What are wavelets used for?
A wavelet is a mathematical function used to divide a given function or continuous-time signal into different scale components. Usually one can assign a frequency range to each scale component. Each scale component can then be studied with a resolution that matches its scale.
What is a zero phase wavelet?
A zero phase wavelet is symmetrical with a maximum at time zero. Zero phase wavelets have energy before time zero, which makes them noncausal, and therefore they are not physically realizable.
What is a minimum phase wavelet?
The minimum phase wavelet has a short time duration and a concentration of energy at the start of the wavelet. It is zero before time zero (causal). An ideal seismic source would be a spike (maximum amplitude at every frequency), but the best practical one would be minimum phase.
How do wavelets work?
In principle the continuous wavelet transform works by using directly the definition of the wavelet transform, i.e. we are computing a convolution of the signal with the scaled wavelet. For each scale we obtain by this way an array of the same length N as the signal has.
How many types of wavelets are there?
There are two types of wavelet transforms: the continuous wavelet transform (CWT) and the discrete wavelet transform (DWT). Specifically, the DWT provides an efficient tool for signal coding.
What is a seismic wavelet?
The seismic wavelet is the link between seismic data (traces), interpretations and the geology (reflection coefficients). It must be accurately known (estimated or measured) and quantified in all stages of the seismic cycle (from modelling, acquisition, processing, interpretation, inversion and reservoir work).
What is wavelet length?
To examine the effect of wavelet length, we vary the length of the filter from a minimum of 2 to a maximum of 24. Note that the Daubechies Least Asymmetric family is only defined for lengths greater than or equal to 8, and the Coiflet family is only defined for lengths that are multiples of 6.
What is the special about minimum phase filter?
In control theory and signal processing, a linear, time-invariant system is said to be minimum-phase if the system and its inverse are causal and stable. The most general causal LTI transfer function can be uniquely factored into a series of an all-pass and a minimum phase system.
What is the difference between Wavefront and wavelet?
A wavefront is the locus of all the particles which are in phase. All the points on the circular ring are in phase, such a ring is called a wavefront. A wavelet is an oscillation that starts from zero, then the amplitude increases and later decreases to zero.
What is the best wavelet?
An orthogonal wavelet, such as a Symlet or Daubechies wavelet, is a good choice for denoising signals. A biorthogonal wavelet can also be good for image processing. Biorthogonal wavelet filters have linear phase which is very critical for image processing.
How do you calculate the Ricker wavelet frequency?
THE RICKER WAVELET AND THE FREQUENCY BAND. R(ω)=2ω2√πω3pexp(−ω2ω2p). This frequency spectrum is real and non-negative in value, |R(ω)| = R(ω). Thus, it is just the module of the Fourier transform of the even Ricker wavelet.
Why is the Ricker wavelet called the Marr wavelet?
The Ricker wavelet is frequently employed to model seismic data, and as a broad spectrum source term in computational electrodynamics. It is usually only referred to as the Mexican hat wavelet in the Americas, due to taking the shape of a sombrero when used as a 2D image processing kernel. It is also known as the Marr wavelet for David Marr.
How is the Ricker wavelet related to Stokes differential equation?
The Ricker wavelet is theoretically a solution of the Stokes differential equation, which takes into account the effect of Newtonian viscosity, and is applicable to seismic waves propagated through viscoelastic homogeneous media.
Which is a special case of the Hermitian wavelet transform?
It is a special case of the family of continuous wavelets ( wavelets used in a continuous wavelet transform) known as Hermitian wavelets. The Ricker wavelet is frequently employed to model seismic data, and as a broad spectrum source term in computational electrodynamics.
Which is a special case of the Mexican hat wavelet?
Mexican hat wavelet. In mathematics and numerical analysis, the Ricker wavelet is the negative normalized second derivative of a Gaussian function, i.e., up to scale and normalization, the second Hermite function. It is a special case of the family of continuous wavelets ( wavelets used in a continuous wavelet transform)…