The effects of earth model uncertainty on the inversion of seismic data for seismic source functions

2020 ◽  
Vol 224 (1) ◽  
pp. 100-120
Author(s):  
Christian Poppeliers ◽  
Leiph Preston
Keyword(s):  
Seismic Data ◽  
Model Uncertainty ◽  
Wave Speed ◽  
Moment Tensor ◽  
Synthetic Data ◽  
Seismic Energy ◽  
Seismic Source ◽  
Earth Model ◽  
Seismic Moment Tensor ◽  
Independent Components

SUMMARY We use Monte Carlo simulations to explore the effects of earth model uncertainty on the estimation of the seismic source time functions that correspond to the six independent components of the point source seismic moment tensor. Specifically, we invert synthetic data using Green’s functions estimated from a suite of earth models that contain stochastic density and seismic wave-speed heterogeneities. We find that the primary effect of earth model uncertainty on the data is that the amplitude of the first-arriving seismic energy is reduced, and that this amplitude reduction is proportional to the magnitude of the stochastic heterogeneities. Also, we find that the amplitude of the estimated seismic source functions can be under- or overestimated, depending on the stochastic earth model used to create the data. This effect is totally unpredictable, meaning that uncertainty in the earth model can lead to unpredictable biases in the amplitude of the estimated seismic source functions.

Colored and linear inversions to relative acoustic impedance

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. N15-N27 ◽  
Author(s):  
Carlos A. M. Assis ◽  
Henrique B. Santos ◽  
Jörg Schleicher
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Computational Cost ◽  
Synthetic Data ◽  
Seismic Source ◽  
Alternative Methods ◽  
Well Log ◽  
Linear Inversion ◽  
Amplitude Inversion ◽  
Band Limited

Acoustic impedance (AI) is a widely used seismic attribute in stratigraphic interpretation. Because of the frequency-band-limited nature of seismic data, seismic amplitude inversion cannot determine AI itself, but it can only provide an estimate of its variations, the relative AI (RAI). We have revisited and compared two alternative methods to transform stacked seismic data into RAI. One is colored inversion (CI), which requires well-log information, and the other is linear inversion (LI), which requires knowledge of the seismic source wavelet. We start by formulating the two approaches in a theoretically comparable manner. This allows us to conclude that both procedures are theoretically equivalent. We proceed to check whether the use of the CI results as the initial solution for LI can improve the RAI estimation. In our experiments, combining CI and LI cannot provide superior RAI results to those produced by each approach applied individually. Then, we analyze the LI performance with two distinct solvers for the associated linear system. Moreover, we investigate the sensitivity of both methods regarding the frequency content present in synthetic data. The numerical tests using the Marmousi2 model demonstrate that the CI and LI techniques can provide an RAI estimate of similar accuracy. A field-data example confirms the analysis using synthetic-data experiments. Our investigations confirm the theoretical and practical similarities of CI and LI regardless of the numerical strategy used in LI. An important result of our tests is that an increase in the low-frequency gap in the data leads to slightly deteriorated CI quality. In this case, LI required more iterations for the conjugate-gradient least-squares solver, but the final results were not much affected. Both methodologies provided interesting RAI profiles compared with well-log data, at low computational cost and with a simple parameterization.

Source location with cross-coherence migration

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. KS127-KS138 ◽  
Author(s):  
Yujin Liu ◽  
Yue Ma ◽  
Yi Luo
Keyword(s):  
Field Data ◽  
Random Noise ◽  
Synthetic Data ◽  
Seismic Energy ◽  
Seismic Source ◽  
Spectral Amplitude ◽  
Multiple Sources ◽  
Passive Seismic ◽  
Similar Images ◽  
Resolution Property

Locating microseismic source positions using seismic energy emitted from hydraulic fracturing is essential for choosing optimal fracking parameters and maximizing the fracturing effects in hydrocarbon exploitation. Interferometric crosscorrelation migration (ICCM) and zero-lag autocorrelation of time-reversal imaging (ATRI) are two important passive seismic source locating approaches that are proposed independently and seem to be substantially different. We have proven that these two methods are theoretically identical and produce very similar images. Moreover, we have developed cross-coherence that uses normalization by the spectral amplitude of each of the traces, rather than crosscorrelation or deconvolution, to improve the ICCM and ATRI methods. The adopted method enhances the spatial resolution of the source images and is particularly effective in the presence of highly variable and strong additive random noise. Synthetic and field data tests verify the equivalence of the conventional ICCM and ATRI and the equivalence of their improved versions. Compared with crosscorrelation- and deconvolution-based source locating methods, our approach shows a high-resolution property and antinoise capability in numerical tests using synthetic data with single and multiple sources, as well as field data.

Seismic source inversion using Hamiltonian Monte Carlo and a 3-D Earth model in the Japanese Islands

2020 ◽  
Author(s):  
Saulė Simutė ◽  
Lion Krischer ◽  
Christian Boehm ◽  
Martin Vallée ◽  
Andreas Fichtner
Keyword(s):  
Monte Carlo ◽  
Moment Tensor ◽  
Seismic Source ◽  
Monte Carlo Algorithm ◽  
Earth Model ◽  
Model Parameters ◽  
Hamiltonian Monte Carlo ◽  
Double Couple ◽  
Full Moment Tensor ◽  
Japanese Islands

<p>We present a proof-of-concept catalogue of full-waveform seismic source solutions for the Japanese Islands area. Our method is based on the Bayesian inference of source parameters and a tomographically derived heterogeneous Earth model, used to compute Green’s strain tensors. We infer the full moment tensor, location and centroid time of the seismic events in the study area.</p><p>To compute spatial derivatives of Green’s functions, we use a previously derived regional Earth model (Simutė et al., 2016). The model is radially anisotropic, visco-elastic, and fully heterogeneous. It was constructed using full waveforms in the period band of 15–80 s.</p><p>Green’s strains are computed numerically with the spectral-element solver SES3D (Gokhberg & Fichtner, 2016). We exploit reciprocity, and by treating seismic stations as virtual sources we compute and store the wavefield across the domain. This gives us a strain database for all potential source-receiver pairs. We store the wavefield for more than 50 F-net broadband stations (www.fnet.bosai.go.jp). By assuming an impulse response as the source time function, the displacements are then promptly obtained by linear combination of the pre-computed strains scaled by the moment tensor elements.</p><p>With a feasible number of model parameters and the fast forward problem we infer the unknowns in a Bayesian framework. The fully probabilistic approach allows us to obtain uncertainty information as well as inter-parameter trade-offs. The sampling is performed with a variant of the Hamiltonian Monte Carlo algorithm, which we developed previously (Fichtner and Simutė, 2017). We apply an L2 misfit on waveform data, and we work in the period band of 15–80 s.</p><p>We jointly infer three location parameters, timing and moment tensor components. We present two sets of source solutions: 1) full moment tensor solutions, where the trace is free to vary away from zero, and 2) moment tensor solutions with the isotropic part constrained to be zero. In particular, we study events with significant non-double-couple component. Preliminary results of ~Mw 5 shallow to intermediate depth events indicate that proper incorporation of 3-D Earth structure results in solutions becoming more double-couple like. We also find that improving the Global CMT solutions in terms of waveform fit requires a very good 3-D Earth model and is not trivial.</p>

Tomographic filtering of mantle circulation models via the generalised inverse: A way to account for seismic data uncertainty

2020 ◽  
Author(s):  
Bernhard S.A. Schuberth ◽  
Roman Freissler ◽  
Christophe Zaroli ◽  
Sophie Lambotte
Keyword(s):  
Seismic Data ◽  
Inverse Operator ◽  
Synthetic Data ◽  
Circulation Model ◽  
Model Space ◽  
Seismic Inversion ◽  
Data Uncertainty ◽  
Earth Model ◽  
Model Parameters ◽  
Noise Component

<p>For a comprehensive link between seismic tomography and geodynamic models, uncertainties in the seismic model space play a non-negligible role. More specifically, knowledge of the tomographic uncertainties is important for obtaining meaningful estimates of the present-day thermodynamic state of Earth's mantle, which form the basis of retrodictions of past mantle evolution using the geodynamic adjoint method. A standard tool in tomographic-geodynamic model comparisons nowadays is tomographic filtering of mantle circulation models using the resolution operator <em><strong>R</strong></em> associated with the particular seismic inversion of interest. However, in this classical approach it is not possible to consider tomographic uncertainties and their impact on the geodynamic interpretation. </p><p>Here, we present a new method for 'filtering' synthetic Earth models, which makes use of the generalised inverse operator <strong>G</strong><sup>†</sup>, instead of using <em><strong>R</strong></em>. In our case, <strong>G</strong><sup>†</sup> is taken from a recent global SOLA Backus–Gilbert <em>S</em>-wave tomography. In contrast to classical tomographic filtering, the 'imaged' model is constructed by computing the <em>Generalised-Inverse Projection</em> (GIP) of synthetic data calculated in an Earth model of choice. This way, it is possible to include the effects of noise in the seismic data and thus to analyse uncertainties in the resulting model parameters. In order to demonstrate the viability of the method, we compute a set of travel times in an existing mantle circulation model, add specific realisations of Gaussian, zero-mean seismic noise to the synthetic data and apply <strong>G</strong><sup>†</sup>. <br> <br>Our results show that the resulting GIP model without noise is equivalent to the mean model of all GIP realisations from the suite of synthetic 'noisy' data and also closely resembles the model tomographically filtered using <em><strong>R</strong></em>. Most important, GIP models that include noise in the data show a significant variability of the shape and amplitude of seismic anomalies in the mantle. The significant differences between the various GIP realisations highlight the importance of interpreting and assessing tomographic images in a prudent and cautious manner. With the GIP approach, we can moreover investigate the effect of systematic errors in the data, which we demonstrate by adding an extra term to the noise component that aims at mimicking the effects of uncertain crustal corrections. In our presentation, we will finally discuss ways to construct the model covariance matrix based on the GIP approach and point out possible research directions on how to make use of this information in future geodynamic modelling efforts.</p>

Methods of correlation noise minimization and suppression for multisource acquisition in vibroseis survey

2019 ◽  
pp. 98-106
Author(s):  
A. N. Oshkin ◽  
A. I. Kon’kov ◽  
A. V. Tarasov ◽  
A. A. Shuvalov ◽  
V. I. Ignat’ev
Keyword(s):  
Seismic Data ◽  
Synthetic Data ◽  
Seismic Source ◽  
Recording System ◽  
Signal Separation ◽  
Median Filtering ◽  
Data Recording ◽  
Single Source ◽  
Correlation Noise ◽  
Incoherent Noise

The use of several simultaneously operating sources in seismic operations allows one to obtain large amounts of data per unit of time than for classical works with a single source, and also to improve the seismic data recording system. Depending on the type of seismic source used (vibrating or pulsed), different methods of signal separation are used. When working with vibroseismic method, separation of signals becomes possible at the stage of correlative processing of vibrograms. In this paper, we demonstrate methods for constructing noncorrelating signals for use in vibroseis survey (with an example of using such signals on synthetic data) and hyperbolic median filtering to minimize correlation and incoherent noise.

scholarly journals Understanding Micropolar Theory in the Earth Sciences II: The Seismic Moment Tensor

2021 ◽  
Author(s):  
Rafael Abreu ◽  
Stephanie Durand
Keyword(s):  
Seismic Data ◽  
Moment Tensor ◽  
Vertical Axis ◽  
Seismic Moment Tensor ◽  
Micropolar Theory ◽  
Moment Tensors ◽  
The Earth ◽  
Dynamic Source ◽  
Kaikoura Earthquake ◽  
Proper Theory

AbstractSeismic events produced by block rotations about vertical axis occur in many geodynamic contexts. In this study, we show that these rotations can be accounted for using the proper theory, namely micropolar theory, and a new asymmetric moment tensor can be derived. We then apply this new theory to the Kaikōura earthquake (2016/11/14), Mw 7.8, one of the most complex earthquakes ever recorded with modern instrumental techniques. Using advanced numerical techniques, we compute synthetic seismograms including a full asymmetric moment tensor and we show that it induces measurable differences in the waveforms proving that seismic data can record the effects of the block rotations observed in the field. Therefore, the theory developed in this work provides a full framework for future dynamic source inversions of asymmetric moment tensors.

True‐amplitude frequency‐wavenumber constant‐offset migration

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 915-924 ◽  
Author(s):  
B. O. Ekren ◽  
Bjørn Ursin
Keyword(s):  
Seismic Data ◽  
Synthetic Data ◽  
Earth Model ◽  
Geometrical Spreading ◽  
Amplitude Analysis ◽  
Time Migration ◽  
Amplitude Versus Offset ◽  
Out Of Plane ◽  
Nmo Correction ◽  
Prestack Time Migration

Low S/N ratios, interfering diffractions, and dip‐related problems (e.g., reflector point dispersal, dip‐dependent NMO, and reflection angle) make reliable amplitude versus offset (AVO) analysis a difficult task. Prestack time migration (PSTM) collapses diffractions, increases the S/N ratio, and reduces dip‐related problems. Therefore, PSTM is usually required before offset dependent information can be extracted from seismic data, and PSTM is mandatory before comparing real seismic data with 1-D earth model synthetic data. We present a 2-D frequency‐wavenumber common‐offset prestack time migration algorithm. To treat the amplitudes correctly, a 3-D to 2-D transform of the data is required before doing the migration. This is done by correcting the data for out‐of‐plane geometrical spreading. Migration artifacts are attenuated, exploiting the fact that the maximum dip to be migrated decreases with increasing traveltime and offset. The final processing steps before further processing are 2-D geometrical spreading correction and removal of the implicit NMO correction inherent in the migration. Two marine data examples show improved data quality after prestack time migration, making subsequent amplitude analysis more reliable.

scholarly journals Rotational Ground Motion Measurements for Regional Seismic Moment Tensors: a Review

2021 ◽  
Author(s):  
Stefanie Donner
Keyword(s):  
Ground Motion ◽  
Seismic Moment ◽  
Spatial Scales ◽  
Moment Tensor ◽  
Waveform Inversion ◽  
Seismic Source ◽  
Seismic Moment Tensor ◽  
Moment Tensors ◽  
Rotational Ground Motion ◽  
Motion Measurements

Seismic moment tensors are an important tool in geosciences on all spatial scales and for a broad range of applications. The basic underlying theory is established since decades. However, various factors influence the reliability of the inversion result, several of them are mutually dependent. Hence, a reliable retrieval of seismic moment tensors is still hampered in many cases, especially at regional event-receiver distances.To sample the entire wavefield due to a seismic source we need six components: three translational and three rotational ones. Up to now, only translational ground motion recordings were used for moment tensor retrieval, missing out valuable information. Using rotational in addition to the classical translational ground motions during waveform inversion for moment tensors mainly adds information on the vertical displacement gradient to the inversion problem. Furthermore, having available six instead of only three components per receiver location provides additional constraints on the sampling of the radiation pattern. As a result, the moment tensor components are resolved with higher precision and accuracy, even when the number of recording receivers is considerably reduced. Especially, components with a dependence to depth as well as the centroid depth can benefit significantly from additional rotational ground motion. Up to the time of writing this review only a few studies are published on the topic. Here, I summarise their findings and provide an overview over the possible capabilities of including rotational ground motion measurements to waveform inversion for seismic moment tensor retrieval.

Defining the scalar moment of a seismic source with a general moment tensor

1999 ◽  
Vol 89 (5) ◽  
pp. 1390-1394 ◽  
Author(s):  
David Bowers ◽  
John A. Hudson
Keyword(s):  
Seismic Moment ◽  
Moment Tensor ◽  
Seismic Source ◽  
Second Order ◽  
Seismic Moment Tensor ◽  
Total Moment ◽  
Double Couple ◽  
The Moment ◽  
Deviatoric Part ◽  
Scalar Moment

Abstract We compare several published definitions of the scalar moment M0, a measure of the size of a seismic disturbance derived from the second-order seismic moment tensor M (with eigenvalues m1 ≥ m3 ≥ m2). While arbitrary, a useful definition is in terms of a total moment, MT0 = MI + MD, where MI = |M|, with M = (m1 + m2 + m3)/3, is the isotropic moment, and MD = max(|mj − M|; j = 1, 2, 3), is the deviatoric moment. This definition is consistent with other definitions of M0 if M is a double couple. This definition also gives physically appealing and simple results for the explosion and crack sources. Furthermore, our definitions of MT0, MI and MD are in accord with the parameterization of the moment tensor into a deviatoric part (represented by T which lies in [−1,1]) and a volumetric part (represented by k which lies in [−1, 1]) proposed by Hudson et al. (1989).

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