articles

 

The article provides an overview of the inverse kinematic problem of seismology for the elastic half-space,  and methods for their solution discussed by the author. The first problem is inversion of discontinuous travel-time curves of refracted waves. For this a system of two Fredholm integral equations of the first kind is obtained  whose solution reduces to a quadratic programming in the class of piecewise monotone functions. The second  problem concerns to inversion of travel-times from deep source. The third problem (which similar to the second  one) is the inversion of the reflected wave travel times from a plane boundary. The fourth problem is the  inversion of reflection travel- times from common depth point (CDP) for a medium with curved boundary. It  needs to reveal the velocity distribution over the boundary, depth and the boundary inclination. The fifth  problem relates to the inversion difference in travel-time curves of the longitudinal and converted shear waves.  Solution of the problem is found in the class of monotone functions and the result is the boundary depth and  distribution of velocities of P-and S-waves. The sixth task – smoothing the observed travel-time curves of  seismic waves by convex cubic splines.

In this paper we prove the existence of derivative of residual functional with respect to a coordinate of medium properties discontinuity. We also derive expressions for this derivative.

The method of measurement of attenuation parameters of seismic waves as a rational way to search for  hydrocarbon-bearing deposits is developed. It is proved the utility of attenuation parameters determination  from  the  ratio  between  the  increment  of  the  period  of  the  probing  signal  and  the  travel  times  from  the  source.

A forward problem on seismic wave propagation in an effective model of an isotropic medium with  oriented fractures and attenuation is solved. In this model the symmetry axis is perpendicular to fracture planes.  Phase velocities and attenuation of the three wave types (qP, qSV, SH) are computed from eigenvalues of  Christoffel tensor with the complex-valued tensor of elasticity-attenuation moduli. This tensor includes the velocities V P, iso , V S, iso  in the isotropic medium and the four constants characterize fractures…

Algorithm for spatial AVOA analysis of P-wave reflections used for the study of anisotropic media is  developed. In contrast to the traditional sector-based AVOA analysis, the inverse problem is being solved using  the complete set of data extracted from P-waves of 3D data and related to the common reflecting area. Testing of the method was accomplished using the simulated data for YTZ (Yurubchen-Tohomo Zone – a big  oil-gas field in Russia). Results show a sufficiently high accuracy in determining the horizontal symmetry axis  azimuth for both regular and irregular acquisition grids with signal to noise ratio > 4–5.

An inverse problem of wave propagation in an attenuative transversely isotropic medium is solved. The  medium is represented as an effective model of an isotropic medium with a system of parallel fractures. It is  characterized by the matrix of elasticity-attenuation moduli with elements depending on six parameters: the  two are Lamé constants of an isotropic background, and the four constants describe fractures, which are real  and imaginary parts of complex-valued weaknesses, normal and tangential ones. The inverse problem is posed  as a problem to find the four fracture parameters from the anisotropy of qP-, qSV-, and SH-waves velocities  and attenuations observed in the preset interval of propagation directions. A solution is in minimization by the  least square method of residuals between the observed and theoretical values of velocities and attenuations.  The analysis of the solution of the for ward problem and investigation of the properties of the minimized target  function lead to the following conclusions. Data on the quasi-compressional wave qP permit to determine  reasonably well only the normal weaknesses. The tangential weaknesses are best determined from shear-wave  SH data, whereas the quasi-shear waves qSV are useful only in the absence of loops at the surfaces of ray  velocities. The best results are attained by the joint use of qP- and SH-waves in the vicinity of the symmetry  axis of the medium.

Processing of VSP data for well 830 at Pelyatkinsky area (North of Western Siberia) has been completed  and polarization analysis of shear and converted waves, both reflected and downgoing, has been carried out.  Azimuthal anisotropy of the subsurface is detected in a large depth range, and its parameters are defined.  Stability of symmetry elements of the medium at different depths is uncovered. The anisotropy revealed allows  predicting the direction of maximum permeability in the reservoir which is an important factor in planning  the development. Using azimuthal velocity analysis of 3D seismic data, lateral distribution of anisotropy pa- rameters over the area is obtained consistent with the VSP processing results.

Discrete wavelet decomposition on detailed layers includes division of wavelet coefficients vector into  sum of vectors of coefficients of different detailing level and reconstruction of detailed layers into time domain.  The technique of seismic data processing with use of wavelet filtration based on discrete wavelet decomposition  of  signal  on  detailed  layers  allows  to  expand  the  program  package  of  dynamic  processing,  analysis  and  interpretation of seismic fields. Efficiency of wavelet filtration is demonstrated on real seismic data obtained  during realization of three-component wave soundings (Krasnoyarsk Territory); deep seismic survey (DSS)  that were obtained by “land–sea” observation system (Chukchi Region); detailed acoustic measurements in  coal mined (Kuznetsk Basin). It is important that wavelet filtration based on wavelet decomposition detailed  layers gives possibility to keep local features of signal component.

We develope technology for detecting and to measuring vibro-seismic oscillations on the nanometer level  against the multiply exceeding noise is described. This technology is based on methods of correlated and in-phase accumulation of vibro-seismic oscillations, radiated by precisely controlled vibrators. The results obtained  are applicable for solving the vibro-DSS problems and active vibro-seismic monitoring.

In this paper some important questions of the Prony filtration method and its applications are presented.  The method can be used in seismic data processing and interpretation for various geological and production  tasks. It stands as a tool for estimating target horizons or productive zones. The tool allows to localize zones  of anomalous scattering and absorption (depending on the temporal frequency) of seismic energy, which are  related to the target horizons. Analysis and interpretation of these zones provides better understanding of  features and gives possibility to correlate these features with perspective reservoirs. In the paper special attention  is paid to three points: 1) the theoretical foundations of the Prony decomposition, obtaining stable estimates  of the Prony spectra for signals similar to seismic ones; 2) using Prony spectra in the signal filtration processing,  i.e., construction of the Prony filtration algorithms; and 3) the description of Prony filtration technology and  examples demonstrating its capabilities in practice. Using simple examples, we try to introduce the basic ideas  of the technology, illustrating the main points that are important for the application of this method in the real  seismic data processing.

Autocorrelation and cross-correlation functions of seismograms obtained from the same source point and  along receiver spread make it possible to build nonlinear equation system solvable for signal and noise. The  solution of this system can produce more reliable estimates of signals amplitude spectrum of compare with  independent source parameters estimation.

In the logarithmic scale the relation between specific surface and the number of instable solutions of  equations of motion is close to experimental relation between the energy and the number of earthquakes. This  law is not specific for seismology only. The metastable phenomena, which introduce catastrophic processes,  are special states between statics and dynamics.