Related Experiment Video
Updated: Jun 19, 2026
09:16
Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy
Published on: January 9, 2017
On the correlation of non-isotropically distributed ballistic scalar diffuse waves.
Richard Weaver1, Berenice Froment, Michel Campillo
1Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green, Urbana, Illinois 61801, USA.
The Journal of the Acoustical Society of America
|October 10, 2009
Summary
Seismic wave correlations using ambient noise work well even when waves aren't fully equipartitioned. This study quantifies and corrects for errors in apparent travel times, ensuring trustworthy seismic velocity mapping.
Area of Science:
- Seismology
- Wave propagation
- Acoustics
Background:
- Theorems suggest random wave fields correlate like Green's functions.
- Seismic noise correlations are used for travel time and velocity mapping.
- Wave fields are often not fully equipartitioned, raising trust concerns.
Purpose of the Study:
- Evaluate errors in seismic travel time due to non-isotropic wave fields.
- Assess the trustworthiness of seismic noise correlation methods.
- Develop a formula for error estimation and travel time correction.
Main Methods:
- Analysis in the limit of large receiver separation.
- Consideration of far-field noise sources.
- Derivation of an error estimation and correction formula.
Main Results:
- The error in apparent travel time is small, even with significant anisotropy.
- Errors are minimal even for station pairs separated by only a few wavelengths.
- The derived formula accurately estimates and corrects errors, validated with synthetic waveforms.
Conclusions:
- Seismic noise correlation methods are robust despite non-equipartitioned wave fields.
- The derived formula provides a reliable way to correct apparent travel times.
- This enhances the accuracy and trustworthiness of seismic imaging and velocity mapping.
Related Concept Videos
01:07Propagation of Waves
When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
01:30Plane Electromagnetic Waves I
The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...
The EM field is assumed to be a...
02:18Interference and Diffraction
Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
00:51Velocity and Acceleration of a Wave
A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which is not constant. In addition, the velocity of the medium is perpendicular to the velocity of the wave. The variable speed of the particles of the medium implies that there must be acceleration associated with it.
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time. We can...
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time. We can...
01:02Equations of Wave Motion
Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
02:32The de Broglie Wavelength
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...