Conventional Semblance Research Articles

AVO-Friendly Velocity Analysis Based on the High-Resolution PCA-Weighted Semblance

Velocity analysis using the semblance spectrum can provide an effective velocity model for advanced seismic imaging technology, in which the picking accuracy of velocity analysis is significantly affected by the resolution of the semblance spectrum. However, the peak broadening of the conventional semblance spectrum leads to picking uncertainty, and it cannot deal with the amplitude-variation-with-offset (AVO) phenomenon. The well-known AB semblance can process the AVO anomalies, but it has a lower resolution compared with conventional semblance. To improve the resolution of the AB semblance spectrum, we propose a new weighted AB semblance based on principal component analysis (PCA). The principal components or eigenvalues of seismic events are highly sensitive to the components with spatial coherence. Thus, we utilized the principal components of the normal moveout (NMO)-corrected seismic events with different scanning velocities to construct a weighting function. The new function not only has a high resolution for velocity scanning, but it is also a friendly method for the AVO phenomenon. Numerical experiments with the synthetic and field seismic data sets proved that the new method significantly improves resolution and can provide more accurate picked velocities compared with conventional methods.

High-resolution seismic velocity analysis by sign-based weighted semblance

Building an accurate velocity model plays a vital role in routine seismic imaging workflows. Normal-moveout (NMO)-based seismic velocity analysis is a popular method for making the velocity models. However, traditional velocity analysis methodologies are not generally capable of handling amplitude variations across moveout curves, specifically polarity reversals caused by amplitude-variation-with-offset (AVO) anomalies. I have developed an NMO-based velocity analysis approach that circumvents this shortcoming by modifying the conventional semblance (CS) function to include polarity and amplitude correction terms computed using correlation coefficients of seismic traces in the velocity analysis scanning window with a reference trace. Thus, the proposed method workflow is suitable for any class of AVO effects. The approach is evaluated with four synthetic data examples of different conditions and field data consisting of a common-midpoint gather. Lateral resolution enhancement using the proposed method workflow is evaluated by comparison between the results from the workflow and the results obtained by the application of CS and three semblance-based velocity analysis algorithms developed to circumvent the challenges associated with amplitude variations across moveout curves, caused by seismic attenuation and class II AVO anomalies. According to the obtained results, the proposed method is superior to all of the presented workflows in handling such anomalies.

Seismic velocity analysis in the presence of amplitude variations using local semblance

ABSTRACTObtaining accurate velocity models plays a crucial role in many routine seismic imaging algorithms. Seismic velocity models are normally made through seismic velocity analysis workflows. The routine workflows are not capable of dealing with polarity variations across moveout curves. We address this limitation by proposing a straight‐forward and robust semblance‐based workflow, which is a modified version of the conventional semblance function. The coherency function applies semblance analysis on separate clusters of receivers followed by averaging the corresponding coherency measures from all the clusters. The proposed approach is suitable for any case of amplitude variations including attenuation and any class of amplitude‐versus‐offset effects. The ability of the proposed workflow is demonstrated to two synthetic data as well as two field‐recorded common‐midpoint gathers. We perform accuracy analysis by comparing the results from the proposed approach with the results achieved from conventional velocity analysis, and another semblance‐based algorithm that is developed to address the polarity variation task. We also studied noise sensitivity analysis by computing and comparing mathematical expectations between theory and practice.

Method for obtaining high-resolution velocity spectrum based on weighted similarity

Seismic wave velocity is one of the most important processing parameters of seismic data, which also determines the accuracy of imaging. The conventional method of velocity analysis involves scanning through a series of equal intervals of velocity, producing the velocity spectrum by superposing energy or similarity coefficients. In this method, however, the sensitivity of the semblance spectrum to change of velocity is weak, so the resolution is poor. In this paper, to solve the above deficiencies of conventional velocity analysis, a method for obtaining a high-resolution velocity spectrum based on weighted similarity is proposed. By introducing two weighting functions, the resolution of the similarity spectrum in time and velocity is improved. Numerical examples and real seismic data indicate that the proposed method provides a velocity spectrum with higher resolution than conventional methods and can separate cross reflectors which are aliased in conventional semblance spectrums; at the same time, the method shows good noise-resistibility.

A multiple filtering and correlation array signal processing technique for cased-hole acoustic logging and applications

In cased-hole acoustic logging, estimating the formation velocity is often problematic when the casing is poorly bonded with the formation. The overwhelmingly large casing waves dominate the measured waveforms and overlap with the low-coherence, weak formation arrival, contributing to the failure of conventional semblance processing method. To tackle this problem, we have developed a filtered frequency semblance array waveform signal processing technique. The multiple filter technique is first used to filter the measured waveforms. We then apply the [Formula: see text]th root stacking method to the filtered signals. Consequently, the coherence of the formation signal on the obtained 3D semblance correlogram is significantly enhanced and clearly separated with the casing waves. We have applied the method to process synthetic and field cased-hole acoustic waveform data. Our results indicate that the new method significantly enhances the coherence of the desired formation signal and simultaneously estimates the formation of the P- and S-wave velocity.

Estimating normal moveout velocity using the recurrent neural network

Machine learning (ML) has recently gained immense popularity because of its successful application in complex problems. It develops an abstract relation between the input and output. We have evaluated the application of ML to the most basic seismic processing of normal moveout (NMO) correction. The arrival times of reflection events in a common midpoint (CMP) gather follow a hyperbolic trajectory; thus, they require a correction term to flatten the CMP gather before stacking. This correction term depends on an rms velocity, also referred to as the NMO velocity. In general, NMO velocity is estimated using the semblance measures and picking the peaks in the velocity panel. This process requires a lot of human intervention and computation time. We have developed a novel method using one of the tools based on an ML- approach and applied to the NMO velocity estimation problem. We use the recurrent neural network (RNN) to estimate the NMO velocity directly from the seismic data. The input to the network is a seismic gather and corresponding precalculated NMO velocity (as prelabeled data set) to flatten the gather. We first train the network to develop a relationship between the input gathers (before NMO correction) and the corresponding NMO velocities for a few CMPs as a supervised learning process. Adam optimization algorithm is used to train the RNN. The output from the network is then compared against the correct NMO velocity. The error between the two velocities is then used to update the weight of the neurons and to minimize the mean-squared error between the two velocities. After the network is trained, it can be used to calculate the NMO velocity for the rest of the seismic gathers. We evaluate our method on a noisy data set from Poland. We used only 10% of the CMPs to train the network, and then we used the trained network to predict NMO velocity for the remaining CMP locations. The stack section obtained by using RNN-generated NMO velocities is nearly identical to that obtained by the conventional semblance method.

Depth Migration Velocity: Differential Semblance Analysis for Sumatra Forearch Basin

The specific goal of this work is to present a complete velocity map obtained by picking the velocity in Common Image Gather (CIG) map. We simulated a shot gather in order to obtain a synthetic travel time data for depth analysis. We successfully determined the correct migration velocity and presented the velocity interval model. For further study, we also conducted a Semblance analysis in order to obtain a coherency panel between the energy and the depth migration velocity analysis. We successfully interpreted the conventional semblance profile that the correct velocity model maximizes that energy which is represent higher value. For the real case, The data set was acquired by CGGVeritas in 2009 of RMS velocities recorded in 48 CMP points. The results of the semblance analysis shows well coherence with the seismic reflectance data that reveals the Low Velocity Zone of Sumatra fault related to the present of fluid and gas.

Seismic depth imaging of iron‐oxide deposits and their host rocks in the Ludvika mining area of central Sweden

ABSTRACTThe development of cost‐effective and environmentally acceptable geophysical methods for the exploration of mineral resources is a challenging task. Seismic methods have the potential to delineate the mineral deposits at greater depths with sufficiently high resolution. In hardrock environments, which typically host the majority of metallic mineral deposits, seismic depth‐imaging workflows are challenged by steeply dipping structures, strong heterogeneity and the related wavefield scattering in the overburden as well as the often limited signal‐to‐noise ratio of the acquired data. In this study, we have developed a workflow for imaging a major iron‐oxide deposit at its accurate position in depth domain while simultaneously characterizing the near‐surface glacial overburden including surrounding structures like crossing faults at high resolution. Our workflow has successfully been showcased on a 2D surface seismic legacy data set from the Ludvika mining area in central Sweden acquired in 2016. We applied focusing prestack depth‐imaging techniques to obtain a clear and well‐resolved image of the mineralization down to over 1000 m depth. In order to account for the shallow low‐velocity layer within the depth‐imaging algorithm, we carefully derived a migration velocity model through an integrative approach. This comprised the incorporation of the tomographic near‐surface model, the extension of the velocities down to the main reflectors based on borehole information and conventional semblance analysis. In the final step, the evaluation and update of the velocities by investigation of common image gathers for the main target reflectors were used. Although for our data set the reflections from the mineralization show a strong coherency and continuity in the seismic section, reflective structures in a hardrock environment are typically less continuous. In order to image the internal structure of the mineralization and decipher the surrounding structures, we applied the concept of reflection image spectroscopy to the data, which allows the imaging of wavelength‐specific characteristics within the reflective body. As a result, conjugate crossing faults around the mineralization can directly be imaged in a low‐frequency band while the internal structure was obtained within the high‐frequency bands.

Characterization of hydrate and gas reservoirs in plate convergent margin by applying rock physics to high-resolution seismic velocity model

Gas hydrates are widely distributed in the Kumano forearc basin, which is located above accretionary prism in the Nankai margin off the Kii peninsula, Japan. Bottom-Simulating Reflector (BSR) at the base of gas hydrate stability zone has been imaged as a strong acoustic impedance contrast on the reflection seismic profiles. In order to better define the accumulations of gas hydrates and free gases, we performed a high-resolution seismic velocity analysis to 3D seismic data using a method of conventional semblance spectra via automatic velocity picking algorithm. The results revealed that gas hydrate-bearing sediments above the BSR and free gas-bearing sediments below the BSR are characterized by P-wave velocities of 1900–2500 m/s and 1000–1800 m/s, respectively. Then, the velocity model was converted into gas hydrate and free gas saturation using rock physics approaches. The results indicated that saturation of gas hydrates ranges from 0% to 45% in the pore space, and highly concentrated around the outer ridge where faults are densely developed. Additionally, concentrations of free gas ranging from 0% to 20% in the pore space are widely distributed below BSRs and are considerably high above ridge structure generated by displacement of large fault splayed from the deep plate boundary décollement. Based on these results, we suggest that the gas hydrates concentrated due to the free gas influx which migrated upward through the steeply dipping strata and faults (or fractures) cutting through the basin. The accumulations of gas and/or hydrates are further controlled by fault movements in the accretionary prism beneath the forearc basin. Therefore, these factors generated by intensive tectonic movements in the plate subduction zone control the distribution and saturation pattern of gas hydrate and free gas formations.

Obtaining high-resolution velocity spectra using weighted semblance

Velocity analysis employs coherency measurement along a hyperbolic or non-hyperbolic trajectory time window to build velocity spectra. Accuracy and resolution are strictly related to the method of coherency measurements. Semblance, the most common coherence measure, has poor resolution velocity which affects one’s ability to distinguish and pick distinct peaks. Increase the resolution of the semblance velocity spectra causes the accuracy of estimated velocity for normal moveout correction and stacking is improved. The low resolution of semblance spectra depends on its low sensitivity to velocity changes.In this paper, we present a new weighted semblance method that ensures high-resolution velocity spectra. To increase the resolution of semblance spectra, we introduce two weighting functions based on the first to second singular values ratio of the time window and the position of the seismic wavelet in the time window to the semblance equation. We test the method on both synthetic and real field data to compare the resolution of weighted and conventional semblance methods. Numerical examples with synthetic and real seismic data indicate that the new proposed weighted semblance method provides higher resolution than conventional semblance and can separate the reflectors which are mixed in the semblance spectrum.

Bond yields and stock returns comparison using wavelet semblance analysis

Various measures of resemblance are increasingly applied in confrontation of data samples obtained by different sources. Semblance analysis aims at comparison of two sets of data based on their phase and frequency. Conventional semblance analysis following the Fourier transform has several deficiencies resulting from the transform. To overcome these obstacles, another type of semblance analysis was developed applying the wavelet transform. This paper focuses on semblance analysis of stock prices and government bond yields of two major global economies using continuous wavelet transform regarding both scale and time.

Normal move-out correction in anisotropic and laterally heterogeneous media using simultaneous velocity variation with offset

In this paper, we present a new method of normal move-out (NMO) correction that works on a trace by trace basis technique rather than the current conventional sample by sample semblance analysis. The method corrects the pre-stack seismic data due to the NMO effect in both anisotropic and laterally heterogeneous mediums and simultaneously provides a full NMO velocity field that covers every single offset/azimuth in a common depth point (CDP). Also, we introduce a new computational method to recover the anisotropy effect from the extracted NMO velocity field. The presented method gives every single primary seismic reflector in a CDP, three different corrections; Positive correction (where the NMO velocity increases), Negative correction (where NMO velocity decreases) and zero correction (where NMO velocity doesn't change). The first two corrections (positive and negative) work only in case of anisotropy or laterally heterogeneous mediums while the last correction is applicable in case of the seismic reflector is isotropic. The method starts by picking the NMO velocity for each seismic reflector using the conventional semblance plot, then we use these picked NMO velocities as an initial input to our method and since every seismic reflector has three different possibilities, getting all the possible combinations is crucial. To get these combinations, we simply use the combination with repetition mathematical method. To control the degree of the increasing and the decreasing of the NMO velocity correction, we use two parameters called the Anisotropy range parameter(Ar) and its increment. The Ar parameter is used to modify the picked NMO velocity of the primary seismic reflector N times (by adding and subtracting a correction value) based on the number of combinations. The total number of times where initial NMO velocities are modified is based on both the Ar parameter and the number of the seismic reflectors. After all the picked NMO velocities are modified then, we use each of the modified NMO velocity traces (after the interpolation between the modified NMO velocities) to correct the corresponding seismic trace due to the NMO effect then, measure the similarity/semblance between the pilot trace (e.g. Zero offset trace but it dynamically changes) and that seismic trace under the NMO correction. This corresponding seismic trace is corrected due to the NMO effect N times and at each time we measure the semblance value. The modified NMO velocity trace that gives the highest semblance measure is selected. The process is repeated for all the other seismic traces in a CDP. We tested the method on different real and synthetic examples; Isotropic, anisotropic and laterally heterogeneous mediums synthetic examples are presented. Furthermore, we tested the method on a pre-stack CDP real example using Alaska dataset. The results show an excellent flattening to the seismic reflectors and provides a reasonably accurate normal move-out velocity field that covers every offset in a CDP.

A high-resolution weighted AB semblance for dealing with amplitude-variation-with-offset phenomenon

Velocity analysis is an essential step in seismic reflection data processing. The conventional and fastest method to estimate how velocity changes with increasing depth is to calculate semblance coefficients. Traditional semblance has two problems: low time and velocity resolution and an inability to handle amplitude variation-with-offset (AVO) phenomenon. Although a method known as the AB semblance can arrive at peak velocities in the areas with an AVO anomaly, it has a lower velocity resolution than conventional semblance. We have developed a weighted AB semblance method that can handle both problems simultaneously. We have developed two new weighting functions to weight the AB semblance to enhance the resolution of velocity spectra in the time and velocity directions. In this way, we increase the time and velocity resolution while eliminating the AVO problem. The first weighting function is defined based on the ratio between the first and the second singular values of the time window to improve the resolution of velocity spectra in velocity direction. The second weighting function is based on the position of the seismic wavelet in the time window, thus enhancing the resolution of velocity spectra in time direction. We use synthetic and field data examples to show the superior performance of our approach over the traditional one.

Velocity analysis using high-resolution semblance based on sparse hyperbolic Radon transform

Semblance measures the lateral coherency of the seismic events in a common mid-point gather, and it has been widely used for the normal-moveout-based velocity estimation. In this paper, we propose a new velocity analysis method by using high-resolution semblance based on sparse hyperbolic Radon transform (SHRT). Conventional semblance can be defined as the ratio of signal energy to total energy in the time gate. We replace the signal energy with the square of the sparse Radon panel and replace the total energy with the sparse Radon panel of the square data. Because of the sparsity-constrained inversion of SHRT, the new approach can produce higher resolution semblance spectra than the conventional semblance. We test this new semblance on synthetic and field data to demonstrate the improvements in velocity analysis.

Implementation aspects of eigendecomposition‐based high‐resolution velocity spectra

ABSTRACTIn this paper, we discuss high‐resolution coherence functions for the estimation of the stacking parameters in seismic signal processing. We focus on the Multiple Signal Classification which uses the eigendecomposition of the seismic data to measure the coherence along stacking curves. This algorithm can outperform the traditional semblance in cases of close or interfering reflections, generating a sharper velocity spectrum. Our main contribution is to propose complexity‐reducing strategies for its implementation to make it a feasible alternative to semblance. First, we show how to compute the multiple signal classification spectrum based on the eigendecomposition of the temporal correlation matrix of the seismic data. This matrix has a lower order than the spatial correlation used by other methods, so computing its eigendecomposition is simpler. Then we show how to compute its coherence measure in terms of the signal subspace of seismic data. This further reduces the computational cost as we now have to compute fewer eigenvectors than those required by the noise subspace currently used in the literature. Furthermore, we show how these eigenvectors can be computed with the low‐complexity power method. As a result of these simplifications, we show that the complexity of computing the multiple signal classification velocity spectrum is only about three times greater than semblance. Also, we propose a new normalization function to deal with the high dynamic range of the velocity spectrum. Numerical examples with synthetic and real seismic data indicate that the proposed approach provides stacking parameters with better resolution than conventional semblance, at an affordable computational cost.

Coherence measures in automatic time-migration velocity analysis

Time-migration velocity analysis can be carried out automatically by evaluating the coherence of migrated seismic events in common-image gathers (CIGs). The performance of gradient methods for automatic time-migration velocity analysis depends on the coherence measures used as the objective function. We compare the results of four different coherence measures, being conventional semblance, differential semblance, an extended differential semblance using differences of more distant image traces and the product of the latter with conventional semblance. In our numerical experiments, the objective functions based on conventional semblance and on the product of conventional semblance with extended differential semblance provided the best velocity models, as evaluated by the flatness of the resulting CIGs. The method can be easily extended to anisotropic media.

Velocity analysis using weighted semblance

Increasing the resolution of semblance-based velocity spectra, or semblance spectra, is useful for estimating normal moveout velocities, as increased resolution can help to distinguish peaks in the spectra. The resolution of semblance spectra depends on the sensitivity of semblance to changes in velocity. By weighting terms in the semblance calculation that are more sensitive to changes in velocity, we can increase resolution. Our implementation of weighted semblance is a straightforward extension of conventional semblance. Somewhat surprisingly, we increase resolution by choosing an offset-dependent weighting function that minimizes semblance. We test our method on synthetic and field data, and our tests confirm that weighted semblance provides higher resolution than conventional semblance.

A comparison of semblances of different order in common-reflection-surface parameter estimation

Conventional common-reflection-surface (CRS) parameter estimation is based on coherence analysis using the second-order semblance function. Extensions of the usual semblance can be defined by replacing second-order by higher-order quantities. Here we tested such extensions in an application to CRS parameter estimation. We found encouraging results by a natural extension of semblance to the fourth order. Numerical examples show that for low noise levels, results for all tested orders of the semblance were equivalent, whereas for high noise levels, the new fourth-order semblance function worked better in the linear search. This measure is less dependent on the aperture and noise level, thus resulting in reliable estimates of the local slope more often than when using conventional semblance.

Velocity estimation by image-focusing analysis

Migration velocity can be estimated from seismic data by analyzing, focusing, and defocusing of residual-migrated images. The accuracy of these velocity estimates is limited by the inherent ambiguity between velocity and reflector curvature. However, velocity resolution improves when reflectors with different curvatures are present. Image focusing is measured by evaluating coherency across structural dips, in addition to coherency across aperture/azimuth angles. The inherent ambiguity between velocity and reflector curvature is directly tackled by introducing a curvature correction into the computation of the semblance functional that estimates image coherency. The resulting velocity estimator provides velocity estimates that are (1) unbiased by reflector curvature and (2) consistent with the velocity information that is routinely obtained by measuring coherency over aperture/azimuth angles. Applications to a 2D synthetic prestack data set and a 2D field prestack data set confirm that the proposed method provides consistent and unbiased velocity information. They also suggest that velocity estimates based on the new image-focusing semblance may be more robust and have higher resolution than estimates based on conventional semblance functionals. Applying the proposed method to zero-offset field data recorded in New York Harbor yields a velocity function that is consistent with available geologic information and clearly improves the focusing of the reflectors.

Automatic velocity analysis using bootstrapped differential semblance and global search methods

The goal of automatic velocity analysis is to extract accurate velocity from voluminous seismic data with efficiency. In this study, we developed an efficient automatic velocity analysis algorithm by using bootstrapped differential semblance (BDS) and Monte Carlo inversion. To estimate more accurate results from automatic velocity analysis, the algorithm we have developed uses BDS, which provides a higher velocity resolution than conventional semblance, as a coherency estimator. In addition, our proposed automatic velocity analysis module is performed with a conditional initial velocity determination step that leads to enhanced efficiency in running time of the module. A new optional root mean square (RMS) velocity constraint, which prevents picking false peaks, is used. The developed automatic velocity analysis module was tested on a synthetic dataset and a marine field dataset from the East Sea, Korea. The stacked sections made using velocity results from our algorithm showed coherent events and improved the quality of the normal moveout-correction result. Moreover, since our algorithm finds interval velocity (vint) first with interval velocity constraints and then calculates a RMS velocity function from the interval velocity, we can estimate geologically reasonable interval velocities. Boundaries of interval velocities also match well with reflection events in the common midpoint stacked sections.