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## Scientific Bulletin. Physical and Mathematical Research

#### Abstract

This article is devoted to the construction of spline models for signals measured at unequal intervals. Cubic spline models built at unequal intervals have a high accuracy of signal interpolation, which allows professionals to make informed decisions as a result of digital signal processing. As an example, a cubic spline interpolation model was constructed for digital processing of geophysical signals measured at unequal intervals. Geophysical signals are very important to us, because the ever-growing demand for natural resources around the world requires ever-increasing oil and gas production. This, in its turn, requires a more consistent and extensive exploration of oil and gas fields. Many scientific works in the field of geophysics are aimed at identifying reserves of underground resources or “informants” of seismic hazards. Sudden changes in a particular geophysical or seismic signal and observed abnormal changes are called “transmitters”, and with their help, scientists make predictions. The prediction result will allow you to predict in advance the location of the amount of underground wealth, as well as to predict the location, time and strength of future seismic events. This is one of the most widely used methods for studying magnetic fields and gravimetric studies in detecting smugglers. In scientific research, these methods are mainly used in aviation. In this case, with the help of airplanes and helicopters equipped with special measuring instruments, the Earth's magnetic field (magnetic field) or gravitational field is measured. The measurement results are recorded in memory as a flash. If the measured land is uneven, then the measurements will be uneven.

The use of splines gives good results when restoring function values at unequal intervals. Because splines require less computation than classical polynomials, and there are efficient algorithms for determining spline parameters.

Thus, cubic spline models built at unequal intervals can be widely used in solving digital signal processing and recovery problems because of their efficiency, accuracy, and requiring less action to determine spline parameters. In this paper, a geophysical signal (the Earth's magnetic field) measured from an uneven surface of the earth using magnetic intelligence was taken as the first experimental data, and an interpolation cubic spline model at unequal intervals was constructed based on this data. An algorithm for solving a linear system of linear equations for constructing an interpolation cubic spline is presented. The article also presents the results of comparing the sweep and Gauss methods by a number of necessary actions.

#### First Page

86

#### Last Page

94

#### References

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#### Recommended Citation

Azimov, Rahimjon K.; Mahkamov, Madaminjon K.; and Azimov, Bunyod R.
(2020)
"METHOD OF LOCAL SPLINS OF MODELING SIGNALS MEASURED AT UNEQUAL INTERVALS,"
*Scientific Bulletin. Physical and Mathematical Research*: Vol. 2
:
Iss.
1
, Article 11.

Available at:
https://uzjournals.edu.uz/adu/vol2/iss1/11