Getting pre-stack time migration travel times from the single square root operator

Improving the focusing capability of pre-stack time migration allows the imaged section to reflect structural characteristics, depth, and interface shape and it is a key step for the preparation of the initial depth migration velocity model. The traditional symmetrical travel time equation is derived based on the assumption of a layered model. It is difficult to achieve the desired effect of focusing in media with strong lateral variation. The nonsymmetrical travel time equation based on Lie algebra and a pseudo-differential operator contains a lateral velocity derivative which can improve the focusing capability even in strongly lateral variable media and also the computation precision of the weight coefficients for relative amplitude preservation. Compared with the symmetrical methods, the nonsymmetrical method is more effective. In this paper, we describe several key steps of nonsymmetric pre-stack travel time calculation and present some test results using synthetic and real data.

Acoustic Borehole Images for Fracture Extraction and Analysis in Second Pre-pilot Drillhole of CCSD

Ultrasonic imaging logging provides continuous and oriented images of structures vs. depth. In the Chinese Continental Scientific Drilling (CCSD) Project, acoustic borehole images were recorded in the second pre-pilot drillhole which penetrates the metamorphic rocks. This paper focuses on fracture evaluation of the drillhole with these images. Both least square fit and a modified Hough transform are used for fracture extraction, and 269 fractures were mapped in the interval from 69.5 to 1 020 m. Most fractures dip steeply, with an average angle of 54°. Fracture dip directions are dominantly in the range of 220°-280° above the depth of 267 m, but 80°-120° in the lower zones. These observations may indicate the differences in structural movements or in-situ stress fields between the upper and lower zones in the drillhole.

Forward Modeling of Gravity,Gravity Gradients,and Magnetic Anomalies due to Complex Bodies

On the basis of the results of improved analytical expression of computation of gravity anomalies due to a homogeneous polyhedral body composed of polygonal facets, and applying the forward theory with the coordinate transformation of vectors and tensors, we deduced both the analytical expressions for gravity gradient tensors and for magnetic anomalies of a polygon, and obtained new analytical expressions for computing vertical gradients of gravity anomalies and vertical component of magnetic anomalies caused by a polyhedral body. And also we developed explicitly the complete unified expressions for the calculation of gravity anomalies, gravity gradient, and magnetic anomalies due to the homogeneous polyhedron. Furthermore, we deduced new analytical expressions for computing vertical gradients of gravity anomalies due to a finite rectangular prism by applying the newly obtained expressions for gravity gradient tensors due to a polyhedral target body. Comparison with forward calculation of models shows the correctness of these new expressions. It will reduce forward calculation time of gravity-magnetic anomalies and improve computational efficiency by applying our unified expressions for joint forward modeling of gravity-magnetic anomalies due to homogeneous polyhedral bodies.

Prediction of Apparent Equivalent Thickness Using the Spontaneous Potential Method and Its Application to Oilfield Development

The upper spontaneous potential produced by oil and gas accumulation is of a stable potential field, and its intensity is directly proportional to the content of the source and inversely proportional to the radius apart from the source. Theoretical research and practical results show that anomalies of spontaneous potential can indicate oil-bearing sandstone bodies and locate the areas of oil and gas accumulation. In oil areas which have fewer reservoir beds, the petroleum reservoir thickness can be predicted by determining the linear relationship between potential intensity and apparent equivalent thickness. In the Weixing （卫星） oilfield, which is devoid of sufficient reservoir beds, its apparent equivalent thickness can be predicted by the linear equation h= -0.19x＋0.74. On the basis of geological research, we use the spontaneous potential method to predict the equivalent thickness, helping in the selection of the most appropriate drill sites to enhance the probability of successful well boring so as to serve the next round development of the oilfield.

3D wavefield extrapolation with optimal separable approximation

An accurate and wide-angle one-way propagator for wavefield extrapolation is an important topic for research on wave-equation prestack depth migration in the presence of large and rapid velocity variations. Based on the optimal separable approximation presented in this paper, the mixed domain algorithm with forward and inverse Fourier transforms is used to construct the 3D one-way wavefield extrapolation operator. This operator separates variables in the wavenumber and spatial domains. The phase shift operation is implemented in the wavenumber domain while the time delay for lateral velocity variation is corrected in the spatial domain. The impulse responses of the one-way wave operator show that the numeric computation is consistent with the theoretical value for each velocity, revealing that the operator constructed with the optimal separable approximation can be applied to lateral velocity variations for the case of small steps. Imaging results of the SEG/EAGE model and field data indicate that the new method can be used to image complex structure.

Three-Dimensional P-Wave Velocity Structure of the Crust of North China

Since the Xingtai （邢台） earthquake in 1966, China Earthquake Administration has carried out a survey campaign along more than thirty deep seismic sounding （DSS） profiles altogether about twenty thousand kilometers long in North China to study the velocity structure of the crust and the upper mantle in this region, and has obtained a great number of research findings. However, these researches have not provided a 3D velocity structure model of the crust of North China and cannot provide seismic evidence for the study of the deep tectonic characteristics of the crust of the whole region. Hence, based on the information from the published data of the DSS profiles, we have chosen 14 profiles to obtain a 3D velocity structure model of North China using the vectorization function of the GIS software （Arc/Info） and the Kriging data gridding method. With this velocity structure model, we have drawn the following conclusions： （1） The P-wave velocity of the uppermost crust of North China changes dramatically, exhibiting a complicated velocity structure in plane view. It can be divided into three velocity zones mainly trending towards north-west. In the research area, the lowest-velocity zones lie in the Haihe （海河） plain and Bohai （渤海） Bay. Although the geological structure of the sedimentary overburden in the study area is somewhat inherited by the upper crust, there are still several differences between them. （2） Generally, the P-wave velocity of the crust increases with depth in the study area, but there still exists local velocity reversion. In the east, low-velocity anomalies of the Haihe plain gradually disappear with increasing depth, and the Shanxi （山西） graben in the west is mainly characterized by relatively low velocity anomalies. Bounded by the Taihang （太行） Mountains, the eastern and western parts differ in structural trend of stratum above the crystalline basement. The structural trend of the Huanghuaihai （黄淮海） block in the east is mainly north-east, while that of the Shanxi block and the eastern edge of the Ordos block is mainly north-west. （3） According to the morphological features of Moho, the crust of the study area can be divided into six blocks. In the Shanxi block, Moho apppears like a nearly south-north trending depression belt with a large crustal thickness. In the southern edge of the Inner Mongolia block and the south of the Yanshan （燕山） block,the Moho exhibits a feature of fold belt, trending nearly towards east-west. In the eastern edge of the Ordos block, the structure of Moho is relatively complex, presenting a pattern of fold trending nearly towards north-west with alternating convexes and concaves. Beneath the Huanghuaihai block, the middle and northern parts of the North China rift zone, the Moho is the shallowest in the entire region, with alternating uplifts and depressions in its shape. For the anteclise zone in the west of Shandong （山东） Province, the Moho is discontinuous for the fault depression extending in the north-west direction along Zaozhuang （枣庄） -Qufu （曲阜）.

Sedimentary Facies Models on Carbonatite in the Upper Shuaiba Member of Lower Cretaceous in Daleel Field, Oman

The Upper Shuaiba Member （USH） is the main force pay bed in the Daleel field in northern Oman; 5 layers including A, B, C, D, and E were divided in profile, and layer D and layer E are the main beds. With the development of exploration in the Daleel oil field, studying the sedimentary systems about their inner composition and the collocation in dimension, and setting up the sedimentary models in the USH are becoming more and more necessary and important to meet the further exploration requirement. Based on the data of geology, seism, and paleo-biology, according to the analysis method on carbonatite depositional system, the litho-facies assemblage and sedimentary environment in the USH were studied. Intershoal low-lying sub-facies （where the water depth is 10-50 m） and shallow shoal sub-facies （where the water depth is not more than 10 m） were extinguished in the layer D, and storm deposit was found in layer El, in which intershoal low-lying sub-facies also developed. The feature of the sedimentary sub-facies and the sedimentary condition were analyzed, and the sedimentary model was set up in the article： the carbonatite intershoal low-lying developed under the background of open land in shallow sea, where storm events usually occurred in the Lower Cretaceous in the area.