Reply by the authors to E. Szaraniec

Geophysics ◽  
1983 ◽  
Vol 48 (3) ◽  
pp. 401-401
Author(s):  
Peter Hubral ◽  
Sven Treitel ◽  
Paul R. Gutowski
Keyword(s):  
Continued Fractions ◽  
Normal Incidence ◽  
Synthetic Seismogram ◽  
Tel Aviv ◽  
Layered Model ◽  
The Way

We thank Dr. Szaraniec for his interesting comments, which shed new light on the properties of the normal incidence synthetic seismogram. By the way, his equations (D‐4.1) and (D‐4.2) were also given by Nestler and Rösler [1977, equation (4)], although with an error; they write [Formula: see text] rather than [Formula: see text]. We are reminded of a saying by our colleague Prof. Dan Loewenthal of Tel Aviv University: the normal incidence discretely layered model is a rich lode from which a seemingly endless series of interesting formulas can be mined. Dr. Szaraniec has unearthed more nuggets, and we hope that his success will inspire others to continue searching. The relation between our results and the theory of continued fractions should, as Dr. Szaraniec points out, provide further insights.

scholarly journals The Last Mosque in Tel Aviv, and Other Stories of Disjuncture

Arts ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 63
Author(s):  
Ilana Webster-Kogen
Keyword(s):  
Visual Language ◽  
Tel Aviv ◽  
Displaced People ◽  
Urban Sites ◽  
The Way ◽  
Urban Border

Ruins serve as a poignant reminder of loss and destruction. Yet, ruins are not always physical, and they are not always best understood through visual language—the sense memory of loss extends for displaced people far beyond crumbling monuments. Exploring the sonic element of loss and displacement is key to understanding the way people relate to the spaces they have to leave. This article explores the particular disjuncture of staging and commemorating Arabness in Tel Aviv, the “Hebrew City.” The disjuncture of being Arab in Tel Aviv is apparent to any visitor who walks down the beach promenade, and this article examines the main sites of Arab contestation on the border with Jaffa. Most apparent to a visitor is the Hassan Bek Mosque, the most visible Islamic symbol in Tel Aviv; I describe the process of gaining admission as a non-Muslim, and of discussing the painful and indelible memory of 1948 with worshipers. Delving deeper into the affective staging of ruin, I trace Umm Kulthum’s famous concert in Jaffa (officially Palestine at the time), and examine the way her imprint has moved across the troubled urban border of Tel Aviv-Jaffa. A ruins-based analysis of the urban sites of disjuncture in Tel Aviv, therefore, offers a glimpse into underground sonic subcultures that hide in plain sight.

Maximum entropy spectral decomposition of a seismogram into its minimum entropy component plus noise

Geophysics ◽  
1981 ◽  
Vol 46 (8) ◽  
pp. 1108-1115 ◽  
Author(s):  
Sven Treitel ◽  
Enders A. Robinson
Keyword(s):  
Power Spectrum ◽  
White Noise ◽  
Maximum Entropy ◽  
Spectral Decomposition ◽  
Normal Incidence ◽  
Synthetic Seismogram ◽  
Minimum Entropy ◽  
Entropy Spectrum ◽  
Maximum Entropy Spectrum ◽  
Remote Past

We consider an N‐layered elastic medium which is perfectly insulated from its embedding space. Each layer has unit two‐way vertical traveltime, and a coincident source‐receiver pair is located just below the top interface. If the insulated medium is excited in the remote past, the power spectrum of the resulting impulsive normal‐incidence synthetic seismogram is a pure line spectrum; because no random elements exist in the system at the time of measurement, this spectrum is a minimum entropy spectrum. If we add white noise to the seismogram, the power spectrum becomes a maximum entropy spectrum. The maximum entropy spectrum can thus be decomposed into the sum of a minimum entropy spectrum plus white noise; this spectral decomposition is due to Pisarenko (1973). If the insulated medium is excited at time t = 0, the resulting synthetic seismogram differs rather remarkably from the seismogram obtained for excitation in the remote past.

The generalized one‐dimensional synthetic seismogram

Geophysics ◽  
1987 ◽  
Vol 52 (5) ◽  
pp. 589-605 ◽  
Author(s):  
P. R. Gutowski ◽  
S. Treitel
Keyword(s):  
Moving Average ◽  
Normal Incidence ◽  
Synthetic Seismogram ◽  
Stratified Medium ◽  
Autoregressive Moving Average ◽  
Reflection Coefficients ◽  
Source Surface ◽  
Theoretical Treatment ◽  
Surface Source ◽  
Ar Representations

The normal‐incidence synthetic seismogram for an elastic and horizontally stratified medium has been thoroughly studied for a relatively restricted number of source and receiver locations. Most existing treatments are concerned with the special case in which the source as well as the receiver are situated at the surface; few attempts have dealt with completely arbitrary source and receiver geometries. Here we examine arbitrary geometries with the aid of the layer matrix approach, in which upgoing and downgoing wave motion at each interface is expressed in terms of z-transform polynomials. Such an approach brings to light a number of physically important relations that the model satisfies. For example, the synthetic seismograms generally have the familiar autoregressive‐moving average (ARMA) structure for the surface‐source, surface‐receiver case. For particular combinations of reflection coefficients, however, the seismograms reduce to purely autoregressive (AR) representations. In all cases, we work out the delay properties that the respective autoregressive and moving average components must obey. The present solutions are easily reduced to a useful form for practical computation. One application of particular current interest is the simulation of vertical seismic profiling (VSP) surveys, where we have extended the theoretical treatment to include expressions for the derivatives of the seismograms with respect to the reflection coefficients. The resulting time series, which we call Jacobograms, are indicative of the sensitivity of the seismogram to the various reflection coefficients and are thus diagnostic of the model’s behavior.

On Differentiation with respect to a Function

1925 ◽  
Vol 22 (6) ◽  
pp. 924-934 ◽  
Author(s):  
E. C. Francis
Keyword(s):  
Detailed Analysis ◽  
Continued Fractions ◽  
American Mathematical Society ◽  
Mathematical Society ◽  
Stieltjes Integral ◽  
Base Function ◽  
General Base ◽  
The Future ◽  
Definition Of ◽  
The Way

Thirty years ago, in a paper on continued fractions, Stieltjes published a definition of the integral which bears his name. His replacement of the variable of integration x by a more general “base function” φ(x)—a change which throws so much light upon other theories of integration—received at first little attention, but has later sprung into greater prominence; so much so that Professor Hildebrandt, in summarizing these various theories in a paper to the American Mathematical Society, makes the statement that “it [the Stieltjes Integral] seems destined to play the central rôle in the integrational and summational processes of the future.” Yet even now the integral and the allied theory of differentiation with respect to a function have been subjected to little detailed analysis, and the possibilities of extension have been only touched upon. It is the object of this present paper to establish certain results which are of some value in themselves and which prepare the way for an attack upon the integral.

Normal moveout coefficients for horizontally layered triclinic media

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. WA119-WA145 ◽  
Author(s):  
Zvi Koren ◽  
Igor Ravve
Keyword(s):  
Elastic Properties ◽  
Error Term ◽  
Single Layer ◽  
Normal Incidence ◽  
Effective Model ◽  
Pure Mode ◽  
Effective Parameters ◽  
Reflected Waves ◽  
Layered Model ◽  
The Individual

Sedimentary layers affected by vertical compaction and strong lateral tectonic stresses are often characterized by low anisotropic symmetry (e.g., tilted orthorhombic [TOR]/monoclinic or even triclinic). Considering all types of pure-mode and converted waves, we derive the normal moveout (NMO) series coefficients of near normal-incidence reflected waves in arbitrarily anisotropic horizontally layered media, for a leading error term of order six. The NMO series can be either a function of the invariant horizontal slowness (slowness domain) or the surface offset (offset domain). The NMO series coefficients, referred to also as effective parameters, are associated with the corresponding azimuthally varying NMO velocity functions. We distinguish between local (single-layer) and global (overburden multilayer) effective parameters, which are related by forward and inverse Dix-type transforms. We derive the local effective parameters for an arbitrary anisotropic (triclinic) layer, which is the main contribution of this paper. With some additional geologic constraints, the local effective parameters can then be converted into the interval elastic properties. To demonstrate the applicability of our method, we consider a synthetic layered model in which each layer is characterized with TOR symmetry. The corresponding global effective model loses the symmetries of the individual layers and is characterized by triclinic symmetry.

A case study showing the value of multioffset synthetic seismograms in seismic data interpretation

2016 ◽  
Vol 4 (4) ◽  
pp. T455-T459 ◽  
Author(s):  
J. Helen Isaac ◽  
Don C. Lawton
Keyword(s):  
Seismic Data ◽  
Upper Cretaceous ◽  
Normal Incidence ◽  
High Amplitude ◽  
Synthetic Seismogram ◽  
Synthetic Seismograms ◽  
Seismic Survey ◽  
Research Station ◽  
S Wave ◽  
Low Amplitude

A baseline 3D3C seismic survey was acquired in May 2014 at a Field Research Station in Southern Alberta, Canada, which is the site of experimental [Formula: see text] injection into an Upper Cretaceous sandstone at approximately 300 m depth. We have created synthetic seismograms from sonic and density logs to identify reflectors seen on the processed seismic data. The high-amplitude positive response (peak) at the top of the Upper Cretaceous Milk River Formation sandstone on the normal incidence PP synthetic seismogram does not match the response seen on the migrated PP seismic data, which is a very low amplitude peak. For such a high impedance, low Poisson’s ratio sandstone, the Zoeppritz equations predict a high-amplitude reflection coefficient at zero offset, then a decrease in amplitude, and even a change in polarity with increasing source-receiver offset. To match the stacked seismic data better, we have created offset synthetic seismograms using P- and S-wave sonic logs and density logs. The character of the top Milk River reflection on the seismic data stacked using all offset traces resembles that observed on the stacked offset synthetic seismogram, which is a similar low-amplitude peak. The character of the top Milk River reflection on the seismic data stacked using only near-offset traces to 250 m looks like that seen on the normal incidence synthetic seismogram.

Self-sacrifice for in-group's history: A diachronic perspective

2018 ◽  
Vol 41 ◽  
Author(s):  
Maria Babińska ◽  
Michal Bilewicz
Keyword(s):  
Clinical Psychology ◽  
Historical Events ◽  
Emotional Events ◽  
Reciprocal Process ◽  
The Way

AbstractThe problem of extended fusion and identification can be approached from a diachronic perspective. Based on our own research, as well as findings from the fields of social, political, and clinical psychology, we argue that the way contemporary emotional events shape local fusion is similar to the way in which historical experiences shape extended fusion. We propose a reciprocal process in which historical events shape contemporary identities, whereas contemporary identities shape interpretations of past traumas.

What is the purpose of cognition?

2020 ◽  
Vol 43 ◽  
Author(s):  
Aba Szollosi ◽  
Ben R. Newell
Keyword(s):  
Infinite Number ◽  
Human Cognition ◽  
The Way

Abstract The purpose of human cognition depends on the problem people try to solve. Defining the purpose is difficult, because people seem capable of representing problems in an infinite number of ways. The way in which the function of cognition develops needs to be central to our theories.

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