A KALMAN FILTER APPROACH TO THE DECONVOLUTION OF SEISMIC SIGNALS

Geophysics ◽  
1974 ◽  
Vol 39 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Norman D. Crump
Keyword(s):  
Kalman Filter ◽  
Wiener Filter ◽  
Seismic Signal ◽  
Seismic Signals ◽  
Discrete State ◽  
Seismic Wavelet ◽  
State Variable ◽  
Deconvolution Technique ◽  
Reflectivity Function ◽  
Filter Approach

It is common practice to model a reflection seismogram as a convolution of the reflectivity function of the earth and an energy waveform referred to as the seismic wavelet. The objective of the deconvolution technique described here is to extract the reflectivity function from the reflection seismogram. The most common approach to deconvolution has been the design of inverse filters based on Wiener filter theory. Some of the disadvantages of the inverse filter approach may be overcome by using a state variable representation of the earth’s reflectivity function and the seismic signal generating process. The problem is formulated in discrete state variable form to facilitate digital computer processing of digitized seismic signals. The discrete form of the Kalman filter is then used to generate an estimate of the reflectivity function. The principal advantages of this technique are its capability for handling continually time‐varying models, its adaptability to a large class of models, its suitability for either single or multi‐channel processing, and its potentially high‐resolution capabilities. Examples based on both synthetic and field seismic data illustrate the feasibility of the method.

Seismic data deconvolution using Kalman filter based on a new system model

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. V31-V42
Author(s):  
Xiaoying Deng ◽  
Zhengjun Zhang ◽  
Dinghui Yang
Keyword(s):  
Kalman Filter ◽  
Wiener Filter ◽  
System Model ◽  
Filter Model ◽  
New Model ◽  
Nonstationary Signals ◽  
Seismic Wavelet ◽  
Seismic Resolution ◽  
Resolution Improvement ◽  
Reflectivity Function

Seismic resolution plays an important role in geologic interpretation and reservoir prediction. To improve the vertical resolution of a seismic image, we have developed a new Kalman filter system model for seismic deconvolution. Similar to the conventional Kalman filter model for seismic deconvolution, our new Kalman model is also based on the common viewpoint that a reflected seismic record can be regarded as a convolution of a seismic wavelet with a reflection coefficient series. The new model uses a reversed seismic wavelet to slide across a reflectivity function to achieve the convolution result, instead of using a reversed reflectivity function to slide across a seismic wavelet in the conventional Kalman filter model. A simpler state equation for the new model is achieved, and the number of parameters to select is fewer than the conventional. Furthermore, the number of parameters can be reduced to only one by a theoretical demonstration for stationary noisy signals, which decreases the requirement for multiple parameters selection in the conventional model. The practical selection for this parameter should be a compromise between resolution improvement and noise amplification. Experimental results in the time and frequency domains on synthetic and field seismic records revealed that the Kalman filter based on the new model has the advantages of a higher resolution and peak signal-to-noise ratio (PS/N) than the conventional Kalman filter for stationary and nonstationary signals, and it works similarly to the Wiener filter for stationary signals, and it is superior to the Wiener filter in resolution and PS/N for nonstationary signals. The Kalman filter based on the new model can be applied to seismic resolution improvement.

scholarly journals On prediction and filtering problem of long-run stationary time series

2016 ◽  
Vol 8 (3) ◽  
pp. 8-18
Author(s):  
Phan Dang Cau
Keyword(s):  
Time Series ◽  
Wiener Filter ◽  
Seismic Signal ◽  
Stationary Time Series ◽  
Usual Sense ◽  
Seismic Signals ◽  
Stationary Time ◽  
The Earth ◽  
Long Run ◽  
Filtering Problem

Suppose by the  irregularity of the reflectivity of the earth a seismic signal is not always stationary in usual sense, but only long-run stationary (see [6,7]). Then  there arises a question: ‘why is wiener filter, which is  as well known is used in prediction and filtering of ergodic stationary time series, also applicable in processing seismic signals? In this paper we try to give answer to this question.

Spatial prediction filtering in the t-x and f-x domains

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 2019-2026 ◽  
Author(s):  
Scott Hornbostel
Keyword(s):  
Adaptive Filtering ◽  
Wiener Filter ◽  
Spatial Prediction ◽  
Seismic Signals ◽  
Coherent Noise ◽  
New Approach ◽  
Noise Characteristics ◽  
Signal Changes ◽  
Filter Approach ◽  
Data Signal

The predictability of seismic signals from nearby traces can be a powerful tool for reducing random or locally coherent noise. The choice of algorithm to reduce noise for a given application is a function of the data signal and noise characteristics. When the signal and noise are relatively consistent over a given design window, an f-x domain Wiener‐filter approach can be used. For cases in which the data are time‐ or space‐varying, a new approach using 2-D adaptive filtering in the t-x domain can be very effective. In either of these approaches, a prediction trace‐gap can often be successfully used to remove locally coherent noise when lateral signal changes are not too rapid.

NOISE AND TARGET SIGNALS SIMULATION IN PASSIVE SEISMIC LOCATION SYSTEMS

2018 ◽  
pp. 73-78
Author(s):  
Yu. V. Morozov ◽  
M. A. Rajfeld ◽  
A. A. Spektor
Keyword(s):  
Pulse Sequence ◽  
Signal To Noise Ratio ◽  
Seismic Signal ◽  
Seismic Signals ◽  
Simulation Procedure ◽  
Proposed Model ◽  
Seismic Location ◽  
Passive Seismic ◽  
System Characteristics ◽  
Primary Pulse

The paper proposes the model of a person seismic signal with noise for the investigation of passive seismic location system characteristics. The known models based on Gabor and Berlage pulses have been analyzed. These models are not able wholly to consider statistical properties of seismic signals. The proposed model is based on almost cyclic character of seismic signals, Gauss character of fluctuations inside a pulse, random amplitude change from pulse to pulse and relatively small fluctuation of separate pulses positions. The simulation procedure consists of passing the white noise through a linear generating filter with characteristics formed by real steps of a person, and the primary pulse sequence modulation by Gauss functions. The model permits to control the signal-to-noise ratio after its reduction to unity and to vary pulse shifts with respect to person steps irregularity. It has been shown that the model of a person seismic signal with noise agrees with experimental data.

Local seismic attributes

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. A29-A33 ◽  
Author(s):  
Sergey Fomel
Keyword(s):  
Image Registration ◽  
Seismic Signal ◽  
Seismic Attributes ◽  
Data Sets ◽  
Local Similarity ◽  
Seismic Signals ◽  
Practical Applications ◽  
Regularized Inversion ◽  
Signal Characteristics ◽  
Land Survey

Local seismic attributes measure seismic signal characteristics not instantaneously, at each signal point, and not globally, across a data window, but locally in the neighborhood of each point. I define local attributes with the help of regularized inversion and demonstrate their usefulness for measuring local frequencies of seismic signals and local similarity between different data sets. I use shaping regularization for controlling the locality and smoothness of local attributes. A multicomponent-image-registration example from a nine-component land survey illustrates practical applications of local attributes for measuring differences between registered images.

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