Different seismic data compression algorithms have been developed in order to make the storage more efficient, and to reduce both the transmission time and cost. In general, those algorithms have three stages: transformation, quantization and coding. The Wavelet transform is highly used to compress seismic data, due to the capabilities of the Wavelets on representing geophysical events in seismic data. We selected the lifting scheme to implement the Wavelet transform because it reduces both computational and storage resources. This work aims to determine how the transformation and the coding stages affect the data compression ratio. Several 2D lifting-based algorithms were implemented to compress three different seismic data sets. Experimental results obtained for different filter type, filter length, number of decomposition levels and coding scheme, are presented in this work. 221|Seismic Data Compression using 2D Lifting-Wavelet Algorithms Compresión de datos sísmicos usando algoritmos lifting-wavelet 2DResumen Diferentes algoritmos para compresión de datos sísmicos han sido desarrollados con el objetivo de hacer más eficiente el uso de capacidad de almacenamiento, y para reducir los tiempos y costos de la transmisión de datos. En general, estos algoritmos tienen tres etapas: transformación, cuantización y codificación. La transformada Wavelet ha sido ampliamente usada para comprimir datos sísmicos debido a la capacidad de las ondículas para representar eventos geofísicos presentes en los datos sísmicos. En este trabajo se usa el esquema Lifting para la implementación de la transformada Wavelet, debido a que este método reduce los recursos computacionales y de almacenamiento necesarios. Este trabajo estudia la influencia de las etapas de transformación y codificación en la relación de compresión de los datos. Además se muestran los resultados de la implementación de diferentes esquemas lifting 2D para la compresión de tres diferentes conjuntos de datos sísmicos. Los resultados obtenidos para diferentes tipos de filtros, longitud de filtros, número de niveles de descomposición y esquemas de compresión son presentados en este trabajo.

The second order scattering information provided by the Hessian matrix and its inverse plays an important role in both, parametric inversion and uncertainty quantification. On the one hand, for parameter inversion, the Hessian guides the descent direction such that the cost function minimum is reached with less iterations. On the other hand, it provides a posteriori information of the probability distribution of the parameters obtained after full waveform inversion, as a function of the a priori probability distribution information. Nevertheless, the computational cost of the Hessian matrix represents the main obstacle in the state-of-the-art for practical use of this matrix from synthetic or real data. The second order adjoint state theory provides a strategy to compute the exact Hessian matrix, reducing its computational cost, because every column of the matrix can be obtained by performing two forward and two backward propagations. In this paper, we first describe an approach to compute the exact Hessian matrix for the acoustic wave equation with constant density. We then provide an analysis of the use of the Hessian matrix for uncertainty quantification of the full waveform inversion of the velocity model for a synthetic example, using the 2D acoustic and isotropic wave equation operator in time.

No abstract