Velocity calibration for microseismic monitoring: A very fast simulated annealing (VFSA) approach for joint-objective optimization

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCB47-WCB55 ◽  
Author(s):  
Donghong Pei ◽  
John A. Quirein ◽  
Bruce E. Cornish ◽  
Dan Quinn ◽  
Norman R. Warpinski
Keyword(s):  
Simulated Annealing ◽  
Velocity Structure ◽  
Velocity Model ◽  
Microseismic Monitoring ◽  
S Wave ◽  
Wave Velocities ◽  
Very Fast Simulated Annealing ◽  
Occam’S Inversion ◽  
Synthetic Test ◽  
Ray Parameter

To accurately locate microearthquakes that are genetically related to hydraulic fracture stimulation, a thorough knowledge of the velocity structure between monitoring and fracturing treatment wells is essential. Very fast simulated annealing (VFSA) is implemented to invert for a flat-layered velocity model between wells using perforation or string-shot data. A two-point ray-tracing method is used to find the ray parameter [Formula: see text] for a ray traveling from a source to a receiver. The original traveltime-calculation formula is modified to account for the borehole source-receiver geometry. VFSA is used as a tool to optimize P- and S-wave velocities simultaneously. Unlike previous applications of VFSA, two improvements result from a new study: (1) both P- and S-wave arrival-time misfits are considered in a joint-objective function, and (2) P- and S-wave velocities are perturbed simultaneously during annealing. The inverted velocities follow the true values closely with a very small root-mean-square error, indicating the inverted model is close to the global minimum solution whose rms error should be zero for synthetic examples. Data noise contaminates inverted models, but not substantially in synthetic test results. A comparison of models inverted using VFSA and Occam’s inversion technique indicates that inverted models using VFSA are superior to those using Occam’s method in terms of velocity accuracy.

scholarly journals One dimensional seismic velocity structure beneath Western Nepal

2002 ◽  
Vol 27 ◽  
Author(s):  
S. Rajaure
Keyword(s):  
Arrival Time ◽  
Velocity Structure ◽  
Seismic Velocity ◽  
Velocity Model ◽  
Compressional Wave ◽  
S Wave ◽  
Time Data ◽  
Seismic Velocity Structure ◽  
One Dimensional ◽  
Wave Velocities

An attempt has been made to study the velocity structure of western Nepal. Arrival time data of local earthquakes occurring in that region were used to derive the model. A three layered velocity model both for the P- as well as S-wave velocity has been estimated. The compressional wave velocities in the first, second and the third layers have been estimated to be 5.53 km/sec. 6.29 km/sec and 8.13 km/sec respectively. Similarly the corresponding S-wave velocities are 3.18, 3.62, 4.66 km/sec respectively. The model for the Western Nepal and that for the Centre-East Nepal are almost same. The crust and the mantle beneath west and center-east are homogeneous.

Shallow velocity structure and poisson's ratio at the Tarzana, California, strong-motion accelerometer site

1996 ◽  
Vol 86 (6) ◽  
pp. 1704-1713 ◽  
Author(s):  
R. D. Catchings ◽  
W. H. K. Lee
Keyword(s):  
Urban Areas ◽  
Velocity Structure ◽  
Strong Motion ◽  
P Wave ◽  
S Wave ◽  
Near Surface ◽  
Velocity Models ◽  
Wave Velocities ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Abstract The 17 January 1994, Northridge, California, earthquake produced strong ground shaking at the Cedar Hills Nursery (referred to here as the Tarzana site) within the city of Tarzana, California, approximately 6 km from the epicenter of the mainshock. Although the Tarzana site is on a hill and is a rock site, accelerations of approximately 1.78 g horizontally and 1.2 g vertically at the Tarzana site are among the highest ever instrumentally recorded for an earthquake. To investigate possible site effects at the Tarzana site, we used explosive-source seismic refraction data to determine the shallow (<70 m) P-and S-wave velocity structure. Our seismic velocity models for the Tarzana site indicate that the local velocity structure may have contributed significantly to the observed shaking. P-wave velocities range from 0.9 to 1.65 km/sec, and S-wave velocities range from 0.20 and 0.6 km/sec for the upper 70 m. We also found evidence for a local S-wave low-velocity zone (LVZ) beneath the top of the hill. The LVZ underlies a CDMG strong-motion recording site at depths between 25 and 60 m below ground surface (BGS). Our velocity model is consistent with the near-surface (<30 m) P- and S-wave velocities and Poisson's ratios measured in a nearby (<30 m) borehole. High Poisson's ratios (0.477 to 0.494) and S-wave attenuation within the LVZ suggest that the LVZ may be composed of highly saturated shales of the Modelo Formation. Because the lateral dimensions of the LVZ approximately correspond to the areas of strongest shaking, we suggest that the highly saturated zone may have contributed to localized strong shaking. Rock sites are generally considered to be ideal locations for site response in urban areas; however, localized, highly saturated rock sites may be a hazard in urban areas that requires further investigation.

Random objective waveform inversion of surface waves

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. EN49-EN61
Author(s):  
Yudi Pan ◽  
Lingli Gao
Keyword(s):  
Objective Function ◽  
Surface Waves ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Initial Model ◽  
S Wave ◽  
Data Set ◽  
Near Surface ◽  
Synthetic Test ◽  
Ground Penetrating

Full-waveform inversion (FWI) of surface waves is becoming increasingly popular among shallow-seismic methods. Due to a huge amount of data and the high nonlinearity of the objective function, FWI usually requires heavy computational costs and may converge toward a local minimum. To mitigate these problems, we have reformulated FWI under a multiobjective framework and adopted a random objective waveform inversion (ROWI) method for surface-wave characterization. Three different measure functions were used, whereas the combination of one measure function with one shot independently provided one of the [Formula: see text] objective functions ([Formula: see text] is the total number of shots). We have randomly chose and optimized one objective function at each iteration. We performed a synthetic test to compare the performance of the ROWI and conventional FWI approaches, which showed that the convergence of ROWI is faster and more robust compared with conventional FWI approaches. We also applied ROWI to a field data set acquired in Rheinstetten, Germany. ROWI successfully reconstructed the main geologic feature, a refilled trench, in the final result. The comparison between the ROWI result and a migrated ground-penetrating radar profile further proved the effectiveness of ROWI in reconstructing the near-surface S-wave velocity model. We also ran the same field example by using a poor initial model. In this case, conventional FWI failed whereas ROWI still reconstructed the subsurface model to a fairly good level, which highlighted the relatively low dependency of ROWI on the initial model.

A new inversion method to construct a 3-D crustal shear-wave velocity model from P-to-S converted waves and application to the Central Alps

2020 ◽  
Author(s):  
Leonardo Colavitti ◽  
György Hetényi ◽  
AlpArray Working Group
Keyword(s):  
Simulated Annealing ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Ambient Noise ◽  
Velocity Structure ◽  
Receiver Function ◽  
Velocity Model ◽  
Central Alps ◽  
Travelling Salesman ◽  
The Given

<p>We developed a new method where teleseismic P-to-S converted waves are used to construct a fully 3-D shear-wave velocity model of the crust. The method differs from ambient noise and local earthquake tomography in its ray-paths being closer to vertical. Our approach requires a dense seismological network, and we first focus on the Central Alps considering the available permanent and temporary station datasets (e.g., Hetényi et al., 2018, Surv. Geophys.).</p><p>We implemented an accurate ray-propagator which respects Snell’s law in 3-D at any interface geometry. Following a teleseismic P ray propagator (Knapmeyer, 2004) from event to station which uses a 1-D global velocity model (iasp91), P-to-S conversion at the Moho is calculated for the crustal S ray considering the true local dip. The corresponding arrival to the surface is typically several km away from the station, which we then adjust by changing the ray-parameter. In the Central Alps, using the 3-D P-velocity structure of Diehl et al. (2009) and the local Moho geometry of Spada et al. (2013), the mean distance between the arriving S-wave and the station is about 150 m (median ca. 40 m).</p><p>For our approach we adopt a new model parameterization of velocities. It is rectangular in map view (nodes at 25x25 km in the Alps), while in depth we define a 2-layer model with separate velocities above and below each discontinuity. The introduction of this flexibility allows us to accommodate a velocity gradient within each layer and investigate velocity jumps across discontinuities.</p><p>The inversion proceeds iteratively, by visiting every node of the map following a Travelling Salesman Path. At each node, receiver function rays in the surrounding volume are considered for inversion, and bundled into sub-blocks and ranges of back-azimuth (5x5 km size, 45° or 60° bins for the Central Alps). The velocity model at the given node is inverted using the technique of Simulated Annealing, followed by a pattern search algorithm to avoid falling in a local minimum. During iterations of the Simulated Annealing, individual velocity model corresponding to each receiver function is extracted from the 3-D model along its ray path.</p><p>The inversion proceeds for 4 or 5 independent parameters: Moho and a hypothetical intra-crustal discontinuity depth, Vp/Vs ratio (either full crust, or separately for upper and lower crust) and the P-wave velocity jump at the intra-crustal discontinuity. Finally, the velocity structure is updated with the result obtained at the given node. We observe that a few rounds of Travelling Salesman Paths improve the overall misfit.</p><p>First results on the Central Alps show that the Moho depth generally reflects well the roots of the Alpine orogen. Resolving crustal Vp/Vs ratio is more stable when considering the full crust, instead of two separate layers. The Conrad discontinuity remains difficult to resolve. The obtained velocity structure is compared along profiles to recent Vs results from 3-D ambient noise tomography (Lu et al., 2018).</p>

PS Energy Imaging Condition for Microseismic Data - Part 1: Theory and Applications in 3D Isotropic Media

Geophysics ◽  
2020 ◽  
pp. 1-79
Author(s):  
Can Oren ◽  
Jeffrey Shragge
Keyword(s):  
Wave Velocity ◽  
Model Building ◽  
Velocity Model ◽  
Microseismic Monitoring ◽  
Elastic Model ◽  
S Wave ◽  
Imaging Condition ◽  
Velocity Models ◽  
Monitoring Programs ◽  
Imaging Conditions

Accurately estimating event locations is of significant importance in microseismic investigations because this information greatly contributes to the overall success of hydraulic fracturing monitoring programs. Full-wavefield time-reverse imaging (TRI) using one or more wave-equation imaging conditions offers an effective methodology for locating surface-recorded microseismic events. To be most beneficial in microseismic monitoring programs, though, the TRI procedure requires using accurate subsurface models that account for elastic media effects. We develop a novel microseismic (extended) PS energy imaging condition that explicitly incorporates the stiffness tensor and exhibits heightened sensitivity to isotropic elastic model perturbations compared to existing imaging conditions. Numerical experiments demonstrate the sensitivity of microseismic TRI results to perturbations in P- and S-wave velocity models. Zero-lag and extended microseismic source images computed at selected subsurface locations yields useful information about 3D P- and S-wave velocity model accuracy. Thus, we assert that these image volumes potentially can serve as the input into microseismic elastic velocity model building algorithms.

The structure of Archean–Ketilidian crust along the continental shelf of southwestern Greenland from a seismic refraction profile

1992 ◽  
Vol 29 (2) ◽  
pp. 301-313 ◽  
Author(s):  
Deping Chian ◽  
Keith Louden
Keyword(s):  
Lower Crust ◽  
Velocity Structure ◽  
Seismic Refraction ◽  
Mobile Belt ◽  
Ocean Bottom ◽  
Upper Crust ◽  
S Wave ◽  
Seismic Line ◽  
Wave Velocities ◽  
Air Gun

The velocity structure of the continental crust on the outer shelf of southwestern Greenland is determined from dense wide-angle reflection–refraction data obtained with large air-gun sources and ocean bottom seismometers along a 230 km seismic line. This line crosses the geological boundary between the Archean block and the Ketilidian mobile belt. Although the data have high noise levels, P- and S-wave arrivals from within the upper, intermediate, and lower crust, and at the Moho boundary, can be consistently identified and correlated with one-dimensional WKBJ synthetic seismograms. In the Archean, P- and S-wave velocities in the upper crust are 6.0 and 3.4 km/s, while in the intermediate crust they are 6.4 and 3.6 km/s. These velocities match for the upper crust a quartz–feldspar gneiss composition and for the intermediate crust an amphibolitized pyroxene granulite. In the Ketilidian mobile belt, P- and S-wave velocities are 5.6 and 3.3 km/s for the upper crust and 6.3 and 3.6 km/s for the intermediate crust. These velocities may represent quartz granite in the upper crust and granite and granitic gneiss in the intermediate crust. The upper crust is ~5 km thick in the Archean block and the Ketilidian mobile belt, and thickens to ~9 km in the southern part of the Archean. This velocity structure supports a Precambrian collisional mechanism between the Archean block and Ketilidian mobile belt. The lower crust has a small vertical velocity gradient from 6.6 km/s at 15 km depth to 6.9 km/s at 30 km depth (Moho) along the refraction line, with a nearly constant S-wave velocity around 3.8 km/s. These velocities likely represent a gabbroic and hornblende granulite composition for the lower crust. This typical (but somewhat thin) Precambrian crustal velocity structure in southwestern Greenland shows no evidence for a high-velocity, lower crustal, underplated layer caused by the Mesozoic opening of the Labrador Sea.

Global optimization strategies for implementing 3D common-reflection-surface stack using the very fast simulated annealing algorithm: Application to real land data

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. V253-V261 ◽  
Author(s):  
German Garabito
Keyword(s):  
Global Optimization ◽  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Computational Cost ◽  
Velocity Model ◽  
Global Search ◽  
Optimization Strategy ◽  
Very Fast Simulated Annealing ◽  
Common Reflection Surface ◽  
Annealing Algorithm

The 3D common-reflection-surface (CRS) stack operator depends on eight kinematic wavefield attributes that must be extracted from the prestack data. These attributes are obtained by an efficient optimization strategy based on the maximization of the coherence measure of the seismic reflection events included by the CRS stacking operator. The main application of these kinematic attributes is to simulate zero-offset stacked data; however, they can also be used for regularization of the prestack data, prestack migration, and velocity model determination. The initial implementations of the 3D CRS stack used grid-search techniques to determine the attributes in several steps with the drawback that accumulated errors can deteriorate the final result. In this work, the global optimization very fast simulated annealing algorithm is used to search for the kinematic attributes by applying three optimization strategies for implementing CRS stacking: (1) simultaneous global search of five kinematic attributes of the 3D common-diffraction-surface stacking operator, (2) two-step global optimization strategy to first search for three attributes and then five attributes of the CRS stacking operator, and (3) simultaneous global search of eight kinematic attributes of the CRS operator. The proposed CRS stacking algorithms are applied to land data of the Potiguar Basin, Brazil. It is demonstrated that the one-step optimization strategy of the eight parameters produces the best results, however, with a higher computational cost.

Estimation of Velocity Structures in the Grenoble Basin, France, Using Pseudo Earthquake Horizontal-to-Vertical Spectral Ratio from Microtremors

2021 ◽  
Vol 111 (2) ◽  
pp. 627-653
Author(s):  
Eri Ito ◽  
Cécile Cornou ◽  
Fumiaki Nagashima ◽  
Hiroshi Kawase
Keyword(s):  
Wave Velocity ◽  
Velocity Structure ◽  
Strong Motion ◽  
Spectral Ratio ◽  
Empirical Method ◽  
S Wave ◽  
Wave Velocities ◽  
Strong Linear Correlation ◽  
Large Velocity ◽  
The Difference

ABSTRACT Based on the diffuse field concept for a horizontal-to-vertical spectral ratio of earthquakes (eHVSR), the effectiveness of eHVSRs to invert P- and S-wave velocity structures down to the seismological bedrock (with the S-wave velocity of 3  km/s or higher) has been shown in several published works. An empirical method to correct the difference between eHVSR and a horizontal-to-vertical ratio of microtremors (mHVSR), which is called earthquake-to-microtremor ratio (EMR), has also been proposed for strong-motion sites in Japan. However, the applicability of EMR outside of Japan may not be warranted. We test EMR applicability for the Grenoble basin in France with plentiful microtremor data together with observed weak-motion recordings at five sites. We thereby establish a systematic procedure to estimate the velocity structure from microtremors and delineate the fundamental characteristics of the velocity structures. We first calculate the EMR specific for the Grenoble basin (EMRG) and calculate pseudo eHVSR (pHVSR) from EMRG and mHVSR. We compare the pHVSRs with the eHVSRs at five sites and find sufficient similarity to each other. Then, we invert velocity structures from eHVSRs, pHVSRs, and mHVSRs. The velocity structures from eHVSRs are much closer to those from pHVSRs than those from mHVSRs. We need to introduce a number of layers with gradually increasing S-wave velocities below the geological basin boundary from a previous gravity study because the theoretical eHVSR of the model with a large velocity contrast has larger peak amplitudes than the observed. The depth of the S-wave velocity of 1.3  km/s (Z1.3) shows a strong, linear correlation with the geological boundary depth. Finally, we apply our validated methodology and invert velocity structures using pHVSRs at 14 sites where there are no observed earthquakes. The overall picture of Z1.3 at a cross section in the northeastern part of the basin corresponds to the geological boundary.

Microearthquake location: A nonlinear approach that makes use of a simplex stepping procedure

1988 ◽  
Vol 78 (2) ◽  
pp. 799-815
Author(s):  
Arnfinn F. Prugger ◽  
Don J. Gendzwill
Keyword(s):  
Least Squares ◽  
Velocity Structure ◽  
Velocity Model ◽  
Microseismic Monitoring ◽  
Simplex Algorithm ◽  
Earthquake Location ◽  
Small Computer ◽  
Monitoring Systems ◽  
Nonlinear Approach ◽  
Direct Iteration

Abstract We present an earthquake location scheme that uses the simplex algorithm in the solution. This method of direct iteration is conceptually simple, does not require derivative calculations, and avoids matrix inversions. The algorithm can be programmed on a small computer and its performance compares favorably with other methods of earthquake location. The method can be used for any velocity structure for which source to geophone times can be calculated. We use a horizontally layered velocity model, and consider both critically and noncritically refracted rays. It is easy to incorporate any time residual misfit norm into the location calculation. We generally use the L1 or L2 (least-squares) norm. The routine we present is used in two different microseismic monitoring systems at two potash mines in Saskatchewan, Canada.

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