• full-waveform inversion
• genetic algorithms
• multi-grid
• stochastic methods

During my Ph.D. program, I have investigated two different topics. The first topic (major topic) addresses the issue of determining a suitable starting model for Full-Waveform Inversion (FWI); this topic has occupied the majority of my Ph.D. work. The second topic concerns determining a method to remove peg-legs from marine data sets acquired with a towed dual-sensor streamer. I worked on this subject during the first year of my Ph.D. In the following paragraphs, I outline my work on both of these subjects.

Estimating velocity macro-models using stochastic full-waveform inversion

I have developed a procedure that estimates an acoustic 2D macro-model of the subsurface using a genetic algorithm and that uses the information of the entire seismic wavefield in the objective function. The aim of this work is to demonstrate that such an estimated 2D macro-model is well-suited to act as the starting model for high-resolution gradient-based full-waveform inversion.

High-resolution gradient-based full-waveform inversion (which is usually referred to simply as full-waveform inversion (FWI)) is an iterative local optimization method that exploits all information from the seismogram to produce a high-resolution image of the subsurface. In the last twenty years, FWI has received increasing interest from both the oil and gas exploration industry and academia. In spite of being a very promising method, FWI is limited by its local nature, i.e., it terminates in the nearest local minimum. For this reason, starting the inversion from a good first-guess model is a crucial factor. To the best of our knowledge, an efficient method to determine a reliable starting model for FWI has not yet been found. Industry and academia have developed a number of procedures that might provide an adequate starting model, but they are usually very time-consuming. Furthermore, the majority of these procedures requires the picking for the arrival time of a number of seismic events and, generally, picking is a time-consuming task, which is tedious, subject to interpretation, and prone to errors.

The approach that I propose does not require a tedious picking procedure, and, at the same time, it is resistant to falling into local minima. It is well-known that a starting model for FWI is a model that lies in the valley of the global minimum of a certain misfit surface. Consequently, the basic idea behind our approach is to attack the local nature of FWI by developing a global optimization method. A global method is able to escape from a local minimum because it is not driven by local derivatives of a misfit functional. A strong limitation of stochastic methods in geophysical inversion problems, and especially in FWI, is the so-called curse of dimensionality. To mitigate this issue, I have developed a simple strategy to reduce the number of unknowns of the model space in the synthetic inversions: each model of such a model space contains only the low wave-numbers and, hence, can be referred to as a macro-model. Another issue faced in this work is the high computational-cost of the stochastic full-waveform inversion. To reduce the overall computational-cost, I limited the seismic propagation from 3D to 2D and I performed several tests on an area of the subsurface smaller in size than those typically used in FWI tests. The time-step and space-step may be changed to further reduce the computational cost of each single forward-modeling.

The most popular stochastic methods in Exploration Geophysics are genetic algorithms (GAs) and the simulated annealing (SA) method. Another popular method that originated in global seismology, is the neighborhood algorithm (NA). In this work, I compared a specific implementation of GAs, the Adaptive Simulated Annealing, and NA using two analytic objective functions and using a 1D elastic FWI problem. GA resulted the best performing method among the three for high-dimensional model spaces (>40). Consequently, I selected the GA, and I employed this method for the 2D acoustic full-waveform inversions on synthetic seismic data.

The synthetic tests have been performed on both a portion and the entire Marmousi model. The Marmousi model is a synthetic model characterized by an intense layering, several faults, folds, and velocity inversions. Because of its complexity, it has been used widely as benchmark to test FWI algorithms. The outcomes of the synthetic tests have been employed as starting models for local FWI. I proved the validity of my methodology by comparing the final outcome after local FWI, with a reference workflow started from a smoothed version of the Marmousi model.

A two-step depeg-leg method for marine acquisitions with towed dual-sensor streamers

I present a two-step method that predicts (prediction step) and attenuates (subtraction step) peg-leg reflections in pre-stack seismic data acquired with towed dual-sensor streamers. The towed dual-sensor streamer permits to separate the wavefield in the down-going and up-going components. The advantage of having both the up-going and down-going wavefields separately available is exploited in the method.

In this method, a key role is played by the shaping deconvolution in local windows of the data, which is applied to the predicted peg-leg wavefield prior to the subtraction step. I show that for windows in which no peg-leg signal is present, the shaping deconvolution may alter the primary reflections and it must not by applied. Hence, I added an automatic control to the local shaping deconvolution that preserves the primary signals during the peg-leg removal.

Such a procedure has been applied to a synthetic data set generated by the reflectivity method. Using this data set, I verified the validity of the method and that the control added to the procedure dramatically improves the final result.