Inversion of near-source S polarization for parameters of double-couple point sources

1989 ◽  
Vol 79 (6) ◽  
pp. 1779-1809
Author(s):  
Pascal Bernard ◽  
Aldo Zollo
Keyword(s):  
Frequency Band ◽  
Strike Slip ◽  
Point Sources ◽  
Inversion Method ◽  
Reasonable Assumption ◽  
Good Resolution ◽  
Angular Difference ◽  
Amplitude Data ◽  
Highly Nonlinear ◽  
Double Couple

Abstract We propose an inversion method for retrieving the focal parameters of small to moderate earthquakes by using the near-source S-wave polarizations, which are expected to be less sensitive than amplitude data to source details or propagation effects. We first studied the variability of the polarization vector for complete synthetic records generated in simple media with a shallow low-velocity layer, for various distances (0 to 50 km), source depths (1 to 15 km), and mechanisms. In the frequency band 1 to 2 Hz, a polarization fluctuation of less than 20° is found for sources deeper than 5 km. The mean angular difference between ray theory and complete field polarization is less than 10° when the complete waveform meets the two following criteria: (1) The polarization is nearly stable (less than 30° of variability) and (2) the motion is nearly horizontal (vector dip less than 30°). The inversion method uses a norm related to the angular difference in polarization between the real and synthetic waveforms generated by a point double couple. As the problem is highly nonlinear, the model space (strike, dip, slip, location) should be finely sampled and systematically explored in the whole domain of interest. We tested the inversion resolution with synthetic data for a strike-slip and a dip-slip source at 10 km in depth (no error in location) recorded at eight stations within 30 km, assuming an error of 25° on the synthetic polarization. The dip-slip inversion gives a good resolution in dip (15° of uncertainty), but a strong correlation between strike and slip, because no recording site was close to the near vertical principal axis of the stress tensor in the test. On the contrary, the near horizontal major axis of the tensor is very well constrained. The strike-slip inversion gives a good resolution in the three parameters, with uncertainties of about 10°. A 25° change in the strike, dip, or slip angle statistically results in a 25° rotation of the polarization. With numerous stations, the overdetermination of the problem reduces the model error to values lower than 25°. The absence of records in specific areas introduces additional solutions for the possible mechanisms. Finally, the sensitivity of polarization to 3 km shift in source location is globally smaller than for 25° of rotation of any fault angle. The application of this method to real data requires the evaluation of the reliability in the polarizations computed for simplified media. An uncertainty of 25° is expected to be a reasonable assumption for distances smaller than 30 km in the 1 to 2 Hz frequency band; more generally, the error is expected to increase with distance and frequency.

Dense surface seismic data confirm non-double-couple source mechanisms induced by hydraulic fracturing

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. KS207-KS217 ◽  
Author(s):  
Jeremy D. Pesicek ◽  
Konrad Cieślik ◽  
Marc-André Lambert ◽  
Pedro Carrillo ◽  
Brad Birkelo
Keyword(s):  
Hydraulic Fracturing ◽  
Seismic Data ◽  
P Wave ◽  
Source Modeling ◽  
Moment Tensors ◽  
Amplitude Data ◽  
Double Couple ◽  
Source Mechanisms ◽  
Source Models ◽  
Favorable Conditions

We have determined source mechanisms for nine high-quality microseismic events induced during hydraulic fracturing of the Montney Shale in Canada. Seismic data were recorded using a dense regularly spaced grid of sensors at the surface. The design and geometry of the survey are such that the recorded P-wave amplitudes essentially map the upper focal hemisphere, allowing the source mechanism to be interpreted directly from the data. Given the inherent difficulties of computing reliable moment tensors (MTs) from high-frequency microseismic data, the surface amplitude and polarity maps provide important additional confirmation of the source mechanisms. This is especially critical when interpreting non-shear source processes, which are notoriously susceptible to artifacts due to incomplete or inaccurate source modeling. We have found that most of the nine events contain significant non-double-couple (DC) components, as evident in the surface amplitude data and the resulting MT models. Furthermore, we found that source models that are constrained to be purely shear do not explain the data for most events. Thus, even though non-DC components of MTs can often be attributed to modeling artifacts, we argue that they are required by the data in some cases, and can be reliably computed and confidently interpreted under favorable conditions.

A teleseismic body-wave analysis of the May 1980 Mammoth Lakes, California, earthquakes

1983 ◽  
Vol 73 (2) ◽  
pp. 419-434
Author(s):  
Jeffery S. Barker ◽  
Charles A. Langston
Keyword(s):  
Body Wave ◽  
Moment Tensor ◽  
Normal Fault ◽  
Strike Slip ◽  
Body Waves ◽  
P Wave ◽  
Moment Tensors ◽  
Double Couple ◽  
The Moment ◽  
Mammoth Lakes

abstract Teleseismic P-wave first motions for the M ≧ 6 earthquakes near Mammoth Lakes, California, are inconsistent with the vertical strike-slip mechanisms determined from local and regional P-wave first motions. Combining these data sets allows three possible mechanisms: a north-striking, east-dipping strike-slip fault; a NE-striking oblique fault; and a NNW-striking normal fault. Inversion of long-period teleseismic P and SH waves for the events of 25 May 1980 (1633 UTC) and 27 May 1980 (1450 UTC) yields moment tensors with large non-double-couple components. The moment tensor for the first event may be decomposed into a major double couple with strike = 18°, dip = 61°, and rake = −15°, and a minor double couple with strike = 303°, dip = 43°, and rake = 224°. A similar decomposition for the last event yields strike = 25°, dip = 65°, rake = −6°, and strike = 312°, dip = 37°, and rake = 232°. Although the inversions were performed on only a few teleseismic body waves, the radiation patterns of the moment tensors are consistent with most of the P-wave first motion polarities at local, regional, and teleseismic distances. The stress axes inferred from the moment tensors are consistent with N65°E extension determined by geodetic measurements by Savage et al. (1981). Seismic moments computed from the moment tensors are 1.87 × 1025 dyne-cm for the 25 May 1980 (1633 UTC) event and 1.03 × 1025 dyne-cm for the 27 May 1980 (1450 UTC) event. The non-double-couple aspect of the moment tensors and the inability to obtain a convergent solution for the 25 May 1980 (1944 UTC) event may indicate that the assumptions of a point source and plane-layered structure implicit in the moment tensor inversion are not entirely valid for the Mammoth Lakes earthquakes.

Use of reciprocity theorem for obtaining Rayleigh wave radiation patterns

1966 ◽  
Vol 56 (4) ◽  
pp. 925-936 ◽  
Author(s):  
I. N. Gupta
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Three Dimensional ◽  
Reciprocity Theorem ◽  
Point Sources ◽  
Dimensional Case ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
Homogeneous Half Space ◽  
Double Couple

abstract The reciprocity theorem is used to obtain Rayleigh wave radiation patterns from sources on the surface of or within an elastic semi-infinite medium. Nine elementary line sources first considered are: horizontal and vertical forces, horizontal and vertical double forces without moment, horizontal and vertical single couples, center of dilatation (two dimensional case), center of rotation, and double couple without moment. The results are extended to the three dimensional case of similar point sources in a homogeneous half space. Haskell's results for the radiation patterns of Rayleigh waves from a fault of arbitrary dip and direction of motion are reproduced in a much simpler manner. Numerical results on the effect of the depth of these sources on the Rayleigh wave amplitudes are shown for a solid having Poisson's ratio of 0.25.

scholarly journals Long-period mechanism of the 8 November 1980 Eureka, California, earthquake

1982 ◽  
Vol 72 (2) ◽  
pp. 439-456
Author(s):  
Thorne Lay ◽  
Jeffrey W. Given ◽  
Hiroo Kanamori
Keyword(s):  
Point Source ◽  
Seismic Moment ◽  
Moment Tensor ◽  
Strike Slip ◽  
The Body ◽  
Body Waves ◽  
Long Period ◽  
Amplitude Data ◽  
The Moment ◽  
Scalar Moment

Abstract The seismic moment and source orientation of the 8 November 1980 Eureka, California, earthquake (Ms = 7.2) are determined using long-period surface and body wave data obtained from the SRO, ASRO, and IDA networks. The favorable azimuthal distribution of the recording stations allows a well-constrained mechanism to be determined by a simultaneous moment tensor inversion of the Love and Rayleigh wave observations. The shallow depth of the event precludes determination of the full moment tensor, but constraining Mzx = Mzy = 0 and using a point source at 16-km depth gives a major double couple for period T = 256 sec with scalar moment M0 = 1.1 · 1027 dyne-cm and a left-lateral vertical strike-slip orientation trending N48.2°E. The choice of fault planes is made on the basis of the aftershock distribution. This solution is insensitive to the depth of the point source for depths less than 33 km. Using the moment tensor solution as a starting model, the Rayleigh and Love wave amplitude data alone are inverted in order to fine-tune the solution. This results in a slightly larger scalar moment of 1.28 · 1027 dyne-cm, but insignificant (<5°) changes in strike and dip. The rake is not well enough resolved to indicate significant variation from the pure strike-slip solution. Additional amplitude inversions of the surface waves at periods ranging from 75 to 512 sec yield a moment estimate of 1.3 ± 0.2 · 1027 dyne-cm, and a similar strike-slip fault orientation. The long-period P and SH waves recorded at SRO and ASRO stations are utilized to determine the seismic moment for 15- to 30-sec periods. A deconvolution algorithm developed by Kikuchi and Kanamori (1982) is used to determine the time function for the first 180 sec of the P and SH signals. The SH data are more stable and indicate a complex bilateral rupture with at least four subevents. The dominant first subevent has a moment of 6.4 · 1026 dyne-cm. Summing the moment of this and the next three subevents, all of which occur in the first 80 sec of rupture, yields a moment of 1.3 · 1027 dyne-cm. Thus, when the multiple source character of the body waves is taken into account, the seismic moment for the Eureka event throughout the period range 15 to 500 sec is 1.3 ± 0.2 · 1027 dyne-cm.

2-D and 3-D resistivity image reconstruction using crosshole data

Geophysics ◽  
1992 ◽  
Vol 57 (10) ◽  
pp. 1270-1281 ◽  
Author(s):  
Hiromasa Shima
Keyword(s):  
Field Test ◽  
Numerical Models ◽  
Electrical Potential ◽  
Nonlinear Least Squares ◽  
Three Dimensions ◽  
Inversion Method ◽  
Good Resolution ◽  
Inversion Algorithm ◽  
Linear Inversion ◽  
Resistivity Model

Theoretical changes in the distribution of electrical potential near subsurface resistivity anomalies have been studied using two resistivity models. The results suggest that the greatest response from such anomalies can be observed with buried electrodes, and that the resistivity model of a volume between boreholes can be accurately reconstructed by using crosshole data. The distributive properties of crosshole electrical potential data obtained by the pole‐pole array method have also been examined using the calculated partial derivative of the observed apparent resistivity with respect to a small cell within a given volume. The results show that for optimum two‐dimensional (2-D) and three‐dimensional (3-D) target imaging, in‐line data and crossline data should be combined, and an area outside the zone of exploration should be included in the analysis. In this paper, the 2-D and 3-D resistivity images presented are reconstructed from crosshole data by the combination of two inversion algorithms. The first algorithm uses the alpha center method for forward modeling and reconstructs a resistivity model by a nonlinear least‐squares inversion. Alpha centers express a continuously varying resistivity model, and the distribution of the electrical potential from the model can be calculated quickly. An initial general model is determined by the resistivity backprojection technique (RBPT) prior to the first inversion step. The second process uses finite elements and a linear inversion algorithm to improve the resolution of the resistivity model created by the first step. Simple 2-D and 3-D numerical models are discussed to illustrate the inversion method used in processing. Data from several field studies are also presented to demonstrate the capabilities of using crosshole resistivity exploration techniques. The numerical experiments show that by using the combined reconstruction algorithm, thin conductive layers can be imaged with good resolution for 2-D and 3-D cases. The integration of finite‐element computations is shown to improve the image obtained by the alpha center inversion process for 3-D applications. The first field test uses horizontal galleries to evaluate complex 2-D features of a zinc mine. The second field test illustrates the use of three boreholes at a dam site to investigate base rock features and define the distribution of an altered zone in three dimensions.

Modeling teleseismic SV waves from underground explosions with tectonic release: Results for Southern Novaya Zemlya

1988 ◽  
Vol 78 (3) ◽  
pp. 1158-1178
Author(s):  
Brian P. Cohee ◽  
Thorne Lay
Keyword(s):  
Source Region ◽  
Test Site ◽  
Strike Slip ◽  
Destructive Interference ◽  
Ray Theory ◽  
Source Strength ◽  
Sh Waves ◽  
Waveform Modeling ◽  
Novaya Zemlya ◽  
Double Couple

Abstract Detailed forward modeling of long-period shear waves for two large underground explosions at the Southern Novaya Zemlya test site indicates that the appropriate equivalent double-couple orientation for the tectonic release radiation is vertical strike-slip. Previous studies of observed teleseismic SH waveforms and SV amplitudes for the 27 October 1973 and 2 November 1974 events using geometric ray theory could not distinguish between vertical strike-slip and 45°-dipping thrust geometries. Either mechanism can match the observed four-lobed SH radiation pattern, and the two-lobed SV amplitude pattern can be produced by interference with an appropriate size explosion pS signal. However, the complexity of the observed SV waveforms arising from Sp conversions near the receiver, diffracted Sp, and shear-coupled PL phases is not accounted for in the ray theory synthetics. Incorporating more realistic Green's functions using Baag and Langston's (1985b) WKBJ spectral method allows more complete modeling of the SV signals. Due to differences in frequency content between the explosion and double-couple SV waveforms, constructive interference occurs more efficiently than destructive interference when the two signals are linearly superimposed. As a result, using tectonic release moments determined from the SH waves and the optimum F factors required to match the SV amplitude patterns, the waveforms produced by the strike-slip and thrust orientations differ substantially at some azimuths. The strike-slip solution yields a consistently superior match to the data. Using the EU2 model of Lerner-Lam and Jordan (1987) for the source region and either EU2 or TNA (Grand and Helmberger, 1984) for the receiver structure, together with an attenuation model similar to SL8, we obtain a double-couple moment, M0 = 3.2 × 1024 dyne-cm and explosion source strength, ψ∞ = 3.8 ± 0.5 × 1011 cm3 for the 27 October 1973 event, and M0 = 1.7 × 1024 dyne-cm and ψ∞ = 2.0 ± 0.3 × 1011 cm3 for the 2 November 1974 event. Complete waveform modeling of SV signals can thus provide improved constraints on tectonic release radiation and explosion source strength.

scholarly journals Monitoring of induced distributed double-couple sources using Marchenko-based virtual receivers

Solid Earth ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1301-1319 ◽  
Author(s):  
Joeri Brackenhoff ◽  
Jan Thorbecke ◽  
Kees Wapenaar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Synthetic Data ◽  
Real Data ◽  
Point Sources ◽  
Reflection Data ◽  
Double Couple ◽  
Source Mechanisms ◽  
Source Signal ◽  
Time Part

Abstract. We aim to monitor and characterize signals in the subsurface by combining these passive signals with recorded reflection data at the surface of the Earth. To achieve this, we propose a method to create virtual receivers from reflection data using the Marchenko method. By applying homogeneous Green’s function retrieval, these virtual receivers are then used to monitor the responses from subsurface sources. We consider monopole point sources with a symmetric source signal, for which the full wave field without artifacts in the subsurface can be obtained. Responses from more complex source mechanisms, such as double-couple sources, can also be used and provide results with comparable quality to the monopole responses. If the source signal is not symmetric in time, our technique based on homogeneous Green’s function retrieval provides an incomplete signal, with additional artifacts. The duration of these artifacts is limited and they are only present when the source of the signal is located above the virtual receiver. For sources along a fault rupture, this limitation is also present and more severe due to the source activating over a longer period of time. Part of the correct signal is still retrieved, as is the source location of the signal. These artifacts do not occur in another method that creates virtual sources as well as receivers from reflection data at the surface. This second method can be used to forecast responses to possible future induced seismicity sources (monopoles, double-couple sources and fault ruptures). This method is applied to field data, and similar results to the ones on synthetic data are achieved, which shows the potential for application on real data signals.

scholarly journals Traveltime inversion for 2‐D anomaly structures

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1481-1487 ◽  
Author(s):  
Danilo R. Velis
Keyword(s):  
Optimization Problem ◽  
Inversion Method ◽  
Unknown Parameters ◽  
New Approach ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Highly Nonlinear ◽  
Small Set ◽  
A Cell ◽  
Parametric Functions

This work presents a traveltime inversion method that uses parametric functions to represent 2‐D anomaly structures. These functions are described by a small set of unknown parameters which in turn are obtained after solving a highly nonlinear optimization problem via simulated annealing (SA). The procedure favors neither smooth nor high contrasting anomalies and keeps the number of unknowns very small so as to make the problem tractable using SA. Yet the strategy allows one to accommodate a large class of velocity models. Results indicate that this new approach typically yields better images than a standard linearized inversion based on a cell parameterization scheme.

scholarly journals Seismic pre-stack AVA inversion scheme based on lithology constraints

2020 ◽  
Vol 17 (3) ◽  
pp. 411-428
Author(s):  
Shuang Xiao ◽  
Jing Ba ◽  
Qiang Guo ◽  
J M Carcione ◽  
Lin Zhang ◽  
...  
Keyword(s):  
Model Updating ◽  
Optimal Solution ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Good Resolution ◽  
S Wave ◽  
Elastic Parameters ◽  
Multivariate Gaussian Distribution ◽  
Stability Performance ◽  
The Stability

Abstract Seismic pre-stack AVA inversion using the Zoeppritz equation and its approximations as a forward engine yields P- and S-wave velocities and density. Due to the presence of seismic noise and other factors, the solution to seismic inversion is generally ill-posed and it is necessary to add constraints to regularize the algorithm. Moreover, since pre-stack inversion is a nonlinear problem, linearized optimization algorithms may fall into false local minima. The simulated annealing (SA) algorithm, on the other hand, is capable of finding the global optimal solution regardless of the initial model. However, when applied to multi-parameter pre-stack inversion, standard SA suffers from instability. Thus, a nonlinear pre-stack inversion method is proposed based on lithology constraints. Specifically, correlations among the elastic parameters are introduced to establish constraints based on a Bayesian framework, with special intention of mitigating the ill-posedness of the inversion problem as well as addressing the lithological characteristics of the formations. In particular, to improve the stability, a multivariate Gaussian distribution of elastic parameters is incorporated into the model updating the SA algorithm. We apply the algorithm to synthetic and field seismic data, indicating that the proposed method has a good resolution and stability performance.

Microseismic moment-tensor inversion and sensitivity analysis in VTI media

Geophysics ◽  
2020 ◽  
pp. 1-74
Author(s):  
Han Li ◽  
Xu Chang ◽  
Xiao-Bi Xie ◽  
Yibo Wang
Keyword(s):  
Hydraulic Fracturing ◽  
Focal Mechanism ◽  
Moment Tensor ◽  
Staggered Grid ◽  
Inversion Method ◽  
Model Parameters ◽  
Seismic Moment Tensor ◽  
Tensor Model ◽  
Double Couple ◽  
The Impact

Through the study of microseismic focal mechanisms, information such as fracture orientation, event magnitude, and in-situ stress status can be quantitatively obtained, thus, providing a reliable basis for unconventional oil and gas exploration. Most source inversion methods assume that the medium is isotropic. However, hydraulic fracturing is usually conducted in sedimentary rocks, which often exhibit strong anisotropy. Neglecting this anisotropy may cause errors in focal mechanism inversion results. We propose a microseismic focal mechanism inversion method that considers velocity anisotropy in a vertically transverse isotropic (VTI) medium. To generate synthetic data, we adopt the moment-tensor model to represent microearthquake sources. We use a staggered-grid finite-difference (SGFD) method to calculate synthetic seismograms in anisotropic media. We perform seismic moment-tensor (SMT) inversion with only P-waves by matching synthetic and observed waveforms. Both synthetic and field datasets are used to test the inversion method. For the field dataset, we investigate the inversion stability using randomly selected partial datasets in the calculation. We pay special attention to analyze the sensitivity of the inversion. We test and evaluate the impact of noise in the data and errors in the model parameters ( VP0, ε, and δ) on the SMT inversion using synthetic datasets. The results indicate that for a surface acquisition system, the proposed method can tolerate moderate noise in the data, and deviations in the anisotropy parameters can cause errors in the SMT inversion, especially for dip-slip events and the inverted percentages of non-double-couple components. According to our study, including anisotropy in the model is important to obtain reliable non-double-couple components of moment tensors for hydraulic fracturing induced microearthquakes.

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