The diminishing residual matrices method for surface-consistent statics — A review

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. V257-V274
Author(s):  
Necati Gülünay
Keyword(s):  
Synthetic Data ◽  
Reconstruction Technique ◽  
Data Set ◽  
Arrival Times ◽  
Long Wavelength ◽  
Iterative Reconstruction Technique ◽  
Land Survey ◽  
First Arrival ◽  
Waveform Distortions ◽  
The Individual

The diminishing residual matrices (DRM) method can be used to surface-consistently decompose individual trace statics into source and receiver components. The statics to be decomposed may either be first-arrival times after the application of linear moveout associated with a consistent refractor as used in refraction statics or residual statics obtained by crosscorrelating individual traces with corresponding model traces (known as pilot traces) at the same common-midpoint (CMP) location. The DRM method is an iterative process like the well-known Gauss-Seidel (GS) method, but it uses only source and receiver terms. The DRM method differs from the GS method in that half of the average common shot and receiver terms are subtracted simultaneously from the observations at each iteration. DRM makes the under-constrained statics problem a constrained one by implicitly adding a new constraint, the equality of the contribution of shots and receivers to the solution. The average of the shot statics and the average of the receiver statics are equal in the DRM solution. The solution has the smallest difference between shot and receiver statics profiles when the number of shots and the number of receivers in the data are equal. In this case, it is also the smallest norm solution. The DRM method can be derived from the well-known simultaneous iterative reconstruction technique. Simple numerical tests as well as results obtained with a synthetic data set containing only the field statics verify that the DRM solution is the same as the linear inverse theory solution. Both algorithms can solve for the long-wavelength component of the statics if the individual picks contain them. Yet DRM method is much faster. Application of the method to the normal moveout-corrected CMP gathers on a 3D land survey for residual statics calculation found that pick-decompose-apply-stack stages of the DRM method need to be iterated. These iterations are needed because of time and waveform distortions of the pilot traces due to the individual trace statics. The distortions lessen at every external DRM iteration.

Improving crosshole radar velocity tomograms: A new approach to incorporating high-angle traveltime data

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. J31-J41 ◽  
Author(s):  
James D. Irving ◽  
Michael D. Knoll ◽  
Rosemary J. Knight
Keyword(s):  
Synthetic Data ◽  
High Angle ◽  
Data Set ◽  
Tomographic Images ◽  
Arrival Times ◽  
Angle Data ◽  
Automatic Picking ◽  
Velocity Images ◽  
First Arrival ◽  
Ground Penetrating

To obtain the highest-resolution ray-based tomographic images from crosshole ground-penetrating radar (GPR) data, wide angular ray coverage of the region between the two boreholes is required. Unfortunately, at borehole spacings on the order of a few meters, high-angle traveltime data (i.e., traveltime data corresponding to transmitter-receiver angles greater than approximately 50° from the horizontal) are notoriously difficult to incorporate into crosshole GPR inversions. This is because (1) low signal-to-noise ratios make the accurate picking of first-arrival times at high angles extremely difficult, and (2) significant tomographic artifacts commonly appear when high- and low-angle ray data are inverted together. We address and overcome thesetwo issues for a crosshole GPR data example collected at the Boise Hydrogeophysical Research Site (BHRS). To estimate first-arrival times on noisy, high-angle gathers, we develop a robust and automatic picking strategy based on crosscorrelations, where reference waveforms are determined from the data through the stacking of common-ray-angle gathers. To overcome incompatibility issues between high- and low-angle data, we modify the standard tomographic inversion strategy to estimate, in addition to subsurface velocities, parameters that describe a traveltime ‘correction curve’ as a function of angle. Application of our modified inversion strategy, to both synthetic data and the BHRS data set, shows that it allows the successful incorporation of all available traveltime data to obtain significantly improved subsurface velocity images.

First-arrival picking with a U-net convolutional network

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. U45-U57 ◽  
Author(s):  
Lianlian Hu ◽  
Xiaodong Zheng ◽  
Yanting Duan ◽  
Xinfei Yan ◽  
Ying Hu ◽  
...  
Keyword(s):  
Seismic Data ◽  
Synthetic Data ◽  
Training Data ◽  
Convolutional Network ◽  
Data Set ◽  
Waveform Data ◽  
Near Surface ◽  
Arrival Times ◽  
Seismic Waveform ◽  
First Arrival

In exploration geophysics, the first arrivals on data acquired under complicated near-surface conditions are often characterized by significant static corrections, weak energy, low signal-to-noise ratio, and dramatic phase change, and they are difficult to pick accurately with traditional automatic procedures. We have approached this problem by using a U-shaped fully convolutional network (U-net) to first-arrival picking, which is formulated as a binary segmentation problem. U-net has the ability to recognize inherent patterns of the first arrivals by combining attributes of arrivals in space and time on data of varying quality. An effective workflow based on U-net is presented for fast and accurate picking. A set of seismic waveform data and their corresponding first-arrival times are used to train the network in a supervised learning approach, then the trained model is used to detect the first arrivals for other seismic data. Our method is applied on one synthetic data set and three field data sets of low quality to identify the first arrivals. Results indicate that U-net only needs a few annotated samples for learning and is able to efficiently detect first-arrival times with high precision on complicated seismic data from a large survey. With the increasing training data of various first arrivals, a trained U-net has the potential to directly identify the first arrivals on new seismic data.

scholarly journals Modeling across-trial variability in the Wald drift rate parameter

2020 ◽  
Author(s):  
Helen Steingroever ◽  
Dominik Wabersich ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Drift Rate ◽  
Model Parameters ◽  
Analysis Tool ◽  
Rate Parameter ◽  
Data Set ◽  
Arrival Times ◽  
First Arrival ◽  
Truncated Normal ◽  
Experimental Trials ◽  
Variance Parameter

Abstract The shifted-Wald model is a popular analysis tool for one-choice reaction-time tasks. In its simplest version, the shifted-Wald model assumes a constant trial-independent drift rate parameter. However, the presence of endogenous processes—fluctuation in attention and motivation, fatigue and boredom—suggest that drift rate might vary across experimental trials. Here we show how across-trial variability in drift rate can be accounted for by assuming a trial-specific drift rate parameter that is governed by a positive-valued distribution. We consider two candidate distributions: the truncated normal distribution and the gamma distribution. For the resulting distributions of first-arrival times, we derive analytical and sampling-based solutions, and implement the models in a Bayesian framework. Recovery studies and an application to a data set comprised of 1469 participants suggest that (1) both mixture distributions yield similar results; (2) all model parameters can be recovered accurately except for the drift variance parameter; (3) despite poor recovery, the presence of the drift variance parameter facilitates accurate recovery of the remaining parameters; (4) shift, threshold, and drift mean parameters are correlated.

Tomographic imaging of velocity and Q, with application to crosswell seismic data from the Gypsy Pilot Site, Oklahoma

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1804-1811 ◽  
Author(s):  
Qingbo Liao ◽  
George A. McMechan
Keyword(s):  
Velocity Ratio ◽  
Synthetic Data ◽  
P Wave ◽  
Reconstruction Technique ◽  
Shift Method ◽  
New Information ◽  
P Wave Velocity ◽  
Iterative Reconstruction Technique ◽  
Interwell Connectivity

The centroid frequency shift method is implemented, tested with synthetic data, and applied to field data from three contiguous crosswell seismic experiments at the Gypsy Pilot in northern Oklahoma. The similtaneous iterative reconstruction technique is used for tomographic estimations of both P‐wave velocity and Q. No amplitude corrections or spreading loss corrections are needed for the Q estimation. The estimated in‐situ velocity and Q distributions correlate well with log data and local lithology. The Q/velocity ratio appears to correlate with the sand/shale ratio (ranging from an average of ∼15 s/km for the sand‐dominated lithologies to an average of ∼8.5 s/km for the shale‐dominated ones), with the result that new information is provided on interwell connectivity.

First-arrival traveltime tomography based on the adjoint-state method

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCB1-WCB10 ◽  
Author(s):  
Cédric Taillandier ◽  
Mark Noble ◽  
Hervé Chauris ◽  
Henri Calandra
Keyword(s):  
Synthetic Data ◽  
Point Of View ◽  
Data Set ◽  
Near Surface ◽  
Traveltime Tomography ◽  
Adjoint State ◽  
Gradient Based ◽  
First Arrival ◽  
State Method ◽  
Adjoint State Method

Classical algorithms used for traveltime tomography are not necessarily well suited for handling very large seismic data sets or for taking advantage of current supercomputers. The classical approach of first-arrival traveltime tomography was revisited with the proposal of a simple gradient-based approach that avoids ray tracing and estimation of the Fréchet derivative matrix. The key point becomes the derivation of the gradient of the misfit function obtained by the adjoint-state technique. The adjoint-state method is very attractive from a numerical point of view because the associated cost is equivalent to the solution of the forward-modeling problem, whatever the size of the input data and the number of unknown velocity parameters. An application on a 2D synthetic data set demonstrated the ability of the algorithm to image near-surface velocities with strong vertical and lateral variations and revealed the potential of the method.

Guided Waves Tomography and Image Fusion for Damage Identification in Pipes

2011 ◽  
Vol 94-96 ◽  
pp. 1585-1589 ◽  
Author(s):  
Hai Yan Zhang ◽  
Jian Bo Yu ◽  
Xian Hua Chen
Keyword(s):  
Image Fusion ◽  
Guided Waves ◽  
Damage Identification ◽  
Tomographic Reconstruction ◽  
Element Model ◽  
Guided Wave ◽  
Reconstruction Technique ◽  
Arrival Times ◽  
Iterative Reconstruction Technique ◽  
Incomplete Datasets

The detection of localized defects such as cracks and corrosion in pipes using guided waves has been shown to be an effective nondestructive evaluation technique for structural health monitoring (SHM). Cross borehole tomography in seismology is introduced into the guided wave inspection of a pipe when the pipe is considered as an unwrapped plate. Guided waves propagating in pipe with a crack defect are simulated using the finite element model and the arrival times for the fastest modes are extracted and sent to the tomographic algorithm. The tomographic reconstruction is based on the simultaneous iterative reconstruction technique (SIRT). For some cylindrical shell geometries such as stacked storage tanks, access to the entire circumference of the structure could be impractical or even impossible, three different image fusion techniques are used to enhance the image equality reconstructed from the incomplete datasets. The results show that the defect is more pronounced after imaging fusion.

Direct P-Wave Travel Time Tomography of the Middle East

2021 ◽  
Author(s):  
Susini Desilva ◽  
Ebru Bozdag ◽  
Guust Nolet ◽  
Rengin Gok ◽  
Ahmed Ali ◽  
...  
Keyword(s):  
Middle East ◽  
Reliable Data ◽  
P Wave ◽  
Good Recovery ◽  
Data Set ◽  
Iranian Plateau ◽  
Arrival Times ◽  
Caucasus Region ◽  
First Arrival ◽  
Tomographic Inversions

<p>High-resolution seismic images of the crust and mantle beneath regions of complex surface geological structures are necessary to gain insights on the underlying geodynamical processes. One such region embodying various plate boundary motions and intraplate deformations is the Middle East, and consequently the region is prone to significant seismic activity. Hence a tomographic investigation using a more recent and reliable data set is vital in understanding the ongoing complicated deformation process driven by the African, Arabian and Eurasian plates. The purpose of our study is to retrieve a detailed  model of the crust and mantle beneath the Middle Eastern region using teleseismic P arrival times from the ISC-EHB bulletin (Engdahl et al., 1998).</p><p>Starting with AK135 as the reference model we invert for tomographic models of compressional wavespeed perturbations down to lower mantle depths in an area bounded by longitudes 22E–66E and latitudes 8N–48N.  The data set used in this study consists of regionally observed P-phase arrival times from over 1000 global events from 1996–2016 culminating in a larger dataset than other similar studies. Selection of a reliable data, ray tracing, preconditioning and inversion steps are carried out using the BD-soft software suite (https://www.geoazur.fr/GLOBALSEIS/Soft.html).</p><p>Preliminary inversion results are consistent with the previous regional tomographic studies. In checkerboard tests, cell sizes as low as ∼ 2.8° × 2.8° ( ∼ 240 × 240 km at surface) are generally well recovered down to a 1000 km depth beneath the Anatolian plateau where we currently have the densest coverage. Additionally the Caucasus region and northern parts of the Iranian plateau shows good recovery of ±4% Vp perturbation amplitudes at depths ∼ 70 – 135 km. There is fair recovery for a minimum cell size of ∼ 2.8° × 2.8° beneath the Iranian Plateau, Zagros mountain region, Persian gulf, and northeast Iraq, along with quite good recovery of cell amplitudes towards the Anatolian-Caucasus region at depth ranges 380 – 430 km, 650 – 700 km, and around 950 km. Tomographic inversions unveil a low P velocity zone stretching from the Afar region to Sinai Peninsula consistent with S wave velocity observations of a similar feature by Chang and van der Lee 2011.</p><p>We are able to further improve coverage especially down to lithospheric depths within the Arabian peninsula using first arrival times measured from waveform data collected from regional networks. Addition of first arrival time delays from waveforms highlights a prominent low velocity in the tomographic inversions beneath the volcanic fields of western Saudi Arabia. Our ultimate goal is to perform full-waveform inversion of the region constrained by the constructed P-wave model.</p>

Integration of diverse physical-property models: Subsurface zonation and petrophysical parameter estimation based on fuzzy c -means cluster analyses

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. H33-H44 ◽  
Author(s):  
Hendrik Paasche ◽  
Jens Tronicke ◽  
Klaus Holliger ◽  
Alan G. Green ◽  
Hansruedi Maurer
Keyword(s):  
Gamma Ray ◽  
Synthetic Data ◽  
Physical Property ◽  
Geophysical Data ◽  
Data Sets ◽  
Data Set ◽  
Petrophysical Parameters ◽  
Fcm Clustering ◽  
The Individual ◽  
Combine Information

Inversions of an individual geophysical data set can be highly nonunique, and it is generally difficult to determine petrophysical parameters from geophysical data. We show that both issues can be addressed by adopting a statistical multiparameter approach that requires the acquisition, processing, and separate inversion of two or more types of geophysical data. To combine information contained in the physical-property models that result from inverting the individual data sets and to estimate the spatial distribution of petrophysical parameters in regions where they are known at only a few locations, we demonstrate the potential of the fuzzy [Formula: see text]-means (FCM) clustering technique. After testing this new approach on synthetic data, we apply it to limited crosshole georadar, crosshole seismic, gamma-log, and slug-test data acquired within a shallow alluvial aquifer. The derived multiparameter model effectively outlines the major sedimentary units observed in numerous boreholes and provides plausible estimates for the spatial distributions of gamma-ray emitters and hydraulic conductivity.

scholarly journals Interferometric identification of surface-related multiples

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. Q41-Q52 ◽  
Author(s):  
Boris Boullenger ◽  
Deyan Draganov
Keyword(s):  
Synthetic Data ◽  
Original Data ◽  
Data Set ◽  
Interferometric Method ◽  
Feedback Information ◽  
Arrival Times ◽  
Surface Reflection ◽  
Reflection Data ◽  
Multiple Prediction ◽  
Virtual Events

The theory of seismic interferometry predicts that crosscorrelations of recorded seismic responses at two receivers yield an estimate of the interreceiver seismic response. The interferometric process applied to surface-reflection data involves the summation, over sources, of crosscorrelated traces, and it allows retrieval of an estimate of the interreceiver reflection response. In particular, the crosscorrelations of the data with surface-related multiples in the data produce the retrieval of pseudophysical reflections (virtual events with the same kinematics as physical reflections in the original data). Thus, retrieved pseudophysical reflections can provide feedback information about the surface multiples. From this perspective, we have developed a data-driven interferometric method to detect and predict the arrival times of surface-related multiples in recorded reflection data using the retrieval of virtual data as diagnosis. The identification of the surface multiples is based on the estimation of source positions in the stationary-phase regions of the retrieved pseudophysical reflections, thus not necessarily requiring sources and receivers on the same grid. We have evaluated the method of interferometric identification with a two-layer acoustic example and tested it on a more complex synthetic data set. The results determined that we are able to identify the prominent surface multiples in a large range of the reflection data. Although missing near offsets proved to cause major problems in multiple-prediction schemes based on convolutions and inversions, missing near offsets does not impede our method from identifying surface multiples. Such interferometric diagnosis could be used to control the effectiveness of conventional multiple-removal schemes, such as adaptive subtraction of multiples predicted by convolution of the data.

Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. J53-J64 ◽  
Author(s):  
Jacques R. Ernst ◽  
Alan G. Green ◽  
Hansruedi Maurer ◽  
Klaus Holliger
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Radar Data ◽  
Data Sets ◽  
Full Waveform Inversion ◽  
Arrival Times ◽  
Full Waveform ◽  
First Arrival ◽  
Radar Wave

Crosshole radar tomography is a useful tool in diverse investigations in geology, hydrogeology, and engineering. Conventional tomograms provided by standard ray-based techniques have limited resolution, primarily because only a fraction of the information contained in the radar data (i.e., the first-arrival times and maximum first-cycle amplitudes) is included in the inversion. To increase the resolution of radar tomograms, we have developed a versatile full-waveform inversion scheme that is based on a finite-difference time-domain solution of Maxwell’s equations. This scheme largely accounts for the 3D nature of radar-wave propagation and includes an efficient method for extracting the source wavelet from the radar data. After demonstrating the potential of the new scheme on two realistic synthetic data sets, we apply it to two crosshole field data sets acquired in very different geologic/hydrogeologic environments. These are the first applications of full-waveform tomography to observed crosshole radar data. The resolution of all full-waveform tomograms is shown to be markedly superior to that of the associated ray tomograms. Small subsurface features a fraction of the dominant radar wavelength and boundaries between distinct geological/hydrological units are sharply imaged in the full-waveform tomograms.

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