THEORETICAL SEISMOGRAMS WITH FREQUENCY AND DEPTH DEPENDENT ABSORPTION

Geophysics ◽  
1962 ◽  
Vol 27 (6) ◽  
pp. 766-785 ◽  
Author(s):  
A. W. Trorey
Keyword(s):  
Absorption Coefficient ◽  
Time Domain ◽  
Network Theory ◽  
Digital Computer ◽  
Arrival Time ◽  
Synthetic Seismograms ◽  
Multiple Reflections ◽  
Frequency Spectra ◽  
Dependent Absorption ◽  
The Time Domain

In the computation of conventional theoretical (or “synthetic”) seismograms, the effects of the variation of frequency‐dependent absorption with depth are presently ignored. Such absorption can produce significant differences in both the relative amplitudes and frequency spectra of primary and multiple reflections having the same arrival time. This paper describes a feasible way, using a digital computer of the IBM 7090 class, for computing theoretical seismograms which properly take into account the variation of absorption with both frequency and depth, it being assumed that the absorption coefficient varies linearly with frequency. It is pointed out that attempts to solve the problem using Fourier analysis in the frequency domain would lead to significant aliasing errors. Consequently a method borrowed from the field of network theory utilizing deconvolution is devised whereby solutions are obtained directly in the time domain. Both “primary” and “primary‐plus‐all‐multiple” traces are computed, the former including the “peg‐leg” multiples described by Anstey (1960) and Webster (1960). These calculations demonstrate that absorption can reduce the multiple content of theoretical seismograms.

scholarly journals Transmission compensated primary reflection retrieval in the data domain and consequences for imaging

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. Q27-Q36 ◽  
Author(s):  
Lele Zhang ◽  
Jan Thorbecke ◽  
Kees Wapenaar ◽  
Evert Slob
Keyword(s):  
Thin Layer ◽  
Time Domain ◽  
Velocity Model ◽  
Original Data ◽  
Transmission Losses ◽  
Multiple Reflections ◽  
Data Set ◽  
Numerical Examples ◽  
The One ◽  
The Time Domain

We have developed a scheme that retrieves primary reflections in the two-way traveltime domain by filtering the data. The data have their own filter that removes internal multiple reflections, whereas the amplitudes of the retrieved primary reflections are compensated for two-way transmission losses. Application of the filter does not require any model information. It consists of convolutions and correlations of the data with itself. A truncation in the time domain is applied after each convolution or correlation. The retrieved data set can be used as the input to construct a better velocity model than the one that would be obtained by working directly with the original data and to construct an enhanced subsurface image. Two 2D numerical examples indicate the effectiveness of the method. We have studied bandwidth limitations by analyzing the effects of a thin layer. The presence of refracted and scattered waves is a known limitation of the method, and we studied it as well. Our analysis indicates that a thin layer is treated as a more complicated reflector, and internal multiple reflections related to the thin layer are properly removed. We found that the presence of refracted and scattered waves generates artifacts in the retrieved data.

Wrap‐around removal from one‐dimensional synthetic seismograms

Geophysics ◽  
1989 ◽  
Vol 54 (7) ◽  
pp. 911-915 ◽  
Author(s):  
Hans Thybo
Keyword(s):  
Frequency Domain ◽  
Computational Methods ◽  
Time Domain ◽  
Synthetic Seismograms ◽  
Seismic Exploration ◽  
One Dimensional ◽  
Borehole Logs ◽  
The Time Domain ◽  
Layered Models

One‐dimensional (1-D) synthetic seismograms are important tools in seismic exploration. They play an important role in the correlation of recorded seismograms with borehole logs and also permit the estimation of delay‐type attenuation in finely layered models. Existing computational methods for computing 1-D seismograms can be grouped according to whether the calculations are performed in the time domain or in the frequency domain.

Symmetric Arc Solutions of ζ¨ = ζn

1968 ◽  
Vol 35 (3) ◽  
pp. 565-570
Author(s):  
C. P. Atkinson ◽  
B. L. Dhoopar
Keyword(s):  
Differential Equation ◽  
Time Domain ◽  
Complex Variable ◽  
Digital Computer ◽  
Nonlinear Differential Equations ◽  
Time Derivative ◽  
Approximate Solutions ◽  
Complex Variables ◽  
Complex Modes ◽  
The Time Domain

This paper, “Symmetric Arc Solutions of ζ¨ = ζn,” presents periodic solutions of this differential equation relating the complex variable ζ(t) = u(t) + iv(t) and its second time derivative ζ¨ The solutions are called symmetric arc solutions since they form such arcs on the ζ = u + iv-plane. The solutions, ζ(t), are “complex modes” of coupled nonlinear differential equations in the complex variables z1 and z2. Symmetric arc solutions are presented for a range of n from n = 3 to n = 101. Approximate solutions are presented and compared with solutions generated by digital computer. Solutions are presented on the ζ-plane and in the time domain as u(t) and v(t).

scholarly journals PENENTUAN HIPOSENTER DAN EPISENTER GEMPA VOLKANIK GUNUNG MERAPI DENGAN HIPO9

2020 ◽  
Vol 6 (1) ◽  
pp. 124
Author(s):  
Syahrial Ayub ◽  
Joni Rokhmat ◽  
Ahmad Harjono ◽  
Wahyudi Wahyudi
Keyword(s):  
Frequency Domain ◽  
Frequency Band ◽  
Time Domain ◽  
Arrival Time ◽  
Band Width ◽  
Volcanic Earthquake ◽  
Volcanic Earthquakes ◽  
The Time Domain

ABSTRAKTelah dilakukan penelitian terhadap gempa volkanik gunung Merapi. Penelitian ini bertujuan menentukan hiposenter dan episenter gempa volkanik gunung Merapi dengan HIPO9. Analisis dilakukan dalam dua kawasan, yaitu kawasan waktu dan kawasan frekuensi. Dalam kawasan waktu ditentukan waktu tiba gempa volkanik. Dalam kawasan frekuensi diperoleh informasi tentang frekuensi sumber dan lebar pita frekuensi yang akan diloloskan. Hasil analisis mendapatkan frekuensi sumber 6 Hz dan lebar pita frekuensi 0,1 Hz. Hasil pengeplotan dengan HIPO9, episenter gempa volkanik cenderung mengumpul di sekitar puncak gunung merapi, dengan hiposenter gempa volkanik terdistribusi pada kedalaman 1200 m sampai 1300 m. Kata kunci : hiposenter; episenter; gunung Merapi; HIPO9; gempa volkanik.                                ABSTRACTVolcanic earthquakes of mount Merapi have been investigated. The aim of the investigation to determine the hypocenter and epicenter of the volcanic earthquake of mount Merapi by HIPO9. The analysis was carried out in two domains, the time domain and the frequency domain. The analysis in the time domain was conducted by the arrival time of volcanic earthquake. The analysis in the frequency domain was done by observing spectrum to get information on frequency of source and frequency band width passed from polarization. The analysis lead to frequency of source 6 Hz and band width of 0,1 Hz. The results of plotting with HIPO9, the epicenter of volcanic earthquakes tend to gather around the top of Mount Merapi, with the hypocenter of the volcanic earthquake distributed at a depth of 1200 m to 1300 m. Keywords: hypocenter; epicenter; mount Merapi; HIPO9; volcanic earthquake.

scholarly journals Archimedean Spiral Antenna Calibration Procedures to Increase the Downrange Resolution of a SFCW Radar

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Ioan Nicolaescu ◽  
Piet van Genderen
Keyword(s):  
Time Domain ◽  
Continuous Wave ◽  
Phase Variation ◽  
Antenna System ◽  
Spiral Antenna ◽  
Multiple Reflections ◽  
Archimedean Spiral ◽  
Wave Radar ◽  
Time Domain Response ◽  
The Time Domain

This paper deals with the calibration procedures of an Archimedean spiral antenna used for a stepped frequency continuous wave radar (SFCW), which works from 400 MHz to 4845 MHz. Two procedures are investigated, one based on an error-term flow graph for the frequency signal and the second based on a reference metallic plate located at a certain distance from the ground in order to identify the phase dispersion given by the antenna. In the second case, the received signal is passed in time domain by applying an ifft, the multiple reflections are removed and the phase variation due to the time propagation is subtracted. After phase correction, the time domain response as well as the side lobes level is decreased. The antenna system made up of two Archimedean spirals is employed by SFCW radar that operates with a frequency step of 35 MHz.

scholarly journals The normal distribution fitting method for frequency distribution characteristics of peak arrival time of earthquake

2020 ◽  
Vol 29 ◽  
pp. 2633366X2092141
Author(s):  
Xu Han ◽  
Yunan Liu ◽  
Lihua Wang
Keyword(s):  
Energy Distribution ◽  
Time Domain ◽  
Seismic Waves ◽  
Arrival Time ◽  
Time History ◽  
Distribution Characteristics ◽  
Acceleration Time ◽  
Acceleration Time History ◽  
Fitting Method ◽  
The Time Domain

The physical meaning of phase difference controls the occurrence time of peak values of triangular series, which can be abbreviated as peak arrival time. This article describes a method for deducing the correspondence between the energy distribution characteristics in the time domain and the peak arrival time. The variation laws of acceleration time–history curve of natural seismic wave can be transformed into its energy distribution characteristics in time domain. Based on the needs of seismic engineering, this article proposes a conversion formula to describe the relationship between the peak arrival time and the energy distribution characteristics in the time domain. To ensure that the variation laws of acceleration time–history curve of artificial seismic waves are more consistent with those of natural seismic waves, a normal-fitting annealing algorithm is proposed based on the normal-fitting method. The proposed method not only considers the frequency distribution characteristics of the peak arrival time comprehensively but also optimizes the fitting parameters according to the actual situation. The results of all the experimental cases verify the rationality and reliability of the proposed method.

scholarly journals Implementation of the Marchenko Multiple Elimination algorithm

Geophysics ◽  
2020 ◽  
pp. 1-54
Author(s):  
Jan Thorbecke ◽  
Lele Zhang ◽  
Kees Wapenaar ◽  
Evert Slob
Keyword(s):  
Time Domain ◽  
Neumann Series ◽  
Transmission Losses ◽  
Multiple Reflections ◽  
Elimination Algorithm ◽  
Domain Truncation ◽  
Internal Multiples ◽  
The Time Domain ◽  
Multiple Elimination ◽  
Elimination Scheme

The Marchenko multiple elimination and transmission compensation schemes retrieve primary reflections in the two-way traveltime domain without model information or using adaptive subtraction. Both schemes are derived from projected Marchenko equations and similar to each other, but use different time-domain truncation operators. The Marchenko multiple elimination scheme retrieves a new dataset without internal multiple reflections. The transmission compensated Marchenko multiple elimination scheme does the same and additionally compensates for transmission losses in the primary reflections. Both schemes can be solved with an iterative algorithm based on a Neumann series. At each iteration, a convolution or correlation between the projected focusing function and the measured reflection response are performed and after each convolution or correlation, a truncation in the time domain is applied. After convergence, the resulting projected focusing function is used for retrieving the transmission compensated primary reflections and the projected Green’s function is used for the physical primary reflections. We demonstrate that internal multiples are removed by using time-windowed input data that only contain primary reflections. We evaluate both schemes in detail and develop an iterative implementation that reproduces the presented numerical examples. The software is part of our open-source suite of programs and fits into the Seismic Unix software suite of the Colorado School of Mines.

Inapplicability of pulse train time‐domain measurements to spectral induced polarization

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 826-827 ◽  
Author(s):  
Heikki Soininen
Keyword(s):  
Time Domain ◽  
Pulse Train ◽  
Apparent Resistivity ◽  
Single Pulse ◽  
Induced Polarization ◽  
Spectral Measurements ◽  
Frequency Spectra ◽  
Voltage Transient ◽  
The Fourier Transform ◽  
The Time Domain

The method of induced polarization (IP) is based on the frequency dependence of resistivity of rocks. In spectral IP the apparent resistivity is measured at a wide‐frequency band (e.g., 1/1024…4096 Hz). The apparent resistivity depends upon the distribution of the resistivity of the earth according to the laws of electromagnetism. On the basis of their spectral measurements Pelton et al. (1978) proposed that variations in mineral texture give rise to variations in the frequency spectra of resistivity. It should thus be feasible to use these spectra to discriminate between, say, graphite and sulfides. The frequency domain and the time domain are equivalent in a linear and causal system, the domains being interrelated through the Fourier transform. The time domain is attractive in that the whole transient can be recorded in a single measurement. Hence, there are devices in commercial use that record spectra in the time domain by measuring the voltage transient at a number of instances after the current pulse has been switched off. The primary current signal in these devices is generally a pulse train composed of pulses of finite duration. The pulse train has advantages over the single pulse because it permits the measurements to be repeated and thus improves the signal‐to‐noise (S/N) ratio of the measurements.

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