Inversion of reflection times in three dimensions

Geophysics ◽  
1981 ◽  
Vol 46 (7) ◽  
pp. 972-983 ◽  
Author(s):  
Håvar Gjøystdal ◽  
Bjørn Ursin
Keyword(s):  
Real Data ◽  
Normal Incidence ◽  
Thin Layers ◽  
Three Dimensions ◽  
Good Resolution ◽  
Inversion Algorithm ◽  
Linear Inversion ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Interval Velocities

When reflection data are available from a grid of crossing seismic lines, it is possible to construct normal incidence time maps from interpreted stacked sections and then apply three‐dimensional (3-D) ray‐tracing techniques following the normal‐incidence raypaths down to the various reflectors. The main disadvantage of this well‐known “time map migration” procedure is that interval velocities must be known a priori, and they must be estimated in advance by some approximate method. A technique is presented here which combines the above procedure with an inversion algorithm, providing direct calculations of interval velocities from the additional use of nonzero offset traveltime observations. A generalized linear inversion scheme is used, making possible a complete calculation of interval velocities and reflection interfaces, the latter represented by bicubic spline functions. To test the method in practice, we have applied it to (1) synthetic data generated from a constructed model, and (2) real data obtained from marine seismic sections. In the latter case, velocities and reflector depths obtained were compared to those obtained directly from a well log in the area. These results show a reasonably good resolution for layers that are not too deep relative to the shot/receiver offsets used. For deep and/or thin layers, the results are not satisfactory. This indicates the general limitation of seismic reflection data to resolve interval velocity, even in the presence of horizontally layered structure.

2-D and 3-D resistivity image reconstruction using crosshole data

Geophysics ◽  
1992 ◽  
Vol 57 (10) ◽  
pp. 1270-1281 ◽  
Author(s):  
Hiromasa Shima
Keyword(s):  
Field Test ◽  
Numerical Models ◽  
Electrical Potential ◽  
Nonlinear Least Squares ◽  
Three Dimensions ◽  
Inversion Method ◽  
Good Resolution ◽  
Inversion Algorithm ◽  
Linear Inversion ◽  
Resistivity Model

Theoretical changes in the distribution of electrical potential near subsurface resistivity anomalies have been studied using two resistivity models. The results suggest that the greatest response from such anomalies can be observed with buried electrodes, and that the resistivity model of a volume between boreholes can be accurately reconstructed by using crosshole data. The distributive properties of crosshole electrical potential data obtained by the pole‐pole array method have also been examined using the calculated partial derivative of the observed apparent resistivity with respect to a small cell within a given volume. The results show that for optimum two‐dimensional (2-D) and three‐dimensional (3-D) target imaging, in‐line data and crossline data should be combined, and an area outside the zone of exploration should be included in the analysis. In this paper, the 2-D and 3-D resistivity images presented are reconstructed from crosshole data by the combination of two inversion algorithms. The first algorithm uses the alpha center method for forward modeling and reconstructs a resistivity model by a nonlinear least‐squares inversion. Alpha centers express a continuously varying resistivity model, and the distribution of the electrical potential from the model can be calculated quickly. An initial general model is determined by the resistivity backprojection technique (RBPT) prior to the first inversion step. The second process uses finite elements and a linear inversion algorithm to improve the resolution of the resistivity model created by the first step. Simple 2-D and 3-D numerical models are discussed to illustrate the inversion method used in processing. Data from several field studies are also presented to demonstrate the capabilities of using crosshole resistivity exploration techniques. The numerical experiments show that by using the combined reconstruction algorithm, thin conductive layers can be imaged with good resolution for 2-D and 3-D cases. The integration of finite‐element computations is shown to improve the image obtained by the alpha center inversion process for 3-D applications. The first field test uses horizontal galleries to evaluate complex 2-D features of a zinc mine. The second field test illustrates the use of three boreholes at a dam site to investigate base rock features and define the distribution of an altered zone in three dimensions.

An improved method to estimate Q based on the logarithmic spectrum of moving peak points

2019 ◽  
Vol 7 (2) ◽  
pp. T255-T263 ◽  
Author(s):  
Yanli Liu ◽  
Zhenchun Li ◽  
Guoquan Yang ◽  
Qiang Liu
Keyword(s):  
Seismic Waves ◽  
Wave Attenuation ◽  
Real Data ◽  
Peak Frequency ◽  
Seismic Reflection Data ◽  
The Real ◽  
Time Frequency ◽  
Reflection Data ◽  
Text Filtering ◽  
The Impact

The quality factor ([Formula: see text]) is an important parameter for measuring the attenuation of seismic waves. Reliable [Formula: see text] estimation and stable inverse [Formula: see text] filtering are expected to improve the resolution of seismic data and deep-layer energy. Many methods of estimating [Formula: see text] are based on an individual wavelet. However, it is difficult to extract the individual wavelet precisely from seismic reflection data. To avoid this problem, we have developed a method of directly estimating [Formula: see text] from reflection data. The core of the methodology is selecting the peak-frequency points to linear fit their logarithmic spectrum and time-frequency product. Then, we calculated [Formula: see text] according to the relationship between [Formula: see text] and the optimized slope. First, to get the peak frequency points at different times, we use the generalized S transform to produce the 2D high-precision time-frequency spectrum. According to the seismic wave attenuation mechanism, the logarithmic spectrum attenuates linearly with the product of frequency and time. Thus, the second step of the method is transforming a 2D spectrum into 1D by variable substitution. In the process of transformation, we only selected the peak frequency points to participate in the fitting process, which can reduce the impact of the interference on the spectrum. Third, we obtain the optimized slope by least-squares fitting. To demonstrate the reliability of our method, we applied it to a constant [Formula: see text] model and the real data of a work area. For the real data, we calculated the [Formula: see text] curve of the seismic trace near a well and we get the high-resolution section by using stable inverse [Formula: see text] filtering. The model and real data indicate that our method is effective and reliable for estimating the [Formula: see text] value.

STACKING OF REFLECTIONS FROM COMPLEX STRUCTURES

Geophysics ◽  
1974 ◽  
Vol 39 (4) ◽  
pp. 427-440 ◽  
Author(s):  
Max K. Miller
Keyword(s):  
Deep Structure ◽  
Control Model ◽  
Layer Model ◽  
Low Velocity ◽  
Seismic Reflection Data ◽  
Near Surface ◽  
Static Correction ◽  
Reflection Data ◽  
Actual Field ◽  
Interval Velocities

Common‐depth‐point seismic reflection data were generated on a computer using simple ray tracing and analyzed with processing techniques currently used on actual field recordings. Constant velocity layers with curved interfaces were used to simulate complex geologic shapes. Two models were chosen to illustrate problems caused by curved geologic interfaces, i.e., interfaces at depths which vary laterally in a nonlinear fashion and produce large spatial variations in the apparent stacking velocity. A three‐layer model with a deep structure and no weathering was used as a control model. For comparison, a low velocity weathering layer also of variable thickness was inserted near the surface of the control model. The low velocity layer was thicker than the ordinary thin weathering layers where state‐of‐the‐art static correction methods work well. Traveltime, moveout, apparent rms velocities, and interval velocities were calculated for both models. The weathering introduces errors into the rms velocities and traveltimes. A method is described to compensate for these errors. A static correction applied to the traveltimes reduced the fluctuation of apparent rms velocities. Values for the thick weathering layer model were “over corrected” so that synclines (anticlines) replaced false anticlines (synclines) for both near‐surface and deep zones. It is concluded that computer modeling is a useful tool for analyzing specific problems of processing CDP seismic data such as errors in velocity estimates produced by large lateral variations in overburden.

SEISMIC VELOCITIES FROM SURFACE MEASUREMENTS

Geophysics ◽  
1955 ◽  
Vol 20 (1) ◽  
pp. 68-86 ◽  
Author(s):  
C. Hewitt Dix
Keyword(s):  
Accurate Determination ◽  
Careful Study ◽  
Seismic Velocities ◽  
Multiple Reflections ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Surface Measurements ◽  
Secondary Objective ◽  
Interval Velocities

The purpose of this paper is to discuss field and interpretive techniques which permit, in favorable cases, the quite accurate determination of seismic interval velocities prior to drilling. A simple but accurate formula is developed for the quick calculation of interval velocities from “average velocities” determined by the known [Formula: see text] technique. To secure accuracy a careful study of multiple reflections is necessary and this is discussed. Although the principal objective in determining velocities is to allow an accurate structural interpretation to be made from seismic reflection data, an important secondary objective is to get some lithological information. This is obtained through a correlation of velocities with rock type and depth.

scholarly journals Monte Carlo reservoir analysis combining seismic reflection data and informed priors

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. R31-R41 ◽  
Author(s):  
Andrea Zunino ◽  
Klaus Mosegaard ◽  
Katrine Lange ◽  
Yulia Melnikova ◽  
Thomas Mejer Hansen
Keyword(s):  
Monte Carlo ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Probabilistic Approach ◽  
Multiple Point ◽  
Petroleum Reservoir ◽  
Inversion Algorithm ◽  
Reservoir Properties ◽  
Seismic Reflection Data ◽  
Reflection Data

Determination of a petroleum reservoir structure and rock bulk properties relies extensively on inference from reflection seismology. However, classic deterministic methods to invert seismic data for reservoir properties suffer from some limitations, among which are the difficulty of handling complex, possibly nonlinear forward models, and the lack of robust uncertainty estimations. To overcome these limitations, we studied a methodology to invert seismic reflection data in the framework of the probabilistic approach to inverse problems, using a Markov chain Monte Carlo (McMC) algorithm with the goal to directly infer the rock facies and porosity of a target reservoir zone. We thus combined a rock-physics model with seismic data in a single inversion algorithm. For large data sets, the McMC method may become computationally impractical, so we relied on multiple-point-based a priori information to quantify geologically plausible models. We tested this methodology on a synthetic reservoir model. The solution of the inverse problem was then represented by a collection of facies and porosity reservoir models, which were samples of the posterior distribution. The final product included probability maps of the reservoir properties in obtained by performing statistical analysis on the collection of solutions.

Stereotomography

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE25-VE34 ◽  
Author(s):  
Gilles Lambaré
Keyword(s):  
Seismic Reflection ◽  
Waveform Inversion ◽  
Data Cube ◽  
Three Dimensions ◽  
Seismic Reflection Data ◽  
Depth Imaging ◽  
Traveltime Tomography ◽  
Reflection Data ◽  
Full Waveform ◽  
Efficiency And Reliability

Stereotomography was proposed [Formula: see text] ago for estimating velocity macromodels from seismic reflection data. Initially, the goal was to retain the advantages of standard traveltime tomography while providing an alternative to difficult interpretive traveltime picking. Stereotomography relies on the concept of locally coherent events characterized by their local slopes in the prestack data cube. Currently, stereotomography has been developed in two and three dimensions, and precious experience has been gained. The expected advantages have been demonstrated fully (in particular, the efficiency and reliability of the semiautomatic stereotomographic picking strategies), and further studies have increased the method’s potential and flexibility. For example, stereotomographic picking can now be done in either the prestack or poststack domain, in either the time (migrated or unmigrated) or depth domain. It appears that the theoretical frame of stereotomography can reconcile, very satisfactorily and efficiently, most methods proposed for velocity-macromodel estimation for depth imaging. Moreover, an extension of the method to full-waveform inversion already exists and opens the way for very interesting developments.

Turning‐ray tomography

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1917-1929 ◽  
Author(s):  
Joseph P. Stefani
Keyword(s):  
Velocity Structure ◽  
Initial Point ◽  
Real Data ◽  
Point Sources ◽  
Surface Velocity ◽  
Inversion Algorithm ◽  
Low Velocity ◽  
Linear Inversion ◽  
Near Surface ◽  
Velocity Inversion

Turning‐ray tomography is useful for estimating near‐surface velocity structure in areas where conventional refraction statics techniques fail because of poor data or lack of smooth refractor/velocity structure. This paper explores the accuracy and inherent smoothing of turning‐ray tomography in its capacity to estimate absolute near‐surface velocity and the statics times derived from these velocities, and the fidelity with which wavefields collapse to point diffractors when migrated through these estimated velocities. The method comprises nonlinear iterations of forward ray tracing through triangular cells linear in slowness squared, coupled with the LSQR linear inversion algorithm. It is applied to two synthetic finite‐ difference data sets of types that usually foil conventional refraction statics techniques. These models represent a complex hard‐rock overthrust structure with a low‐velocity zone and pinchouts, and a contemporaneous near‐shore marine trench filled with low‐ velocity unconsolidated deposits exhibiting no seismically apparent internal structure. In both cases velocities are estimated accurately to a depth of one‐ fifth the maximum offset, as are the associated statics times. Of equal importance, the velocities are sufficiently accurate to correctly focus synthetic wavefields back to their initial point sources, so migration/datuming applications can also use these velocities. The method is applied to a real data example from the Timbalier Trench in the Gulf of Mexico, which exhibits the same essential features as the marine trench synthetic model. The Timbalier velocity inversion is geologically reasonable and yields long and short wavelength statics that improve the CMP gathers and stack and that correctly align reflections to known well markers. Turning‐ray tomography estimates near‐surface velocities accurately enough for the three purposes of lithology interpretation, statics calculations, and wavefield focusing for shallow migration and datuming.

Tomographic determination of velocity and depth in laterally varying media

Geophysics ◽  
1985 ◽  
Vol 50 (6) ◽  
pp. 903-923 ◽  
Author(s):  
T. N. Bishop ◽  
K. P. Bube ◽  
R. T. Cutler ◽  
R. T. Langan ◽  
P. L. Love ◽  
...  
Keyword(s):  
Seismic Reflection ◽  
Seismic Velocity ◽  
Real Data ◽  
Seismic Reflection Data ◽  
Near Surface ◽  
Reflection Data ◽  
Tomographic Method ◽  
Recorded Data ◽  
The Difference

Estimation of reflector depth and seismic velocity from seismic reflection data can be formulated as a general inverse problem. The method used to solve this problem is similar to tomographic techniques in medical diagnosis and we refer to it as seismic reflection tomography. Seismic tomography is formulated as an iterative Gauss‐Newton algorithm that produces a velocity‐depth model which minimizes the difference between traveltimes generated by tracing rays through the model and traveltimes measured from the data. The input to the process consists of traveltimes measured from selected events on unstacked seismic data and a first‐guess velocity‐depth model. Usually this first‐guess model has velocities which are laterally constant and is usually based on nearby well information and/or an analysis of the stacked section. The final model generated by the tomographic method yields traveltimes from ray tracing which differ from the measured values in recorded data by approximately 5 ms root‐mean‐square. The indeterminancy of the inversion and the associated nonuniqueness of the output model are both analyzed theoretically and tested numerically. It is found that certain aspects of the velocity field are poorly determined or undetermined. This technique is applied to an example using real data where the presence of permafrost causes a near‐surface lateral change in velocity. The permafrost is successfully imaged in the model output from tomography. In addition, depth estimates at the intersection of two lines differ by a significantly smaller amount than the corresponding estimates derived from conventional processing.

Shallow 3D seismic-reflection imaging of fracture zones in crystalline rock

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. B149-B160 ◽  
Author(s):  
Cedric Schmelzbach ◽  
Heinrich Horstmeyer ◽  
Christopher Juhlin
Keyword(s):  
Seismic Reflection ◽  
Crystalline Rock ◽  
Three Dimensions ◽  
Disposal Site ◽  
3D Seismic ◽  
Fracture Zones ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Receiver Array

A limited 3D seismic-reflection data set was used to map fracture zones in crystalline rock for a nuclear waste disposal site study. Seismic-reflection data simultaneously recorded along two roughly perpendicular profiles (1850 and [Formula: see text] long) and with a [Formula: see text] receiver array centered at the intersection of the lines sampled a [Formula: see text] area in three dimensions. High levels of source-generated noise required a processing sequence involving surface-consistent deconvolution, which effectively increased the strength of reflected signals, and a linear [Formula: see text] filtering scheme to suppress any remaining direct [Formula: see text]-wave energy. A flexible-binning scheme significantly balanced and increased the CMP fold, but the offset and azimuth distributions remain irregular; a wide azimuth range and offsets [Formula: see text] are concentrated in the center of the survey area although long offsets [Formula: see text] are only found at the edges of the site. Three-dimensional dip moveout and 3D poststack migration were necessary to image events with conflicting dips up to about 40°. Despite the irregular acquisition geometry and the high level of source-generated noise, we obtained images rich in structural detail. Seven continuous to semicontinuous reflection events were traced through the final data volume to a maximum depth of around [Formula: see text]. Previous 2D seismic-reflection studies and borehole data indicate that fracture zones are the most likely cause of the reflections.

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