Toward a full 4D seismic tomography: a case study of an active mine

2021 ◽  
Author(s):  
Nicola Piana Agostinetti ◽  
Christina Dahnér-Lindkvist ◽  
Savka Dineva
Keyword(s):  
Monte Carlo ◽  
Seismic Tomography ◽  
Water Injection ◽  
Elastic Field ◽  
Monte Carlo Sampling ◽  
P Wave ◽  
Travel Times ◽  
S Wave ◽  
Posterior Probability Distribution ◽  
Space And Time

<p>Rock elasticity in the subsurface can change in response to natural phenomena (e.g. massive precipitation, magmatic processes) and human activities (e.g. water injection in geothermal wells, ore-body exploitation). However, understanding and monitoring the evolution of physical properties of the crust is a challenging due to the limited possibility of reaching such depths and making direct measurements of the state of the rocks. Indirect measurements, like seismic tomography, can give some insights, but are generally biased by the un-even distribution (in space and time) of the information collected from seismic observations (travel-times and/or waveforms). Here we apply a Bayesian approach to overcome such limitations, so that data uncertainties and data distribution are fully accounted in the reconstruction of the posterior probability distribution of the rock elasticity  We compute a full 4D local earthquake tomography based on trans-dimensional Markov chain Monte Carlo sampling of 4D elastic models, where the resolution in space and time is fully data-driven. To test our workflow, we make use of a “controlled laboratory”: we record seismic data during one month of mining activities across a 800x700x600 m volume of Kiruna mine (LKAB, Sweden). During such period, we obtain about 260 000 P-wave and 240 000 S-wave travel-times coming from about 36000  seismic events. We operate a preliminary selection of the well-located events, using a Monte Carlo search. Arrival-times of about 19 000 best-located events (location errors less than 20m) are used as input to the tomography workflow. Preliminary results indicate that: (1) short-term (few hours) evolutions of the elastic field are mainly driven by seismic activation, i.e. the occurrence of a seismic swarm, close to the mine ore-passes. Such phenomena partially mask the effects of explosions; (2) long-term (2-3 days) evolutions of the elastic field closely match the local measurements of the stress field at a colocated stress cell. </p>

scholarly journals Seismic Tomography Using Variational Inference Methods

2020 ◽  
Author(s):  
Xin Zhang ◽  
Andrew Curtis
Keyword(s):  
Monte Carlo ◽  
Probability Distribution ◽  
Seismic Tomography ◽  
Posterior Probability ◽  
Sampling Methods ◽  
Probability Distributions ◽  
Monte Carlo Sampling ◽  
Variational Inference ◽  
Posterior Probability Distribution ◽  
Inference Methods

<p><span>In a variety of geoscientific applications we require maps of subsurface properties together with the corresponding maps of uncertainties to assess their reliability. Seismic tomography is a method that is widely used to generate those maps. Since tomography is significantly nonlinear, Monte Carlo sampling methods are often used for this purpose, but they are generally computationally intractable for large data sets and high-dimensionality parameter spaces. To extend uncertainty analysis to larger systems, we introduce variational inference methods to conduct seismic tomography. In contrast to Monte Carlo sampling, variational methods solve the Bayesian inference problem as an optimization problem yet still provide fully nonlinear, probabilistic results. This is achieved by minimizing the Kullback-Leibler (KL) divergence between approximate and target probability distributions within a predefined family of probability distributions.</span></p><p><span>We introduce two variational inference methods: automatic differential variational inference (ADVI) and Stein variational gradient descent (SVGD). In ADVI a Gaussian probability distribution is assumed and optimized to approximate the posterior probability distribution. In SVGD a smooth transform is iteratively applied to an initial probability distribution to obtain an approximation to the posterior probability distribution. At each iteration the transform is determined by seeking the steepest descent direction that minimizes the KL-divergence. </span></p><p><span>We apply the two variational inference methods to 2D travel time tomography using both synthetic and real data, and compare the results to those obtained from two different Monte Carlo sampling methods: Metropolis-Hastings Markov chain Monte Carlo (MH-McMC) and reversible jump Markov chain Monte Carlo (rj-McMC). The results show that ADVI provides a biased approximation because of its Gaussian approximation, whereas SVGD produces more accurate approximations to the results of MH-McMC. In comparison rj-McMC produces smoother mean velocity models and lower standard deviations because the parameterization used in rj-McMC (Voronoi cells) imposes prior restrictions on the pixelated form of models: all pixels within each Voronoi cell have identical velocities. This suggests that the results of rj-McMC need to be interpreted in the light of the specific prior information imposed by the parameterization. Both variational methods estimate the posterior distribution at significantly lower computational cost, provided that gradients of parameters with respect to data can be calculated efficiently. We therefore expect that the methods can be applied fruitfully to many other types of geophysical inverse problems.</span></p>

Bayesian Variational Seismic Tomography using Normalizing Flows

2021 ◽  
Author(s):  
Xuebin Zhao ◽  
Andrew Curtis ◽  
Xin Zhang
Keyword(s):  
Monte Carlo ◽  
Seismic Tomography ◽  
Computational Cost ◽  
Large Data ◽  
Optimization Methods ◽  
Monte Carlo Sampling ◽  
New Method ◽  
Posterior Probability Distribution ◽  
Computationally Expensive ◽  
A Chain

<p>Seismic travel time tomography is used widely to image the Earth's interior structure and to infer subsurface properties. Tomography is an inverse problem, and computationally expensive nonlinear inverse methods are often deployed in order to understand uncertainties in the tomographic results. Monte Carlo sampling methods estimate the posterior probability distribution which describes the solution to Bayesian tomographic problems, but they are computationally expensive and often intractable for high dimensional model spaces and large data sets due to the curse of dimensionality. We therefore introduce a new method of variational inference to solve Bayesian seismic tomography problems using optimization methods, while still providing fully nonlinear, probabilistic results. The new method, known as normalizing flows, warps a simple and known distribution (for example a Uniform or Gaussian distribution) into an optimal approximation to the posterior distribution through a chain of invertible transforms. These transforms are selected from a library of suitable functions, some of which invoke neural networks internally. We test the method using both synthetic and field data. The results show that normalizing flows can produce similar mean and uncertainty maps to those obtained from both Monte Carlo and another variational method (Stein varational gradient descent), at significantly decreased computational cost. In our tomographic tests, normalizing flows improves both accuracy and efficiency, producing maps of UK surface wave speeds and their uncertainties at the finest resolution and the lowest computational cost to-date, allowing results to be interrogated efficiently and quantitatively for subsurface structure.</p>

scholarly journals Probabilistic lowermost mantle P-wave tomography from hierarchical Hamiltonian Monte Carlo and model parametrization cross-validation

2020 ◽  
Vol 223 (3) ◽  
pp. 1630-1643
Author(s):  
Jack B Muir ◽  
Hrvoje Tkalčić
Keyword(s):  
Monte Carlo ◽  
Cross Validation ◽  
Inner Core ◽  
Monte Carlo Sampling ◽  
P Wave ◽  
Model Complexity ◽  
S Wave ◽  
Hamiltonian Monte Carlo ◽  
Short Period ◽  
Lowermost Mantle

SUMMARY Bayesian methods, powered by Markov Chain Monte Carlo estimates of posterior densities, have become a cornerstone of geophysical inverse theory. These methods have special relevance to the deep Earth, where data are sparse and uncertainties are large. We present a strategy for efficiently solving hierarchical Bayesian geophysical inverse problems for fixed parametrizations using Hamiltonian Monte Carlo sampling, and highlight an effective methodology for determining optimal parametrizations from a set of candidates by using efficient approximations to leave-one-out cross-validation for model complexity. To illustrate these methods, we use a case study of differential traveltime tomography of the lowermost mantle, using short period P-wave data carefully selected to minimize the contributions of the upper mantle and inner core. The resulting tomographic image of the lowermost mantle has a relatively weak degree 2—instead there is substantial heterogeneity at all low spherical harmonic degrees less than 15. This result further reinforces the dichotomy in the lowermost mantle between relatively simple degree 2 dominated long-period S-wave tomographic models, and more complex short-period P-wave tomographic models.

scholarly journals Applicability of time-lapse refraction seismic tomography for the detection of ground ice degradation

2010 ◽  
Vol 4 (1) ◽  
pp. 77-119 ◽  
Author(s):  
C. Hilbich
Keyword(s):  
Seismic Tomography ◽  
Time Lapse ◽  
Swiss Alps ◽  
P Wave ◽  
Permafrost Degradation ◽  
Travel Times ◽  
Ground Ice ◽  
Refraction Seismic ◽  
Velocity Changes ◽  
Ice Content

Abstract. The ice content of the subsurface is a major factor controlling the natural hazard potential of permafrost degradation in alpine terrain. Monitoring of changes in ground ice content is therefore similarly important as temperature monitoring in mountain permafrost. Although electrical resistivity tomography monitoring (ERTM) has proved to be a valuable tool for the observation of ground ice degradation, results are often ambiguous or contaminated by inversion artefacts. In theory, the P-wave velocity of seismic waves is similarly sensitive to phase changes between unfrozen water and ice. Provided that the general conditions (lithology, stratigraphy, state of weathering, pore space) remain unchanged over the observation period, temporal changes in the observed travel times of repeated seismic measurements should indicate changes in the ice and water content within the pores and fractures of the subsurface material. In this paper, the applicability of refraction seismic tomography monitoring (RSTM) as an independent and complementary method to ERTM is analysed for two test sites in the Swiss Alps. The development and validation of an appropriate RSTM approach involves a) the comparison of time-lapse seismograms and analysis of reproducibility of the seismic signal, b) the analysis of time-lapse travel time curves with respect to shifts in travel times and changes in P-wave velocities, and c) the comparison of inverted tomograms including the quantification of velocity changes. Results show a high potential of the RSTM approach concerning the detection of altered subsurface conditions caused by freezing and thawing processes. For velocity changes on the order of 3000 m/s even an unambiguous identification of significant ground ice loss is possible.

Travel times and amplitudes of S waves from nuclear explosions in Nevada

1969 ◽  
Vol 59 (1) ◽  
pp. 385-398 ◽  
Author(s):  
Otto W. Nuttli
Keyword(s):  
Stress Field ◽  
Body Wave ◽  
P Wave ◽  
Travel Times ◽  
S Wave ◽  
Low Velocity ◽  
Time Curve ◽  
Regional Stress ◽  
S Waves ◽  
Regional Stress Field

Abstract The underground Nevada explosions HALF-BEAK and GREELEY were unique in creating relatively large amplitude and long-period body S waves which could be detected at teleseismic distances. Observations of the travel times of these S waves provide a surface focus travel-time curve which in its major features is similar to a curve calculated from the upper mantle velocity model of Ibrahim and Nuttli (1967). This model includes a low-velocity channel at a depth of 150 to 200 km and regions of rapidly increasing velocity beginning at depths of 400 and 750 km. Observations of the S wave amplitudes suggest that a discontinuous increase in velocity occurs at 400 km, whereas at 750 km the velocity is continuous but the velocity gradient discontinuous. Body wave magnitudes calculated from S amplitudes are 5.3 ± 0.2 for GREELEY and 4.9 ± 0.2 for HALF-BEAK. These are about one unit less than body wave magnitudes from P amplitudes as reported by others. The shape and orientation of the radiation pattern of SH for both explosions are consistent with the Rayleigh and P-wave amplitude distribution of BILBY as given by Toksoz and Clermont (1967). This suggests that the regional stress field is the same at all three sites, and that the direction of cracking as well as the strain energy release in the elastic zone outside the cavity is determined by the regional stress field.

scholarly journals Joining forces of Bayesian and frequentist methodology: a study for inference in the presence of non-identifiability

2013 ◽  
Vol 371 (1984) ◽  
pp. 20110544 ◽  
Author(s):  
Andreas Raue ◽  
Clemens Kreutz ◽  
Fabian Joachim Theis ◽  
Jens Timmer
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Probability Distribution ◽  
Cell Biology ◽  
Posterior Probability ◽  
Monte Carlo Sampling ◽  
Posterior Probability Distribution ◽  
Model Predictions

Increasingly complex applications involve large datasets in combination with nonlinear and high-dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take advantage of both Bayesian and frequentist methods. The elegance of Bayesian methodology is founded in the propagation of information content provided by experimental data and prior assumptions to the posterior probability distribution of model predictions. However, for complex applications, experimental data and prior assumptions potentially constrain the posterior probability distribution insufficiently. In these situations, Bayesian Markov chain Monte Carlo sampling can be infeasible. From a frequentist point of view, insufficient experimental data and prior assumptions can be interpreted as non-identifiability. The profile-likelihood approach offers to detect and to resolve non-identifiability by experimental design iteratively. Therefore, it allows one to better constrain the posterior probability distribution until Markov chain Monte Carlo sampling can be used securely. Using an application from cell biology, we compare both methods and show that a successive application of the two methods facilitates a realistic assessment of uncertainty in model predictions.

scholarly journals Time-lapse refraction seismic tomography for the detection of ground ice degradation

2010 ◽  
Vol 4 (3) ◽  
pp. 243-259 ◽  
Author(s):  
C. Hilbich
Keyword(s):  
Seismic Tomography ◽  
Time Lapse ◽  
Phase Changes ◽  
Swiss Alps ◽  
P Wave ◽  
Permafrost Degradation ◽  
Travel Times ◽  
Refraction Seismic ◽  
Velocity Changes ◽  
Ice Content

Abstract. The ice content of the subsurface is a major factor controlling the natural hazard potential of permafrost degradation in alpine terrain. Monitoring of changes in ice content is therefore similarly important as temperature monitoring in mountain permafrost. Although electrical resistivity tomography monitoring (ERTM) proved to be a valuable tool for the observation of ice degradation, results are often ambiguous or contaminated by inversion artefacts. In theory, the sensitivity of P-wave velocity of seismic waves to phase changes between unfrozen water and ice is similar to the sensitivity of electric resistivity. Provided that the general conditions (lithology, stratigraphy, state of weathering, pore space) remain unchanged over the observation period, temporal changes in the observed travel times of repeated seismic measurements should indicate changes in the ice and water content within the pores and fractures of the subsurface material. In this paper, a time-lapse refraction seismic tomography (TLST) approach is applied as an independent method to ERTM at two test sites in the Swiss Alps. The approach was tested and validated based on a) the comparison of time-lapse seismograms and analysis of reproducibility of the seismic signal, b) the analysis of time-lapse travel time curves with respect to shifts in travel times and changes in P-wave velocities, and c) the comparison of inverted tomograms including the quantification of velocity changes. Results show a high potential of the TLST approach concerning the detection of altered subsurface conditions caused by freezing and thawing processes. For velocity changes on the order of 3000 m/s even an unambiguous identification of significant ice loss is possible.

scholarly journals Recognition of gasogeodynamic zones in the rock mass using seismic tomography in Rudna copper ore mine

2018 ◽  
Vol 66 ◽  
pp. 01012
Author(s):  
Krzysztof Porębski ◽  
Eugeniusz Koziarz ◽  
Arkadiusz Anderko ◽  
Krzysztof Krawiec ◽  
Rafał Czarny ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Seismic Tomography ◽  
Seismic Waves ◽  
Measurement Data ◽  
Young Modulus ◽  
Research Area ◽  
P Wave ◽  
S Wave ◽  
Copper Ore ◽  
Seismic Parameters

In this work, the results of four seismic tomography surveys are presented. The research was conducted to identify the zones exposed to the threat of gas and rock outburst. The changes to the dolomite layer stiffness in the mining excavation roofs were analyzed. The surveys were conducted in the Rudna copper ore mine in the field of XXVIII/1. The research area was about 0.21 km2. The seismic waves were generated by a small amount of explosive material (100 - 300 g) located and installed in short blast holes (1.5 - 2.0 m). The processing and the interpretation of the measurement data did not cause serious problems due to the more favourable elastic properties of the dolomite layer compared to the adjacent anhydrite and sandstone layers. As a result, the maps of parameters like the longitudinal wave velocity (P-wave), the shear wave velocity (S-wave), and the ratio of the Pwave velocity to S-wave velocity and the dynamic Young modulus were estimated. The results showed that the changes in the seismic parameters were relatively small over most of the research area. This may be evidence of the minor effects of gas and rock outbursts.

Seismicity in the Rangely, Colorado, area: 1962-1970

1973 ◽  
Vol 63 (5) ◽  
pp. 1557-1570 ◽  
Author(s):  
James F. Gibbs ◽  
John H. Healy ◽  
C. Barry Raleigh ◽  
John Coakley
Keyword(s):  
Seismic Data ◽  
Water Injection ◽  
Seismic Energy ◽  
Seismic Signal ◽  
Oil Field ◽  
P Wave ◽  
S Wave ◽  
Uinta Basin ◽  
Wave Measurements

abstract Seismic data recorded for a 7-year period at the Uinta Basin Observatory were searched for earthquakes originating near an oil field at Rangely, Colorado, 65 km ESE of the observatory. Changes in the number of earthquakes recorded per year appear to correlate with changes in the quantity of fluid injected per year. Between November 1962 and January 1970, 976 earthquakes were detected near the oil field by the UBO station; 320 earthquakes were larger than magnitude 1. Richter local magnitudes are estimated from both S-wave and P-wave measurements; a method based on the duration of the seismic signal is used to estimate the magnitude of the larger shocks. Magnitude of the two largest shocks was 3.4 and 3.3. The total seismic energy released was 1017 ergs. During this same period, the energy used for water injection, measured at the wellhead, was 1021 ergs.

Applying cluster analysis to seismic tomography models: Uncovering similarities and differences in the spatial and spectral domains

2021 ◽  
Author(s):  
Moloud Rahimzadeh Bajgiran ◽  
Lorenzo Colli
Keyword(s):  
Seismic Tomography ◽  
Spatial Scales ◽  
Three Dimensional ◽  
Weighted Average ◽  
Geological Structure ◽  
P Wave ◽  
Damping Factor ◽  
S Wave ◽  
Average Technique ◽  
Similarities And Differences

<p>In recent years, several types of Machine Learning (ML) methods have been employed by Earth scientists to extract patterns and structures from multi-dimensional feature spaces. In this regard, images of the mantle obtained by different seismic tomography (ST) models are diverse datasets with varying structures due to their different theoretical approximations and input data. In this work, we apply an unsupervised ML method, K-means clustering, on ST models to explore their similarities and differences to improve our physical understanding of the Earth’s interior. The K-means clustering method requires ST models to be standardized in a three-dimensional domain. For this purpose, we implement a weighted average technique to resample ST models to radial structural zones with uniform horizontal grid resolutions. However, the homogenized ST models still have 10<sup>3</sup>-10<sup>4</sup> parameters, which need to be distilled into a small number of summary features. Feature selection is thus a key part of this study: features should be independent from unphysical effects of inversion choices (e.g., the damping factor) and should instead capture the essence of the geological structure. Preliminary results obtained using the center of mass as the attribute to represent the longest wavelength part of the mantle structure show that P-wave and S-wave models do not cluster separately. Therefore, compositional anomalies do not play an essential role at these spatial scales. We plan to expand our analysis by including more summary attributes from both the spatial as well as the frequency domain. </p>

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