. Spatial resolution of the seismic impedance response is controlled by the dominant wavelength corresponding to the source time wavelet; aperture limitations control the resolution of material impedance and interval velocity. Analysis of a linearization‐approximation approach shows that this method degenerates into a single‐parameter estimator for material impedance when using only small‐offset data and for velocity when using only far‐offset data. A nonlocal inversion method is introduced to estimate the material impedance and interval velocity by exploring interval velocity space and computing an associated variance estimate surface. Using this method, the resolution of the material impedance and compressional and shear interval velocities is shown to be poor in the elastic case because of a “valley” feature in the variance estimate surface; in the acoustic problem, resolution of the material impedance and interval velocity is excellent.

High-accuracy wavefront tracing traveltime calculation

Geophysics ◽  
1993 ◽  
Vol 58 (2) ◽  
pp. 284-292 ◽  
Author(s):  
Robert. L. Coultrip
Keyword(s):  
Three Dimensional ◽  
Computation Time ◽  
High Accuracy ◽  
Minimum Time ◽  
Model Complexity ◽  
Earth Model ◽  
Arrival Times ◽  
Multiple Paths ◽  
First Arrival ◽  
Tracing Algorithm

Conventional ray-tracing algorithms for first-arrival calculation suffer from drawbacks such as (1) no guarantee of finding the globally minimum traveltime path when multiple paths exist, (2) shadow zones, and (3) trouble finding minimum traveltime paths containing refraction and/or diffraction energy. Algorithms that trace wavefronts circumvent these problems. The new wavefront-tracing algorithm presented here is based on an earth model consisting of uniform-velocity triangular cells with nodes placed at vertices and along cell edges. Nodes are places where traces of first arrival wavefronts (propagation directions and arrival times) are stored. The algorithm works by propagating wavefronts (sampled at the nodes) away from the source throughout the entire model. Wavefronts are propagated locally as diffraction, direct arrival, or critically refracted energy that implicitly describe minimum time paths. Once the first arrival wavefront is sampled throughout the model, traveltimes and raypaths from the source to receivers are easily calculated. This algorithm computes the globally minimum time paths from the source to all points in the model regardless of model complexity and the number of locally minimum traveltime paths. Traveltime calculations are highly accurate and computation time is O(n log2 n) for n nodes. Use of triangular cells allows for cell boundaries that follow, say, fault planes and dipping beds, without resorting to stair-step approximations inherent with rectangular cells. This method can be extended to three dimensional (3-D) problems.

The nonuniqueness of the determination of interval velocities from moveout velocities

Geophysics ◽  
1989 ◽  
Vol 54 (9) ◽  
pp. 1209-1211 ◽  
Author(s):  
Theodor C. Krey
Keyword(s):  
Seismic Profile ◽  
Layered Earth ◽  
Interval Velocity ◽  
Offset Time ◽  
Zero Offset ◽  
Interval Velocities

In earlier papers (Krey, 1976; Hubral and Krey, 1980) I described how to obtain an equation for [Formula: see text], the nth interval velocity in an isovelocity layered earth having interfaces with arbitrary dips and curvatures, provided the velocities [Formula: see text], [Formula: see text], … to [Formula: see text] for the first n − 1 layers and the depths of the first n − 1 interfaces [Formula: see text], K = 1, 2, …, n − 1, are known and have continuous derivatives. Moreover, we assume that the zero‐offset time for the reflection from the base of the nth layer and gradient of the traveltime with respect to the horizontal coordinates are known. Finally, the normal moveout (NMO) velocity [Formula: see text] for the nth interface is observed in one arbitrary azimuth (one only), defined by ϕ, the angle between the x‐axis and the seismic profile.

Frequency-dependent reflection wave-equation traveltime inversion from walkaway vertical seismic profile data

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R947-R961
Author(s):  
Yikang Zheng ◽  
Yibo Wang ◽  
Qiang Luo ◽  
Xu Chang ◽  
Rongshu Zeng ◽  
...  
Keyword(s):  
Wave Equation ◽  
Calculated Data ◽  
Velocity Model ◽  
Seismic Profile ◽  
Initial Model ◽  
Vertical Seismic Profile ◽  
Frequency Dependent ◽  
Traveltime Inversion ◽  
Time Migration ◽  
Vsp Data

To accurately image the geologic structures from walkaway vertical seismic profile (VSP) data, it is necessary to estimate the subsurface velocity field with high resolution and enhanced illumination of deep reservoirs. Because full-waveform inversion (FWI) suffers from cycle skipping when the initial model is far from the true model, we have adopted frequency-dependent reflection wave-equation traveltime inversion (FRWT) to generate the background velocity model for VSP migration. The upgoing reflection data are separated from the original shot gathers, and dynamic warping is used to evaluate the traveltime differences between the observed data and the calculated data. Different frequency bands of the data are inverted in sequence to reconstruct the velocity model with higher resolution. We also implement wavefield decomposition on the gradient field to extract the contributions of reflection components and improve the updated model. The inverted results obtained from FRWT can be used as the initial model for conventional FWI or the velocity model for reverse time migration. The experiments on synthetic data and field data demonstrate that our approach can effectively recover the background velocity model from walkaway VSP data.

Traveltime inversion of both direct and reflected arrivals in vertical seismic profile data

Geophysics ◽  
1989 ◽  
Vol 54 (1) ◽  
pp. 49-56 ◽  
Author(s):  
Edward L. Salo ◽  
Gerard T. Schuster
Keyword(s):  
Least Squares ◽  
Velocity Structure ◽  
Seismic Profile ◽  
Profile Data ◽  
Vertical Seismic Profile ◽  
Data Set ◽  
Traveltime Inversion ◽  
Sonic Log ◽  
Vsp Data

Traveltimes from both direct and reflected arrivals in a VSP data set (Bridenstein no. 1 well in Oklahoma) are inverted in a least‐squares sense for velocity structure. By comparing the structure from inversion to the sonic log, we conclude that the accuracy of the reconstructed velocities is greater than that found when only the direct arrivals are used. Extensive tests on synthetic VSP data confirm this observation. Apparently, the additional reflection traveltime equations aid in averaging out the traveltime errors, as well as reducing the slowness variance in reflecting layers. These results are consistent with theory, which predicts a decrease in a layer’s slowness variance with an increase in the number and length of terminating reflected rays. For the Bridenstein data set, 130 direct traveltimes and 399 primary reflection traveltimes were used in the inversion.

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