Synthetic Seismogram Generation Using Convolution

Synthetic seismogram generation using convolution is a fundamental method in seismology primarily employed to simulate seismic wave propagation through subsurface media. The core algorithm involves convolving a seismic wavelet (such as a Ricker wavelet) with a reflection coefficient series representing subsurface interfaces. This computational process effectively models how seismic energy interacts with geological boundaries and returns to the surface.

The Ricker wavelet serves as a standard seismic pulse with defined waveform characteristics, commonly used to represent actual seismic signal properties. Its mathematical formulation features distinct peak amplitude and exponential decay properties, making it ideal for simulating wave propagation through stratified media. In code implementation, the Ricker wavelet can be generated using mathematical functions defining its central frequency and time decay parameters.

The reflection coefficient series quantitatively describes impedance contrasts at subsurface interfaces, where acoustic impedance differences between geological layers determine reflection strength values. This series is typically derived from well log data or geological models. Programming implementations often represent this as arrays or matrices where each element corresponds to reflection magnitude at specific depth intervals.

The synthetic seismogram generation workflow consists of three key computational steps: First, parameterize the Ricker wavelet by defining its dominant frequency and attenuation characteristics through mathematical functions. Second, calculate the reflection coefficient series based on subsurface geological structure using impedance data. Finally, perform convolution between the wavelet and reflection series using digital signal processing techniques. The convolution operation essentially applies time-shifted and amplitude-scaled versions of the wavelet according to reflection coefficient positions, simulating seismic wave propagation and reflection phenomena.

This methodology finds extensive applications in seismic exploration and geological modeling, enabling researchers to interpret subsurface structures, analyze seismic data characteristics, and provide theoretical foundations for subsequent inversion and interpretation processes. Code implementations typically utilize signal processing libraries for efficient convolution operations and visualization tools for result analysis.