Statistical distribution of nonlinear random wave height

A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.

Measurements of ocean wave and current field using dual polarized X-band radar

A new ocean wave and sea surface current monitoring system with horizontally-(HH) and vertically-(VV) polarized X-band radar was developed. Two experiments into the use of the radar system were carried out at two sites, respectively, for calibration process in Zhangzi Island of the Yellow Sea, and for validation in the Yellow Sea and South China Sea. Ocean wave parameters and sea surface current velocities were retrieved from the dual polarized radar image sequences based on an inverse method. The results obtained from dual-polarized radar data sets acquired in Zhangzi Island are compared with those from an ocean directional buoy. The results show that ocean wave parameters and sea surface current velocities retrieved from radar image sets are in a good agreement with those observed by the buoy. In particular, it has been found that the vertically-polarized radar is better than the horizontally-polarized radar in retrieving ocean wave parameters, especially in detecting the significant wave height below 1.0 m.

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

柴达木盆地地震勘探关键技术研究

The rugged surface topography determined the seismic data acquisition construction conditions and the seismic wave explosive and receiver quality in Qaidam Basin. This dissertation systematically researched the seismic acquisition, imaging process and the attribute analysis techniques of complicated oil and gas reservoir. The main research achievements and cognitions are as follows: 1. Through the stimulation effects research and analysis from the aspect of lithologic water-containing differences, it’s specific that stable hydrous sand layer can effectively enhance the stimulation effects combined with the corresponding field tests. The seismic data S/N ratio has been improved due to the combination explosive stimulation. Through the fold number and maximum offset analyses of target horizon, the complicated geometry has been optimized and the S/N ratio of seismic data has been improved, which made an important basis for improvement of 3D seismic data. 2. It has been proved that the first arrival refraction static correction method under the model constraint of fine surface survey is suitable to the Qaidam Basin of western areas by the real seismic data processing. Although the refraction horizon of near surface has some changes in a certain extent, it’s steady basically. The refraction horizon can be continuously traced in sections, so it’s qualified for the refraction static correction method on the whole. 3. The research is based on the curved-ray pre-stack time migration techniques of rough topography, and improved the imaging precision of complex areas. This techniques adopted the constant and variable velocity scanning mode and enhanced the velocity analysis precision. The 3D pre-stack time migration techniques reasonably solved the imaging and velocity multiple solutions problems of steep-dip faults and the intersections of horizontal layers. What’s more, fine velocity analysis and mute are very important to enhance the imaging precision of the seismic data in complicated Wunan areas. 4. The 3D seismic data edge-preserving processing methods have been realized due to the image process techniques. Because this method uses the large range filter, it can attenuate the noise maximally. The faults, break points, lithologic pinchout points and lithologic body of small scale such as river will not be influenced by blur because of the edge-preserving characterization of the method which is really an effective assistant technique of low S/N ratio seismic data attribute analysis. 5. The use of spectral decomposition technique can effectively identify the reservoirs. The special geology body which will not be identified (or without obvious characters) in the seismic profile may be found through the details changes of different frequencies in the amplitude profiles.

陆地三分量三维地震勘探技术研究与应用

With the development of oil and gas field exploration, it becomes harder to search new reserves. So a higher demand of seismic exploration comes up. Now 3C3D seismic exploration technology has been applied in petroleum exploration domains abroad. Comparing with the traditional P-wave exploration, the seismic attributes information which provided by 3C3D seismic exploration will increase quickly. And it can derive various combined parameters. The precision of information about lithology, porosity, fracture, oil-bearing properties, etc which estimated by above parameters was higher than that of pure P-wave exploration. These advantages mentioned above lead to fast development of 3C3D seismic technology recently. Therefore, how to apply the technology in petroleum exploration field in China, how to obtain high quality seismic data, and how to process and interpret real data, become frontier topics in geophysical field nowadays, which have important practical significance in research and application. In this paper, according to the propagation properties of P-wave and converted wave, a study of 3C3D acquisition parameters design method was completed. Main parameters included: trace interval, shot interval, maximum offset, bin size, the interval of receiving lines, the interval of shooting lines, migration aperture, maximum cross line distance, etc. Their determination principle was given. The type of 3C3D seismic exploration geometry was studied. By calculating bin attributes and analyzing parameters of geometry, some useful conclusions were drawn. With the method in this paper, real geometries for continental lithology stratum gas reservoir and fractured gas reservoir were studied and determined. In the static method of multi-wave, the near surface P-wave, S-wave parameter investigation method has been advanced, and this method has been applied for the patent successfully; the near surface P-wave, S-wave parameter investigation method and the converted refraction wave first arrival static techniques have been integrally used to improve the effectiveness of converted wave static. In the aspect of converted wave procession, the rotation of horizontal component data, the calculation of converted wave common conversion bin, the residual static of converted wave, the velocity analysis of the common conversion point (CCP), the Kirchhoff pre-stack time migration of converted wave techniques have been applied for setting up the various 3C3D seismic data processing flows based on different geologic targets, and the high quality P-wave, converted-wave profiles have been acquired in the actual data processing. In the aspect of P-wave and converted-wave comprehensive interpretation, the thoughts and methods of using zero-offset S-wave VSP data to calibrate horizon have been proposed; the method of using P-wave and S-wave amplitude ratio to predict the areas of oil and gas enrichment has been studied; the method of inversion using P-wave combined with S-wave has been studied; the various P-wave, S-wave parameters(velocity ratio, amplitude ratio, poisson ratio) have been used to predict the depth, physical properties, gas-bearing properties of reservoirs; the method of predicting the continental stratum lithology gas reservoir has been built. The above techniques have all been used in various 3D3C seismic exploration projects in China, and the better effects have been gotten. By using these techniques, the 3C3D seismic exploration level has been improved.

人工源宽角地震资料中的广角效应及其对地壳速度成像的影响

The seismic wide-angle reflection/refraction method is the one of the most effective method for probing the crustal and upper mantle structure. It mainly uses the wide-angle reflection information from the boundary in the crust and the top boundary of the upper mantle to rebuild the crust and upper mantle structure. Through analyzing the reflection and transmission coefficients of various incident waves on the interface, we think relative to the pre-critical angle reflection information the post critical angle reflection information that received by wide-angle seismic data exists a time-shift effect with the offset variation, and then it must cause the error for velocity analysis and structure image. The feature of the wide-angle seismic wave field of the fourteen representative crust columns tell us that the wide-angle effects in the different representative tectonic units for the interface depth and the interval velocity in crust. We studied the features of the wide-angle seismic wave field through building the crust model and inverse its travel time by GA method to know the wide-angle influence on crustal velocity image. At last we finished the data processing of the Tunxi-Wenzhou wide-angle seismic profile. The results are as following: (1) Through building crust model, we labeled the travel time for all the phases by ray tracing method and remove wide-angle effects method, it revealed the wide-angle effect exists in the seismic data. (2) The travel time inversion by GA method can tell us that the depth by traditional ray tracing method is shallower than the result by remove wide-angle effects method, the latter can recover the crust structure model in effect. (3) We applied the two method mentioned before to the fourteen representative crust columns in China. It indicates that the removed wide-angle effect method in travel time inversion is reasonable and effective. (4) The real data processing from Tunxi-Wenzhou wide-angle seismic profile give us the basic structure through the two ways. The main influence exhibits in the difference of the interval velocity of the curst, and the wide-angle effects in shallow interface are stronger than the deep interface.

接收函数方法与中国及邻区上地幔间断面的研究

The receiver function method applied in researching the discontinuities in upper mantle was systematically studied in this paper. Using the theoretical receiver functions, the characteristics of P410S and P660S phases were analyzed, and the influencing factors for detection of these phases were discussed. The stability of receiver function was studied, and a new computational method of receiver function, RFSSMS (Receiver Function of Stack and Smooth of Multi seismic-records at a Single station), was put forward. We built initial reference velocity model for the media beneath each of 18 seismic stations respectively; then estimated the buried depths of 410-km and 660-km discontinuities(simply marked as '410' and '660') under the stations by using the arrive time differences of P410S and P660S with P. We developed a new receiver function inversion method -PGARFI (Peeling-Genetic Algorithm of Receiver Function Inversion), to obtain the whole crust and upper mantle velocity structure and the depths of discontinuities beneath a station. The major works and results could be summarized as follows: (1) By analysis of the theoretical receiver functions with different velocity models and different ray parameters, we obtain the knowledge: The amplitudes of P410S and P660S phases are decreasing with the increasing of epicentral distance A , and the arrival time differences of these phases with P are shorter as A is longer. The multiple refracted and/or reflected waves yielded on Moho and the discontinuities in the crust interfere the identification of P410S. If existing LVZ under the lithosphere, some multiple waves caused by LVZ will interfere the identification of P410S. The multiple waves produced by discontinuity lied near 120km depth will mix with P410s phase in some range of epicentral distance; and the multiple waves concerned with the discontinuity lied near 210km depth will interfere the identification of P660S. The epicentral distance for P4i0s identification is limited, the upper limit is 80° . The identification of P660S is not restricted by the epicenter distance obviously. The identification of P410S and P6gos in the theoretical receiver functions is interfered weakly from the seismic wave attenuation caused by the media absorption if the Q value in a reasonable range. (2) The stability of receiver function was studied by using synthetic seismograms with different kind of noise. The results show that on the condition of high signal-noise-ratio of seismic records, the high frequency background noise and the low frequency microseism noise do not influence the calculating result of receiver function. But the media "scattering noise" influence the stability of receiver function. When the scattering effect reach some level, the identification of P4iOs and P66os is difficult in single receiver function which is yielded from only one seismic record. We provided a new method to calculate receiver function, that is, with a group of earthquake records, stacking the R and Z components respectively in the frequency domain, and weighted smooth the stacked Z component, then compute the complex spectrum ratio of R to Z. This method can improve the stability of receiver function and protrude the P4i0s and P66os in the receiver function curves. (3) 263 receiver functions were provided from 1364 three component broadband seismograms recorded at 18 stations in China and adjacent areas for the tele-earthquakes. The observed arrival time differences of P410S and P660S with P were obtained in these receiver functions. The initial velocity model for every station was built according to the prior research results. The buried depths of '410' and '660' under a station were acquired by the way of adjusting the depths of these two discontinuities in the initial velocity model until the theoretical arrival time differences of P410S and P660S with P well conformed to the observed. The results show an obvious lateral heterogeneity of buried depths of ' 410' and (660' . The depth of '410' is shallower beneath BJI, XAN, LZH and ENH, but deeper under QIZ and CHTO, and the average is 403km . The average depth of '660' is 663km, deeper under MDJ and MAJO, but shallower under QIZ and HYB. (4) For inversing the whole crust and upper mantle velocity structure, a new inversion method -PGARFI (Peeling-Genetic Algorithm of Receiver Function Inversion) has- been developed here. The media beneath a station is divided into segments, then the velocity structure is inversed from receiver function from surface to deep successively. Using PGARFI, the multi reflection / refraction phases of shallower discontinuities are isolated from the first order refraction transform phase of deep discontinuity. The genetic algorithm with floating-point coding was used hi the inversion of every segment, and arithmetical crossover and non-uniform mutation technologies were employed in the genetic optimization. 10 independent inversions are completed for every segment, and 50 most excellent velocity models are selected according to the priority of fitness from all models produced in the inversion process. The final velocity structure of every segment is obtained from the weighted average of these 50 models. Before inversion, a wide range of velocity variation with depth and depth range of the main discontinuities are given according to priori knowledge. PGARFI was verified with numerical test and applied in the inversion of the velocity structure beneath HIA station down to 700km depth.

用宽频带远震体波波形研究中国及邻近地区地壳构造及地质意义初探

The theory and approach of the broadband teleseismic body waveform inversion are expatiated in this paper, and the defining the crust structure's methods are developed. Based on the teleseismic P-wave data, the theoretic image of the P-wave radical component is calculated via the convolution of the teleseismic P-wave vertical component and the transform function, and thereby a P-wavefrom inversion method is built. The applied results show the approach effective, stable and its resolution high. The exact and reliable teleseismic P waveforms recorded by CDSN and IRIS and its geodynamics are utilized to obtain China and its vicinage lithospheric transfer functions, this region ithospheric structure is inverted through the inversion of reliable transfer functions, the new knowledge about the deep structure of China and its vicinage is obtained, and the reliable seismological evidence is provided to reveal the geodynamic evolution processes and set up the continental collisional theory. The major studies are as follows: Two important methods to study crustal and upper mantle structure -- body wave travel-time inversion and waveform modeling are reviewed systematically. Based on ray theory, travel-time inversion is characterized by simplicity, crustal and upper mantle velocity model can be obtained by using 1-D travel-time inversion preliminary, which introduces the reference model for studying focal location, focal mechanism, and fine structure of crustal and upper mantle. The large-scale lateral inhomogeneity of crustal and upper mantle can be obtained by three-dimensional t ravel-time seismic tomography. Based on elastic dynamics, through the fitting between theoretical seismogram and observed seismogram, waveform modeling can interpret the detail waveform and further uncover one-dimensional fine structure and lateral variation of crustal and upper mantle, especially the media characteristics of singular zones of ray. Whatever travel-time inversion and waveform modeling is supposed under certain approximate conditions, with respective advantages and disadvantages, and provide convincing structure information for elucidating physical and chemical features and geodynamic processes of crustal and upper mantle. Because the direct wave, surface wave, and refraction wave have lower resolution in investigating seismic velocity transitional zone, which is inadequate to study seismic discontinuities. On the contrary, both the converse and reflected wave, which sample the discontinuities directly, must be carefully picked up from seismogram to constrain the velocity transitional zones. Not only can the converse wave and reflected wave study the crustal structure, but also investigate the upper mantle discontinuities. There are a number of global and regional seismic discontinuities in the crustal and upper mantle, which plays a significant role in understanding physical and chemical properties and geodynamic processes of crustal and upper mantle. The broadband teleseismic P waveform inversion is studied particularly. The teleseismic P waveforms contain a lot of information related to source time function, near-source structure, propagation effect through the mantle, receiver structure, and instrument response, receiver function is isolated form teleseismic P waveform through the vector rotation of horizontal components into ray direction and the deconvolution of vertical component from the radial and tangential components of ground motion, the resulting time series is dominated by local receiver structure effect, and is hardly irrelevant to source and deep mantle effects. Receiver function is horizontal response, which eliminate multiple P wave reflection and retain direct wave and P-S converted waves, and is sensitive to the vertical variation of S wave velocity. Velocity structure beneath a seismic station has different response to radial and vertical component of an accident teleseismic P wave. To avoid the limits caused by a simplified assumption on the vertical response, the receiver function method is mended. In the frequency domain, the transfer function is showed by the ratio of radical response and vertical response of the media to P wave. In the time domain, the radial synthetic waveform can be obtained by the convolution of the transfer function with the vertical wave. In order to overcome the numerical instability, generalized reflection and transmission coefficient matrix method is applied to calculate the synthetic waveform so that all multi-reflection and phase conversion response can be included. A new inversion method, VFSA-LM method, is used in this study, which successfully combines very fast simulated annealing method (VFSA) with damped least square inversion method (LM). Synthetic waveform inversion test confirms its effectiveness and efficiency. Broadband teleseismic P waveform inversion is applied in lithospheric velocity study of China and its vicinage. According to the data of high quality CDSN and IRIS, we obtained an outline map showing the distribution of Asian continental crustal thickness. Based on these results gained, the features of distribution of the crustal thickness and outline of crustal structure under the Asian continent have been analyzed and studied. Finally, this paper advances the principal characteristics of the Asian continental crust. There exist four vast areas of relatively minor variations in the crustal thickness, namely, northern, eastern southern and central areas of Asian crust. As a byproduct, the earthquake location is discussed, Which is a basic issue in seismology. Because of the strong trade-off between the assumed initial time and focal depth and the nonlinear of the inversion problems, this issue is not settled at all. Aimed at the problem, a new earthquake location method named SAMS method is presented, In which, the objective function is the absolute value of the remnants of travel times together with the arrival times and use the Fast Simulated Annealing method is used to inverse. Applied in the Chi-Chi event relocation of Taiwan occurred on Sep 21, 2000, the results show that the SAMS method not only can reduce the effects of the trade-off between the initial time and focal depth, but can get better stability and resolving power. At the end of the paper, the inverse Q filtering method for compensating attenuation and frequency dispersion used in the seismic section of depth domain is discussed. According to the forward and inverse results of synthesized seismic records, our Q filtrating operator of the depth domain is consistent with the seismic laws in the absorbing media, which not only considers the effect of the media absorbing of the waves, but also fits the deformation laws, namely the frequency dispersion of the body wave. Two post stacked profiles about 60KM, a neritic area of China processed, the result shows that after the forward Q filtering of the depth domain, the wide of the wavelet of the middle and deep layers is compressed, the resolution and signal noise ratio are enhanced, and the primary sharp and energy distribution of the profile are retained.

井间地震技术研究和应用

Cross well seismic technique is a new type of geophysical method, which observes the seismic wave of the geologic body by placing both the source and receiver in the wells. By applying this method, it averted the absorption to high-frequency component of seismic signal caused by low weathering layers, thus, an extremely high-resolution seismic signal can be acquired. And extremely fine image of cross well formations, structure, and reservoir can be achieved as well. An integrated research is conducted to the high-frequency S-wave and P-wave data and some other data to determine the small faults, small structure and resolving the issues concerning the thin bed and reservoir's connectivity, fluid distribution, steam injection and fracture. This method connects the high-resolution surface seismic, logging and reservoir engineering. In this paper, based on the E & P situation in the oilfield and the theory of geophysical exploration, a research is conducted on cross well seismic technology in general and its important issues in cross well seismic technology in particular. A technological series of integrated field acquisition, data processing and interpretation and its integrated application research were developed and this new method can be applied to oilfield development and optimizing oilfield development scheme. The contents and results in this paper are as listed follows: An overview was given on the status quo and development of the cross well seismic method and problems concerning the cross well seismic technology and the difference in cross well seismic technology between China and international levels; And an analysis and comparison are given on foreign-made field data acquisition systems for cross-well seismic and pointed out the pros and cons of the field systems manufactured by these two foreign companies and this is highly valuable to import foreign-made cross well seismic field acquisition system for China. After analyses were conducted to the geometry design and field data for the cross well seismic method, a common wave field time-depth curve equation was derived and three types of pipe waves were discovered for the first time. Then, a research was conducted on the mechanism for its generation. Based on the wave field separation theory for cross well seismic method, we believe that different type of wave fields in different gather domain has different attributes characteristics, multiple methods (for instance, F-K filtering and median filtering) were applied in eliminating and suppressing the cross well disturbances and successfully separated the upgoing and downgoing waves and a satisfactory result has been achieved. In the area of wave field numerical simulation for cross well seismic method, a analysis was conducted on conventional ray tracing method and its shortcomings and proposed a minimum travel time ray tracing method based on Feraiat theory in this paper. This method is not only has high-speed calculation, but also with no rays enter into "dead end" or "blinded spot" after numerous iterations and it is become more adequate for complex velocity model. This is first time that the travel time interpolation has been brought into consideration, a dynamic ray tracing method with shortest possible path has been developed for the first arrivals of any complex mediums, such as transmission, diffraction and refraction, etc and eliminated the limitation for only traveling from one node to another node and increases the calculation accuracy for minimum travel time and ray tracing path and derives solution and corresponding edge conditions to the fourth-order differential sonic wave equation. The final step is to calculate cross well seismic synthetics for given source and receivers from multiple geological bodies. Thus, real cross-well seismic wave field can be recognized through scientific means and provides important foundation to guide the cross well seismic field geometry designing. A velocity tomographic inversion of the least square conjugated gradient method was developed for cross well seismic velocity tomopgraphic inversion and a modification has been made to object function of the old high frequency ray tracing method and put forward a thin bed oriented model for finite frequency velocity tomographic inversion method. As the theory model and results demonstrates that the method is simple and effective and is very important in seismic ray tomographic imaging for the complex geological body. Based on the characteristics of the cross well seismic algorithm, a processing flow for cross well seismic data processing has been built and optimized and applied to the production, a good section of velocity tomopgrphic inversion and cross well reflection imaging has been acquired. The cross well seismic data is acquired from the depth domain and how to interprets the depth domain data and retrieve the attributes is a brand new subject. After research was conducted on synthetics and trace integration from depth domain for the cross well seismic data interpretation, first of all, a research was conducted on logging constraint wave impedance of cross well seismic data and initially set up cross well seismic data interpretation flows. After it applied and interpreted to the cross well seismic data and a good geological results has been achieved in velocity tomographic inversion and reflection depth imaging and a lot of difficult problems for oilfield development has been resolved. This powerful, new method is good for oilfield development scheme optimization and increasing EOR. Based on conventional reservoir geological model building from logging data, a new method is also discussed on constraining the accuracy of reservoir geological model by applying the high resolution cross well seismic data and it has applied to Fan 124 project and a good results has been achieved which it presents a bight future for the cross well seismic technology.

The experimental studies on electrical conductivities and P-wave velocities of anorthosite at high pressure and high temperature

National Science Foundation of China (No. 10032040 and No. 49874013) and Joint Earthquake Science Foundation of China (No. 101119).