Semblance Values Research Articles

Analysis of the Spatiotemporal Changes of Ice Sheet Mass and Driving Factors in Greenland

With the warming of the global climate, the mass loss of the Greenland ice sheet is intensifying, having a profound impact on the rising of the global sea level. Here, we used Gravity Recovery and Climate Experiment (GRACE) RL06 data to retrieve the time series variations of ice sheet mass in Greenland from January 2003 to December 2015. Meanwhile, the spatial changes of ice sheet mass and its relationship with land surface temperature are studied by means of Theil–Sen median trend analysis, the Mann–Kendall (MK) test, empirical orthogonal function (EOF) analysis, and wavelet transform analysis. The results showed: (1) in terms of time, we found that the total mass of ice sheet decreases steadily at a speed of −195 ± 21 Gt/yr and an acceleration of −11 ± 2 Gt/yr2 from 2003 to 2015. This mass loss was relatively stable in the two years after 2012, and then continued a decreasing trend; (2) in terms of space, the mass loss areas of the Greenland ice sheet mainly concentrates in the southeastern, southwestern, and northwestern regions, and the southeastern region mass losses have a maximum rate of more than 27 cm/yr (equivalent water height), while the northeastern region show a minimum rate of less than 3 cm/yr, showing significant changes as a whole. In addition, using spatial distribution and the time coefficients of the first two models obtained by EOF decomposition, ice sheet quality in the southeastern and northwestern regions of Greenland show different significant changes in different periods from 2003 to 2015, while the other regions showed relatively stable changes; (3) in terms of driving factors temperature, there is an anti-phase relationship between ice sheet mass change and land surface temperature by the mean XWT-based semblance value of −0.34 in a significant oscillation period variation of 12 months. Meanwhile, XWT-based semblance values have the largest relative change in 2005 and 2012, and the smallest relative change in 2009 and 2010, indicating that the influence of land surface temperature on ice sheet mass significantly varies in different years.

Velocity inversion by global optimization using finite-offset common-reflection-surface stacking applied to synthetic and Tacutu Basin seismic data

Estimation of an accurate velocity macromodel is an important step in seismic imaging. We have developed an approach based on coherence measurements and finite-offset (FO) beam stacking. The algorithm is an FO common-reflection-surface tomography, which aims to determine the best layered depth-velocity model by finding the model that maximizes a semblance objective function calculated from the amplitudes in common-midpoint (CMP) gathers stacked over a predetermined aperture. We develop the subsurface velocity model with a stack of layers separated by smooth interfaces. The algorithm is applied layer by layer from the top downward in four steps per layer. First, by automatic or manual picking, we estimate the reflection times of events that describe the interfaces in a time-migrated section. Second, we convert these times to depth using the velocity model via application of Dix’s formula and the image rays to the events. Third, by using ray tracing, we calculate kinematic parameters along the central ray and build a paraxial FO traveltime approximation for the FO common-reflection-surface method. Finally, starting from CMP gathers, we calculate the semblance of the selected events using this paraxial traveltime approximation. After repeating this algorithm for all selected CMP gathers, we use the mean semblance values as an objective function for the target layer. When this coherence measure is maximized, the model is accepted and the process is completed. Otherwise, the process restarts from step two with the updated velocity model. Because the inverse problem we are solving is nonlinear, we use very fast simulated annealing to search the velocity parameters in the target layers. We test the method on synthetic and real data sets to study its use and advantages.

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.

Continuous estimation of 3-D reflector orientations along 2-D deep seismic reflection profiles

Interpretation of 2-D deep seismic reflection data can be limited by the recording of out-of-plane reflections that cannot be readily distinguished from those originating beneath a seismic line. Here I present a method analogous to semblance velocity analysis that utilizes varying source-receiver azimuths to derive continuous estimates of 3-D reflector orientations along onshore 2-D reflection profiles. For each zero-offset time within a common depth point supergather, the semblance is calculated along 3-D travel time curves, and the dip and strike of the most coherent reflection is determined. Relative errors in these angles are derived from the range of travel time curves that have semblance values greater than a specified fraction, for example 90%, of the maximum. The method is illustrated using a section from line 10GA-YU1 from the Youanmi terrane of the Yilgarn craton in Australia in which the original field data have been replaced with synthetic in-line and cross-line reflections. Reflector orientations are generally well recovered where the range of available source-receiver azimuths is greater than 20o, but the method fails at lower ranges where the seismic line is almost linear, and this behavior is also observed in analysis of the field data. Nevertheless when using a realistic 1-D velocity function the orientation of upper crustal shear zones can be readily determined, and on unmigrated sections subhorizontal sills can be distinguished on the basis of their geometry from the mid-crustal reflectivity. In future surveys, reflector orientations can be determined along the near-linear sections of a seismic profile by deploying additional receivers, perhaps as cross-line recording spreads, to supplement the limited range of azimuths available from the in-line acquisition. The method can in principle be extended to marine reflection surveys, and more complex sub-surface velocity models.

Automatic NMO Correction and Full Common Depth Point NMO Velocity Field Estimation in Anisotropic Media

We present a new computational method of automatic normal moveout (NMO) correction that not only accurately flattens and corrects the far offset data, but simultaneously provides NMO velocity (\(v_\mathrm{nmo}\)) for each individual seismic trace. The method is based on a predefined number of NMO velocity sweeps using linear vertical interpolation of different NMO velocities at each seismic trace. At each sweep, we measure the semblance between the zero offset trace (pilot trace) and the next seismic trace using a trace-by-trace rather than sample-by-sample based semblance measure; then after all the sweeps are done, the one with the maximum semblance value is chosen, which is assumed to be the most suitable NMO velocity trace that accurately flattens seismic reflection events. Other traces follow the same process, and a final velocity field is then extracted. Isotropic, anisotropic and lateral heterogenous synthetic geological models were built to test the method. A range of synthetic background noise, ranging from 10 to 30 %, was applied to the models. In addition, the method was tested on Hess’s VTI (vertical transverse isotropy) model. Furthermore, we tested our method on a real pre-stack seismic CDP gathered from a gas field in Alaska. The results from the presented examples show an excellent NMO correction and extracted a reasonably accurate NMO velocity field.

Changes in seismicity before and after the 2011 Tohoku earthquake around its southern limit revealed by dense ocean bottom seismic array data

AbstractThe southern limit of the 2011 Tohoku earthquake is considered to be located around off Ibaraki. However, it is not well constrained how far south the large slip extended. To give better constraints, we investigated seismicity including small earthquakes before and after the Tohoku earthquake around off Ibaraki using dense ocean bottom seismic array data. We automatically identified epicenters by backprojecting semblance values resulting in a considerable increase in the number of detected events compared with those listed in the catalog based on onshore observation. The results revealed a couple of seismicity‐activated region. The largest aftershock also occurred ~30 min after the main shock. Our detailed results suggest that this highly activated seismicity was initiated by the largest aftershock instead of the main shock. It, then, suggests that the large coseismic slip zone of the Tohoku earthquake may not have extended off Ibaraki.

3D diffraction imaging of linear features and its application to seismic monitoring

ABSTRACTMany subsurface features, such as faults, fractures, cracks, or fluid content terminations are defined by geological discontinuities. The seismic response from such features is encoded in diffractions. We develop an algorithm for imaging such discontinuities by detecting edge diffractions. The algorithm exploits phase‐reversal phenomena of edge diffractions and uses them as a criterion to separate these diffractions from specular reflections and diffractions produced by a leaner object. The performance of the method is demonstrated on both synthetic and real 3D seismic data. The output image focuses the diffracted energy back to its origin and shows high semblance values at the edge of the object. The method is applied on conventionally stacked data producing an image that contains only diffraction events called the D‐volume. We also reveal the potential of diffractions to image and track the changes of a CO2 plume using time‐lapse analysis and detect any possible CO2 seepage from its primary containment.

Depth and morphology of reflectors from the non‐linear inversion of arrival‐time and waveform semblance data. Part I: method and applications to synthetic data

ABSTRACTWe propose a two‐dimensional, non‐linear method for the inversion of reflected/converted traveltimes and waveform semblance designed to obtain the location and morphology of seismic reflectors in a lateral heterogeneous medium and in any source‐to‐receiver acquisition lay‐out. This method uses a scheme of non‐linear optimization for the determination of the interface parameters where the calculation of the traveltimes is carried out using a finite‐difference solver of the Eikonal equation, assuming an a priori known background velocity model. For the search for the optimal interface model, we used a multiscale approach and the genetic algorithm global optimization technique. During the initial stages of inversion, we used the arrival times of the reflection phase to retrieve the interface model that is defined by a small number of parameters. In the successive steps, the inversion is based on the optimization of the semblance value determined along the calculated traveltime curves. Errors in the final model parameters and the criteria for the choice of the best‐fit model are also estimated from the shape of the semblance function in the model parameter space. The method is tested and validated on a synthetic dataset that simulates the acquisition of reflection data in a complex volcanic structure. This study shows that the proposed inversion approach is a valid tool for geophysical investigations in complex geological environments, in order to obtain the morphology and positions of embedded discontinuities.

Imaging an asperity of the 2003 Tokachi-oki earthquake using a dense strong-motion seismograph network

The 2003 Tokachi-oki earthquake ruptured a large area of approximately 100 km 2 . The location of the largest asperity was estimated to be several dozen kilometres offshore of Hokkaido, Japan. The magnitude measured 8.0 on the Japan Meteorological Agency scale, and several studies used waveform inversion analysis to estimate the moment-magnitude as M w 8.0–8.2. Several studies reported that there was a minor asperity at the northeastern edge of the fault plane, and that the rupture velocity towards the minor asperity was less than that towards the main asperity. One of them illustrated that the location and timing of the minor asperity were poorly constrained. In this paper, we introduce a procedure based on semblance analysis to image the location of the minor northeastern asperity with improved resolution. We group 15 strong-motion seismographs into three arrays, and we perform semblance analysis on impulsive waves that were possibly generated from the minor asperity and were conspicuously observed at stations in eastern Hokkaido. By projecting the semblance values onto the fault plane, we estimate the location of the minor asperity. We find it to be shallower and farther from the coast than the previous results indicated. The average rupture velocity towards the asperity is estimated to be 2.5 km s −1 , which is slower than the 3.6 km s −1 obtained by waveform inversion analysis.

Non‐hyperbolic moveout inversion of wide‐azimuth P‐wave data for orthorhombic media

ABSTRACTThe azimuthally varying non‐hyperbolic moveout of P‐waves in orthorhombic media can provide valuable information for characterization of fractured reservoirs and seismic processing. Here, we present a technique to invert long‐spread, wide‐azimuth P‐wave data for the orientation of the vertical symmetry planes and five key moveout parameters: the symmetry‐plane NMO velocities, V(1)nmo and V(2)nmo, and the anellipticity parameters, η(1), η(2) and η(3). The inversion algorithm is based on a coherence operator that computes the semblance for the full range of offsets and azimuths using a generalized version of the Alkhalifah–Tsvankin non‐hyperbolic moveout equation.The moveout equation provides a close approximation to the reflection traveltimes in layered anisotropic media with a uniform orientation of the vertical symmetry planes. Numerical tests on noise‐contaminated data for a single orthorhombic layer show that the best‐constrained parameters are the azimuth ϕ of one of the symmetry planes and the velocities V(1)nmo and V(2)nmo, while the resolution in η(1) and η(2) is somewhat compromised by the trade‐off between the quadratic and quartic moveout terms. The largest uncertainty is observed in the parameter η(3), which influences only long‐spread moveout in off‐symmetry directions. For stratified orthorhombic models with depth‐dependent symmetry‐plane azimuths, the moveout equation has to be modified by allowing the orientation of the effective NMO ellipse to differ from the principal azimuthal direction of the effective quartic moveout term.The algorithm was successfully tested on wide‐azimuth P‐wave reflections recorded at the Weyburn Field in Canada. Taking azimuthal anisotropy into account increased the semblance values for most long‐offset reflection events in the overburden, which indicates that fracturing is not limited to the reservoir level. The inverted symmetry‐plane directions are close to the azimuths of the off‐trend fracture sets determined from borehole data and shear‐wave splitting analysis. The effective moveout parameters estimated by our algorithm provide input for P‐wave time imaging and geometrical‐spreading correction in layered orthorhombic media.

Scatterer density estimation in the crust by seismic array processing

SUMMARY Both the number density of scatterers and scattering strength are parameters characterizing the inhomogeneity of the Earth’s crust. An attempt is made to estimate the number density of scatterers (n-value) using small-aperture seismic array data. Many estimates of scattering coefficients have been made previously; however, in a medium with a scattering strength, the wave energy scattered by a medium containing strong scatterers with a low number density is identical to that produced by a high density of weak scatterers. Knowledge of the number density besides the scattering strength supplies important information on stress concentration in the crust due to the strong scatterer reflecting strong inhomogeneity. Therefore, the number density of scatterers is estimated with array signal processing. A seismic array can decompose the approach direction of scattered waves arriving at the array. With array processing, it is not only possible to estimate the energy arriving at the array, but also the semblance value. Temporal variation of the energy depends strongly on the scattering coefficient. On the other hand, the difference in number density of the medium appears in the temporal variation of the semblance value. As a first-order approximation, the semblance value is inversely proportional to the n-value. For practical purposes, an array response should be considered for n-value estimation. Comparing simulated and observed semblances, number density and scattering strength can be estimated from the time sequence of semblances and stacking power. This method was applied to seismic array data from the aftershock area of the 2000 Western Tottori earthquake (Mw 6.8). A rough estimate of number density, compared to a simulation, is 3 × 10 −2 km −3 .

Scattering objects in the lower mantle beneath northeastern China observed with a short-period seismic array

Precursor and coda portions of short-period PcP waves (reflected P wave from the core–mantle boundary, CMB) recorded at J-array stations in Japan were analyzed in order to extract weak scattered signals originating from small-scale heterogeneities in the lowermost mantle beneath northeastern China. Two nuclear explosions at Lop Nor in China detonated on 21 May 1992 (Mb=6.5) and 8 June 1996 (Mb=5.9) were used for our analysis. Three-dimensional grids above the CMB were defined in the area around the PcP bounce points beneath northeastern China to calculate theoretical travel times of scattered waves which propagate from the sources to each grid point and arrive at each station based on the IASP91 model. Subsequently the waveforms were aligned with respect to the theoretical travel times and the semblance (an amplitude dependent measure of coherency) was calculated for each grid point. In order to obtain a more accurate travel time correction, we applied a cross correlation method to PcP waveforms in order to reduce picking error of the PcP onset time. A cross convolution method was also applied so that the two events could be analyzed simultaneously without using unstable deconvolutions. We could identify regions with relative high semblance values in semblance contour maps at about 200 and 375 km above the CMB. Stacking waveforms with respect to the theoretical travel times for the grid points with relative high semblance values indicate coherent wavelets originating at those grid points, that is, they correspond to scattered waves originating from small-scale heterogeneities in the lowermost mantle. Our results indicate the existence of small-scale scattering objects in the D″ layer, especially in the depth range of 200 and 375 km above the CMB beneath northeastern China. Considering recent tomographic images of high velocity anomalies in this area, these scattering objects could be fragments of old oceanic crusts which have subducted through the lower mantle and have accumulated in the D″ layer beneath northeastern China.

Small-scale heterogeneity at the top of the lower mantle around the Mariana slab

Short-period waveform data recorded at the western US seismic array for 14 Mariana deep earthquakes near 19°N show two anomalous wave packets within about 30 s after the arrival of the direct P-wave (simply called ‘P’ or ‘P-wave’): one at about 13 s (called ‘X1 phase’) and the other around 29 s (called ‘X2 phase’). We perform array analyses to locate the sources of these phases. In the first step, we measure arrival time, slowness, back-azimuth, and amplitude of these phases relative to P. The amplitudes of the X1 and X2 phases correlate with each other for the individual events, and vary more than an order of magnitude among the events which cluster in a region spanning less than 50 km. The amplitude correlation suggests that the two waves have a similar origin, and the large amplitude variation eliminates receiver side reverberation as the origin of the phases. The X1 phase has a slowness and an arrival azimuth which are not distinguished from those of P-waves across the entire array, and has nearly constant delay times regardless of the focal depths (from 567 to 605 km). The X2 phase arrives as a more emergent wave packet with slowness and azimuth different from those of P. In the second step, we compute composite semblance coefficients for the cases of P-to-P and S-to-P single scattering near the foci. The X1 and X2 phases are best interpreted as S-to-P scattered waves generated in the uppermost lower mantle north of the focal region based on three observations: (1) highest composite semblance values, (2) scatterer locations mutually consistent between the two event groups near the depths of 500 and 600 km, and (3) a reasonable amount of elastic property anomalies required. The X1 phase scatterer is determined at 19.8°±0.3°N, 145.7°±0.3°E, 710±30 km. On the other hand, the scatterer of the X2 phase appears to split into two objects: one at 20.4°±0.4°N, 145.4°±1.0°E, 900±80 km, and the other at 20.6°±0.4°N, 147.4°±0.5°E, 860±40 km. Although the geometries of the scatterers of X1 and X2 phases are not constrained, horizontal or subhorizontal discontinuities are unlikely. The changes in elastic properties associated with these heterogeneous objects probably occur within several kilometers, according to their high efficiency at converting short-period waves. They are thus likely to represent sharp chemical variations in major element composition. These objects are located within a thickened high-velocity anomaly at the top of the lower mantle, which has been determined by previous seismic studies. A plausible tectonic interpretation of these objects is that they are fragments of former oceanic crust which are entrained in the Pacific slab impinging on the more viscous lower mantle.

Estimation of slowness vectors and their uncertainties using multi-wavelet seismic array processing

AbstractWe have developed a new seismic array data processing method to produce slowness vector estimates and an objective measure of their uncertainties in the form of statistical confidence intervals. The slowness vector, which is typically transformed into bearing and velocity, is a key parameter used for identifying seismic phases and for event source location. Our method, multi-wavelet beamforming, is closely related to both time-domain and frequency-domain beamforming. The major advantage of multi-wavelet beamforming is that it produces multiple estimates of the slowness vector that are approximately statistically independent. First, a set of wavelet transforms is applied to the data in a manner analogous to the use of the windowed Fourier transform. Next, for each wavelet transform, we calculate semblance, a measure of signal coherence, for a range of possible slowness vectors. Then, the slowness vector estimate associated with that transform is the vector that produces the largest semblance value. The multiple slowness vector estimates can be treated as samples from a probability distribution, whose “center” we estimate using the mean, the median, and an M-estimator. Uncertainty intervals are calculated for these estimators by applying the jackknife statistical method. The intervals for the mean estimator appear to be true statistical confidence intervals, but the estimates can be biased by a directional noise field in low signal-to-noise circumstances. The median estimates are less biased by a directional noise field but sometimes underestimate the uncertainty. The M-estimator produces less-biased estimates while appearing to estimate correctly their uncertainty.

A SEMBLANCE‐GUIDED MEDIAN FILTER1

AbstractReiter, E.C., Toksoz, M.N. and Purdy, G.M. 1992. A semblance‐guided median filter. Geophysical Prospecting41, 15–41.A slowness selective median filter based on information from a local set of traces is described and implemented. The filter is constructed in two steps, the first being an estimation of a preferred slowness and the second, the selection of a median or trimmed mean value to replace the original data point. A symmetric window of traces defining the filter aperture is selected about each trace to be filtered and the filter applied repeatedly to each time point. The preferred slowness is determined by scanning a range of linear moveouts within the user‐specified slowness passband. Semblance is computed for each trial slowness and the preferred slowness selected from the peak semblance value. Data points collected along this preferred slowness are then sorted from lowest to highest and in the case of a pure median filter, the middle point(s) selected to replace the original data point. The output of the filter is therefore quite insensitive to large amplitude noise bursts, retaining the well‐known beneficial properties of a traditional 1D median filter. Energy which is either incoherent over the filter aperture or lies outside the slowness passband, may be additionally suppressed by weighting the filter output by the measured peak semblance.This approach may be used as a velocity filter to estimate coherent signal within a specified slowness passband and reject coherent energy outside this range. For applications of this type, other velocity estimators may be used in place of our semblance measure to provide improved velocity estimation and better filter performance. The filter aperture may also be extended to provide increased velocity estimation, but will result in additional lateral smearing of signal. We show that, in addition to a velocity filter, our approach may be used to improve signal‐to‐noise ratios in noisy data. The median filter tends to suppress the amplitude of random background noise and semblance weighting may be used to reduce the amplitude of background noise further while enhancing coherent signal.We apply our method to vertical seismic profile data to separate upgoing and downgoing wavefields, and also to large‐offset ocean bottom hydrophone data to enhance weak refracted and post‐critically reflected energy.

High resolution velocity analysis of watergun wide angle reflection data

Two seismic lines each approximately 10km in length were shot over an isolated approximately 250m thick sediment pond on the flanks of the mid-Atlantic Ridge. The source was a 1.32 liter watergun and the receiver was the Woods Hole Oceanographic Institution Digital Ocean Bottom Hydrophone (DOBH). The data were recorded at a sampling rate of 1800 Hz to take full advantage of the high band width source. Analysis was carried out by computing semblance and stack values along T-X trajectories defined in three ways: firstly the conventional hyperbolic stack, secondly the accurate ray traced travel time curve computed assuming isovelocity layering and finally the accurate travel time curve computed assuming a single layer of constant linear gradient. This last option yielded significantly higher values of coherency for the true basement reflection although all our analyses were marred by side reflection interference from the surrounding rough topography. The maximum semblance value obtained for the basement reflection in the linear gradient case was 0.38 for 120 shots, with the peak of both the semblance and the stack occurring at a gradient of 1.9s−1. This work illustrates the capability of a water gun source combined with a high bandwidth receiver and quantitative velocity analysis techniques, to produce high resolution determinations of sediment velocity structure.