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Synthesis of a mathematical model of the transformation core for processing vibroseismic data by reverse filtering

The vibroseismic method of studying the bowels of the earth is widely used to study the structural features of the bowels. The effectiveness of the method is due to the presence of controlled sources of seismic waves. In this case, the sources of seismic waves form a seismic signal, the parameters of which are determined and set by the researcher during the planning of the experiment. Frequency-modulated seismic signals - sweep signals - have become the most popular in field seismology. A special case of these signals are monochromatic signals. During the experiment, the seismic signal generated by the source is recorded by a seismic receiver. Thus, the researcher receives the initial seismic record - a seismogram. Processing of a seismogram, as an element of vibroseismic data, assumes the presence of information about the parameters of the seismic signal of the source. Based on this signal, a conversion core is formed for processing the seismogram. As a result of the operation of convolution of the seismogram with the core of the transformation, a vibrogram is formed. If it is necessary to increase the contrast (resolution) of the vibrogram, an additional filtering function is introduced into the conversion core, which performs the reverse filtering procedure. The purpose of this study is to form a filtering function and a mathematical model of the transformation core, which allows to increase the contrast of the vibrogram. The structurality and simplicity of the analytical expressions of the filtering function and the mathematical model of the transformation kernel is achieved by representing the function and model in operator form by means of the Laplace transform. The result of the study is analytical expressions in the operator form of the filtering function and a mathematical model of the transformation core to increase the contrast of vibrograms.