Amplitude‐ and frequency‐modulated wave motion constitute the ground‐roll noise in seismic reflection prospecting. Hence, it is possible to eliminate ground roll by applying one‐dimensional, linear frequency‐modulated matched filters. These filters effectively attenuate the ground‐roll energy without damaging the signal wavelet inside or outside the ground roll’s frequency interval. When the frequency bands of seismic reflections and ground roll overlap, the new filters eliminate the ground roll more effectively than conventional frequency and multichannel filters without affecting the vertical resolution of the seismic data.

A method of ground-roll elimination

Seismic events recorded by the individual subarrays at LASA were Fourier-analyzed. For any particular subarray the amplitude spectrum was divided by the average spectrum for all twenty-one subarrays. This process produced similar spectra for events with the same epicenter, suggesting that the average amplitude spectrum is that of a ‘primary’ signal and that each subarray has a distance and azimuth-dependent transfer function that operates on this primary signal to produce the amplitude spectrum of the subarray. The assumption is made that the phased summation of the whole array is representative of the primary signal. The time-domain transfer function associated with a subarray is then shown to consist of a series of time-delayed delta functions, each associated with an amplitude coefficient. In other words, the P-wave signal recorded at a particular subarray consists of a series of closely spaced individual arrivals. The interference of these multiple arrivals with one another causes the recorded signal variations between subarrays. It is suggested that deep crustal relief causes multipathing of a P wave incident from below.

Nature of short‐period P‐wave signal variations at LASA

This paper deals with the design of filters for processing data obtained from arrays of sensors used for signal measurements in a variety of applications. The objective of the filters is to optimally suppress undesired signals intercepting the array, while at the same time to preserve the desired signal that the array is attempting to measure. A constrained minimization problem is formulated for determining the filter's coefficients, and the computational requirements necessary for designing and applying the filters are kept to a minimum. When compared to the widely used delay-and-sum and Chebyshev methods, this technique is shown to have a superior frequency reject response which becomes more apparent if the array has a relatively small number of sensors. In order to illustrate the effectiveness of the method, two examples on applying the filters for processing synthetic and real seismic data are worked out in detail.

http://ieeexplore.ieee.org/iel6/29/26178/01164164.pdf

Optimum array filters for array data signal processing

A new nonlinear filter for wave-equation extrapolation-based multiple suppression is designed in the f-k domain. The realization of the new filter in the f-k domain is an extension of the conventional f-k dip filter. However, the new demultiple filter is superior to the conventional f-k dip filter in the sense that the multiple reject zones are determined automatically (based on the information of the input original data and the multiple model traces obtained by the waveextrapolation method) rather than by prior information on multiple moveout (dip) range. Therefore, it can easily cope with situations such as aliasing and the mixture of energy from multiples and primaries in the same quadrant. The new filter is smooth on the boundary of the reject area. Numerical examples demonstrate that the new filter is equivalent to the conventional f-k dip filter in multiple suppression for simple situations. However, when the multiples and primaries are mixed in the same quadrant and have only slight difference in dip, the new filter offers significant advantages over the conventional technique.

Wave‐equation extrapolation‐based multiple attenuation: 2-D filtering in the f-k domain

The separation of upgoing waves and downgoing waves in vertical seismic profiling is effectively accomplished in the frequency‐wavenumber (f‐k) domain using a new technique of contour‐slice filtering. The response of the filter has no straight edge or boundary and preserves the “natural state” of the spectra. The cutoff contour level can be reduced as low as desirable to remove background noise and other unwanted signals. In this sense it can also be viewed as a noise‐rejection filter. The effectiveness of the process has been clearly demonstrated through synthetic and real examples. Its success with the upgoing waves depends on the degree of coherency of events in the VSP record. To enhance the coherency and to avoid velocity aliasing, we use a novel band‐pass frequency filter which is the result of convolving a boxcar spectral window with a frequency‐shifted Gaussian function.

Separation of upgoing and downgoing waves in vertical seismic profiling by contour‐slice filtering

Optimum systems have been developed to correspond to the sub‐optimum moveout discrimination systems presented previously by several authors. The seismic data on the lth trace is assumed to be additive signal S with moveout τl, coherent noise N with moveout τ˜l, and incoherent noise Ul, expressed Il(t)=S(t-τl)+N(t-τ˜l)+Ul(t) where S, N, and Ul are independent, second order stationary random processes and τl and τ˜l are random variables with prescribed probability density functions. The signal estimate S⁁ is produced by filtering each trace with its corresponding filter Gl and summing the outputs S⁁(t)=ΣlGl(t)*Il(t). We choose the system of filters {Gl} to make the signal estimate optimum in the Wiener sense (minimum mean‐square error of the signal ensemble). For the special cases discussed, the moveouts are linear functions of the trace number l determined by the moveout/trace τ for signal and τ˜ for noise. Thus, the optimum system is determined by the probability densities of τ and τ˜ together with the no...

M. R. Foster

Papers

Optimum multichannel velocity filters