Common Scatter Point Gathers Research Articles

Wavefield characteristics of common-scatterpoint gathers and their application to seismic processing and interpretation in the Yin’e Basin

The Yin’e Basin, lying in the west of the Inner Mongolia Autonomous Region of China, embodies a complex geologic setting involving diverse and deformed strata of sedimentary and igneous rocks. Two-dimensional seismic data, collected in the western portion of the basin for the frontier exploration of oil and gas, are highly complicated with low signal-to-noise ratio and interference of reflected and diffracted waves. Seismic imaging using conventional technologies was poor, and the subsurface structures and strata were unreliable for interpretation. We have applied an integrated processing-and-interpretation method based on seismic wavefield characteristics of common-scatterpoint (CSP) gathers to deal with the exploration challenges. First, we enhanced the amplitude of signals and distinguished weak signals from coherent noises by their kinematic characteristics. The signals, including reflected and diffracted waves, appear as scattered waves with highlighted hyperbolic curves, characterized by the vertex of the hyperbola coinciding with the subsurface scatterpoint and the curvature determined by the root-mean-square velocity of the overlying medium. In contrast, the coherent noises, such as surface and refracted waves, present nearly linear curves with remarkably intensified amplitude in CSP gathers. Then, we established an accurate velocity model and investigated the thickness of the strata. Finally, we ran a prestack time migration (PSTM) for reflected and diffracted waves. The images were improved by mapping signals to the correct position with accurate velocity; therefore, the target strata and the fault planes, with the higher lateral resolution, were more visible. With the aid of well control and the velocity model, main faults and target sequences over the surveyed area were interpreted. Our CSP-gather processing technique not only has enabled us to reveal subsurface complexities and reach the exploration target in the area but also has implications for seismic explorations in similar environments where structures and sequences vary dramatically.

Improving prestack time migration by least-squares equivalent offset method

Time migration is an important tool to provide a subsurface image because it is faster and less sensitive to velocity errors than depth migration. However, a reliable and focused time migration image is achievable only with well-determined time-migration velocities. As an alternative of prestack time migration, equivalent offset migration (EOM) provides intermediate common scatterpoint (CSP) gathers that have higher fold and larger offset range than common midpoint (CMP) gathers, which enables precise focusing of the velocity semblance and accurate velocity analysis. However, direct implementation of EOM might introduce coherent mapping noise, which smears the velocity spectra and decreases the resolution of the final stacked image. We reformulate the EOM as a linear operator that maps CMP gathers to CSP gathers and then propose least-squares equivalent offset migration (LS-EOM) method that inverts for optimal CSP gathers by minimising the misfit between simulated and observed CMP gathers. Compared with the EOM method, LS-EOM provides noise-free CSP gathers, leading to better focusing of the velocity semblance and higher resolution of the final stacked image. Both synthetic and field data tests demonstrate the effectiveness of our proposed method.

A New Method to Extract CSP Gather of Topography for Scattered Wave Imaging

The seismic method is one of the major geophysical tools to study the structure of the earth. The extraction of the common scatter point (CSP) gather is a critical step to accomplish the seismic imaging with a scattered wave. Conventionally, the CSP gather is obtained with the assumption that the earth surface is horizontal. However, errors are introduced to the final imaging result if the seismic traces obtained at the rugged surface are processed using the conventional method. Hence, we propose the method of the extraction of the CSP gather for the seismic data collected at the rugged surface. The proposed method is validated by two numerical examples and expected to reduce the effect of the topography on the scattered wave imaging.

Error analysis of the converted wave deduced by equivalent velocity assumption

Based on the assumption of the equivalent velocity and offset, the converted wave travel-time equation, which has a double square root due to the asymmetric ray-path of the down-going P-wave and the up-coming S-wave, can be transformed into a single square root equation if the common scatterpoint (CSP) gathers are binned. This method simplifies the equation and decreases the errors of converted wave migration transferred by P-wave velocity error, compared to the equivalent offset method (EOM) migration proposed by Bancroft, Geiger and Foltinek . In this paper, the errors caused by the introduction of equivalent velocity for the PS-wave are analysed in detail. The discrete errors and effects introduced by discretization of the equivalent offset are presented, and finally the conditions for applying CSP gathers for PS-wave processing under the control of reasonable error limits are derived.

Prestack time migration by common-migrated-reflector-element stacking

Time migration is an attractive tool to produce a subsurface image because it is faster and less sensitive to velocities errors than depth migration. However, a highly focused time image is only achievable with well-determined time-migration velocities. Therefore, a refinement of the initial time-migration velocities often is required. We introduced a new technique for prestack time migration, based on the common-migrated-reflector-element stack of common scatterpoint gathers, including an automatic update of time-migration velocities. The common scatterpoint gathers are generated using a new formulation of the double-square-root equation that is parametrized with the common-offset apex time. The common-migrated-reflector-element stack is a multiparameter stacking technique based on the Taylor expansion of traveltimes of time-migrated reflections in the paraxial vicinity of the image ray. Our 2D synthetic and field data examples demonstrated that the proposed method provides updated time-migration velocities that are more robust and have higher resolution compared with the initial time-migration velocities. The prestack time migration method also showed a clear improvement of the focusing of reflections for such geologic features as faults and salt structures.

Pre-stack time migration and velocity analysis methods with common scatter-point gathers

The pre-stack time migration and velocity analysis methods on common scatter-point (CSP) gathers are based on pre-stack Kirchhoff time migration. The concept of equivalent offset provides a new idea for the research of seismic pre-stack migration and velocity estimation. In this paper, according to the theory of the equivalent offset, we derive the travel-time equation of CSP gathers, introduce the related pre-stack time migration method and discuss velocity analysis methods based on the CSP gathers, and point out the advantages of CSP methods over conventional methods. Processing of a model example and field seismic data show the validity of CSP pre-stack time migration and the velocity analysis methods based on it.

Fourier prestack migration by equivalent wavenumber

Fourier prestack migration is reformulated through a change of variables, from offset wavenumber to a new equivalent wavenumber, which makes the migration phase shift independent of horizontal wavenumber. After the change of variables, the inverse Fourier transform over horizontal wavenumber can be performed to create unmigrated, but fully horizontally positioned, gathers at each output location. A complete prestack migration then results by imaging each gather independently with a poststack migration algorithm. This equivalent wavenumber migration (EWM) is the Fourier analog of the space‐time domain method of equivalent offset migration (EOM). The latter is a Kirchhoff time‐migration technique which forms common scatterpoint (CSP) gathers for each migrated trace and then images those gathers with a Kirchhoff summation. These CSP gathers are formed by trace mappings at constant time, and migration velocity analysis is easily done after the gathers are formed. Both EWM and EOM are motivated by the algebraic combination of a double square root equation into a single square root. This result defines equivalent wavenumber or offset. EWM is shown to be an exact reformulation of prestack f-k migration. The EWM theory provides explicit Fourier integrals for the formation of CSP gathers from the prestack data volume and the imaging of those gathers to form the final prestack migrated result. The CSP gathers are given by a Fourier mapping, at constant frequency, of the unmigrated spectrum followed by an inverse Fourier transform. The mapping requires angle‐dependent weighting factors for full amplitude preservation. The imaging expression (for each CSP gather) is formally identical to poststack migration with the result retained only at zero equivalent offset. Through a numerical simulation, the impulse responses of EOM and EWM are shown to be kinematically identical. Amplitude scale factors, which are exact in the constant velocity EWM theory, are implemented approximately in variable velocity EOM.

The equivalent offset method of prestack time migration

A prestack time migration is presented that is simple, efficient, and provides detailed velocity information. It is based on Kirchhoff prestack time migration and can be applied to both 2-D and 3-D data. The method is divided into two steps: the first is a gathering process that forms common scatterpoint (CSP) gathers; the second is a focusing process that applies a simplified Kirchhoff migration on the CSP gathers, and consists of scaling, filtering, normal moveout (NMO) correction, and stacking. A key concept of the method is a reformulation of the double square‐root equation (of source‐scatterpoint‐receiver traveltimes) into a single square root. The single square root uses an equivalent offset that is the surface distance from the scatterpoint to a colocated source and receiver. Input samples are mapped into offset bins of a CSP gather, without time shifting, to an offset defined by the equivalent offset. The single square‐root reformulation gathers scattered energy to hyperbolic paths on the appropriate CSP gathers. A CSP gather is similar to a common midpoint (CMP) gather as both are focused by NMO and stacking. However, the CSP stack is a complete Kirchhoff prestack migrated section, whereas the CMP stack still requires poststack migration. In addition, the CSP gather has higher fold in the offset bins and a much larger offset range due to the gathering of all input traces within the migration aperture. The new method gains computational efficiency by delaying the Kirchhoff computations until after the CSP gather has been formed. The high fold and large offsets of the CSP gather enables precise focusing of the velocity semblance and accurate velocity analysis. Our algorithm is formulated in the space‐time domain, which enables prestack migration velocity analysis to be performed at selected locations and permits prestack migration of a 3-D volume into an arbitrarily located 2-D line.