Scattering attenuation in sediments modeled by ARMA processes—Validation of simple Q models

Geophysics ◽  
1994 ◽  
Vol 59 (12) ◽  
pp. 1813-1826 ◽  
Author(s):  
Claudia Kerner ◽  
Peter E. Harris
Keyword(s):  
Point Source ◽  
Moving Average ◽  
Normal Incidence ◽  
Distribution Functions ◽  
Depth Interval ◽  
Elastic Plane ◽  
Depth Range ◽  
Source Modeling ◽  
Scattering Attenuation ◽  
Sedimentary Sequences

We investigate the data requirements for a reliable analysis of frequency‐dependent Q caused by scattering in a finely layered geological structure. Numerical wave propagation experiments in stochastic models were performed. We set up autoregressive‐moving average [ARMA(1,1)] models for the reflection coefficients with non‐Gaussian distribution functions and used published parameter sets estimated for sedimentary sequences from real log data. For ARMA models, analytical expressions for the scattering attenuation α and the quality factor Q can be derived from the O’Doherty‐Anstey formula. The aim of this study is to investigate whether scattering attenuation as derived from the O’Doherty‐Anstey formula is measurable with sufficient accuracy with a traditional vertical seismic profile (VSP) configuration in realistic sedimentary sequences, and if so, whether the data can be inverted to yield the statistics of the sediment sequence. The main result is that reliable estimation of scattering attenuation requires VSP data over a considerable depth interval, depending on the magnitude of the attenuation with errors in the estimates increasing inversely as the depth range increases. Extensions of the O’Doherty‐Anstey theory to non‐normal incidence have been given in the literature. We examine the angle dependence of the results using both elastic plane‐wave modeling and acoustic point‐source modeling. For the weak medium variations considered, elastic effects (e.g., mode conversions) and point‐source effects are negligible at angles up to about 25 degrees.

Prestack inversion with plane‐layer point source modeling

Geophysics ◽  
1985 ◽  
Vol 50 (1) ◽  
pp. 77-89 ◽  
Author(s):  
Alastair D. McAulay
Keyword(s):  
Velocity Profile ◽  
Point Source ◽  
Spherical Wave ◽  
Normal Incidence ◽  
Plane Layer ◽  
Source Modeling ◽  
Low Frequencies ◽  
Prestack Inversion ◽  
Band Limited

Prestack inversion with point‐source plane‐layer modeling has many advantages over poststack or normal incidence inversion. For example, it permits the determination of absolute compressional and shear velocities, density variations, and the accurate accounting of interbed and surface multiples. I neglect shear effects in this paper by assuming that they are adequately suppressed by velocity filtering. In the forward modeling step, a spherical wave expansion into plane waves is used to account for the point source. The plane‐wave reflection response for a set of plane layers is extended to the nonnormal incidence case. I use a Hankel transform to account for cylindrical symmetry. Generalized linear inversion is used because the fast recursive approaches available for normal incidence inversion are no longer applicable. I provide the derivation for the required derivative matrix, and I take into account the band‐limited nature of the data in frequency, time, and space. I demonstrate that moveout of events on realistic simulated prestack data enables the determination of absolute compressional velocity in the velocity‐depth profile, even though the data are band‐limited in frequency. I assume that preprocessing has adequately removed the shear and surface effects and that density is constant. Low frequencies in the velocity profile may be obtained more accurately than with velocity analysis used for stacking, because interbed multiples and other modeling phenomena are accounted for in the computation. Autoregressive modeling procedures that predict into the low frequencies of the velocity profile are also less accurate and cannot generate absolute velocity. I suggest future research leading to cost‐effective inversion of real data.

Electromagnetic characterization of epithermal gold deposits: A case study from the Tuoniuhe gold deposit, Northeast China

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. B49-B62 ◽  
Author(s):  
Shan Xu ◽  
Fengming Xu ◽  
Xiangyun Hu ◽  
Qun Zhu ◽  
Yuandong Zhao ◽  
...  
Keyword(s):  
Gold Deposit ◽  
Northeast China ◽  
Depth Interval ◽  
Alteration Zone ◽  
Magnetic Survey ◽  
Depth Range ◽  
Epithermal Gold ◽  
Low Resistivity ◽  
Resistivity Model ◽  
Gold Bearing

A high-resolution electromagnetic study has helped to define the mineralization and alteration system of the Cretaceous volcano-sedimentary hosted epithermal gold (Au) deposit in Tuoniuhe, northeast China. Audio-magnetotelluric (AMT) array data were acquired to map the regional resistivity structure of the Mesozoic volcanic field, whereas an AMT profile and a ground magnetic survey line with denser site spacing were deployed across the deposit to image the alteration and mineralization system. The electrical resistivity model from 2D inversion of the AMT profile data reveals a low-resistivity (approximately [Formula: see text]) cover from the surface to a depth of 0.1 km, which is likely caused by clay and sulfide minerals in the subaerial alteration zone. The magnetic survey and a geologic borehole log assisted in outlining a zone of tonalite and andesite with silicification in the depth interval of 0.1–0.3 km, featuring high resistivity ([Formula: see text]) and high magnetization ([Formula: see text]). This zone is a potential gold target bounded by two channels of moderate resistivity (approximately [Formula: see text]) to its northwest and southeast. The two channels possibly coincide with breccia pipes with fractured stockworks and high permeability to allow gold-bearing fluids to move toward the surface. The 2D and 3D resistivity models reveal regions of low resistivity ([Formula: see text]) at the depth range of 0.5–1.0 km beneath the Cretaceous calderas and the deposit, which might be related to magmatic cryptoexplosion breccia. In the 2D resistivity model, this magmatic cryptoexplosion breccia zone connects to the subaerial alteration zone through the two breccia pipes, indicative of a circulation system of gold-bearing fluids. Given the coincidence of Cretaceous volcanism and the age of mineralization, the Cretaceous magma is inferred to have supplied heat that drove the convective hydrothermal activity and also was a source of magmatic fluids that led to the development of the Tuoniuhe epithermal gold deposit.

Antireflection and Scattering Properties of Two-Dimensional Hexagonal AZO Gratings on Glass Substrates

2013 ◽  
Vol 538 ◽  
pp. 337-340
Author(s):  
Ren Chen Liu ◽  
Yong Gang Wu ◽  
Zi Huan Xia
Keyword(s):  
Normal Incidence ◽  
Distribution Functions ◽  
Interference Lithography ◽  
Two Dimensional ◽  
Glass Substrates ◽  
Azo Thin Film ◽  
Aluminum Doped Zinc Oxide ◽  
Lift Off ◽  
Submicron Gratings ◽  
Total Transmittance

With photoresist dot arrays fabricated by a two-beam interference lithography as an etch mask, two-dimensional (2-D) hexagonal aluminum-doped zinc oxide（AZO）submicron gratings (SMG) with 160nm height (h) and different periods (P) were produced using lift-off transfer process. Results show that as P decreased to 487nm, SMG exhibited excellent antireflection properties, which reduced the average total reflectivity (Rtotal) from 11.8% of AZO thin film to 4.7% in the wavelength range of 400nm-1050nm, and promoted the total transmittance (Ttotal) significantly, especially in the long spectral range of 750nm-1050nm. On the other hand, as P increased from 487nm to 985nm, the haze parameters of reflectance (HR) or transmittance (HT) improved from 25.5% to 40.2% or from 15.1% to 36.8%, respectively. Nevertheless, P increased from 985nm to 1435nm, both Rtotal (or Ttotal) and HR (or HT) varied very slightly. Bidirectional distribution functions at normal incidence not only verified that the larger the P was, the part of diffuse reflectance (or transmittance) were much higher, but also further demonstrate the larger the P, the smaller the diffaction angle. In summary, 2-D hexagonal AZO SMG show promising antireflection effects at P less than 487nm, and show promising scattering abilities at P about 985nm.

On the asymptotic distributions of maxima of trigonometric polynomials with random coefficients

1984 ◽  
Vol 16 (4) ◽  
pp. 819-842 ◽  
Author(s):  
K. F. Turkman ◽  
A. M. Walker
Keyword(s):  
Moving Average ◽  
Random Coefficients ◽  
Distribution Functions ◽  
Asymptotic Distributions ◽  
Trigonometric Polynomials ◽  
Stationary Gaussian Sequence ◽  
Moving Average Representation ◽  
Standard Normal ◽  
Average Representation ◽  
Mutually Independent

Let {ε t, t = 1, 2, ···, n} be a sequence of mutually independent standard normal random variables. Let Xn(λ) and Yn(λ) be respectively the real and imaginary parts of exp iλ t, and let . It is shown that as n tends to∞, the distribution functions of the normalized maxima of the processes {Xn(λ)}, (Yn(λ)}, {In(λ)} over the interval λ∈ [0,π] each converge to the extremal distribution function exp [–e–x], —∞ < x <∞.It is also shown that these results can be extended to the case where {ε t} is a stationary Gaussian sequence with a moving-average representation.

Array based analysis of induced earthquake characteristics using beamforming and back-projection methods in Helsinki, Finland

2021 ◽  
Author(s):  
Bo Li ◽  
Alice-Agnes Gabriel ◽  
Annukka Rintamäki ◽  
Gregor Hillers
Keyword(s):  
Point Source ◽  
Projection Method ◽  
Induced Seismicity ◽  
Epicentral Distance ◽  
Fracture Network ◽  
Projection Methods ◽  
The Body ◽  
Quality Data ◽  
Depth Range ◽  
Back Projection

&lt;p&gt;The evolution and characteristics of induced seismicity in geothermal stimulations can shed light on water pathways and fracture network development. However, these seismic sources are usually difficult to characterize due to their small magnitudes and the low signal-to-noise ratio (SNR) of observational recordings. Heterogeneous and ill-constrained 3D subsurface structure further restricts the local-scale application of array based methods, such as the back-projection method. The 2018 st1 Deep Heat geothermal stimulation experiment in Espoo, Finland, induced thousands of seismic events in the 5-6 km depth range with magnitudes smaller or equal to ML 1.8 (Hillers, et al., 2020). The competent bedrock and absence of a dissipating sedimentary layer results in high SNR seismograms collected by three 4-station arrays, three 25-station arrays and tens of standalone stations located within 5 km distance around the wellhead. These high-quality data facilitate the application of multi-array beamforming and the back-projection methods, to image small-magnitude induced seismicity sources and characterize their properties at reservoir scales.&lt;/p&gt;&lt;p&gt;The beamforming results demonstrate array, frequency and phase (P or S) dependent slowness biases of catalog locations, which are obtained using standard location procedures with manually picked P- and S-wave arrivals. This indicates multi-scale heterogeneity in the study region. Specifically, we find that the back azimuth of the slowness at each array points to inconsistent locations and leads to poorly constrained epicenters. We show that the systematic slowness variability can be reduced and multi-array location estimates can be greatly improved by calibration using well-constrained catalog events.&amp;#160;&amp;#160;&lt;/p&gt;&lt;p&gt;To perform the back-projection, we select unclustered stations from narrow epicentral distance ranges to avoid unfavorably large variations in the duration of the body phases, and we set the azimuth gap threshold to less than 40 degrees. The locations determined by the back-projection are close to the catalog locations, with the majority of them within 150 m, suggesting a successful application of the back-projection technique using local stations to study small events. We repeatedly observe&amp;#160; &amp;#8220;swimming&amp;#8221; artifacts (Ishii et al., 2007; Walker and Shearer, 2009), i.e. the back-projection locations migrate in a certain direction with time. This is typically attributed to array-source directivity effects in teleseismic applications, but in our case the stations are well-distributed around the source. We next use numerical wave propagation simulations, with receivers homogeneously azimuthal distributed at constant epicentral distance to a point-source. We apply the back-projection using synthetic seismograms. The results confirm the consistent appearance of &amp;#8220;swimming&amp;#8221; patterns and the apparent migration direction which changes in dependence on the focal mechanism of the point source. We conclude that the back-projection method may provide useful proxies for source mechanisms to help track and link the evolving fracture network.&lt;/p&gt;

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