# Early-arrival waveform inversion for near-surface velocity estimation. SEP-156 (2014)

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**Table of contents**

- Chapter 1: Introduction
- Chapter 2: Building initial models by WTI
- Chapter 3: Kinematic-based inversion objective function
- Chapter 4: Random boundary condition for efficient gradient computation
- Chapter 5: 3D data examples

**Abstract**

Early-arrival Waveform Inversion is a powerful tool for high-resolution near-surface velocity estimation. By matching observed diving waves and refractions with forward modeled diving waves and refractions, high-resolution near-surface models can be obtained. However, conventional waveform inversion requires accurate starting models and exact matching of data amplitude. Both of these requirements are difficult to meet in field data, especially land data applications. In addition, current industry implementations of waveform inversion encounter serious I/O bottlenecks in large 3D applications.This dissertation addresses these three problems associated with practical applications of waveform inversion.

The constraint of accurate starting models is relaxed by applying wave-equation traveltime inversion before applying the waveform inversion. Accurate starting models for waveform inversion means accurate long wavelength components of the velocity model, since waveform inversion can not correct long wavelength model errors in practical applications where data does not contain enough low frequencies. However in such cases, wave-equation traveltime inversion is able to correct the long wavelength errors in the initial models. As a result, waveform inversion using the wave-equation traveltime inversion result has a much better chance of converging to the right model.

The requirement of exact data amplitude matching is relaxed by applying a new objective function that relies heavily on phase and waveform matching, while ignoring absolute amplitude. Real data amplitude is determined by factors such as source signal strength, earth velocity, earth density, earth attenuation, source/receiver coupling, preprocessing. Most of those factors can not be modeled with the acoustic wave equation used in the inversion. In the new objective function, matching absolute amplitude is de-emphasized by proper scaling of the observed data traces and modeled data traces.

The I/O bottleneck associated with the current industry implementations is eliminated by using a low-frequency random boundary scheme. Waveform inversion gradient calculation requires the correlation of source wavefield and data residual wavefield. The two wavefields propagate in different time directions. Hence to perform the correlation, at least one of the wavefields has to be saved beforehand. These wavefields are large four dimensional cubes for 3D data, and storing is only possible on disk. As a result, correlation involves a lot of I/O cost associated with writing wavefield to disk and read it in. I eliminate this I/O cost by modifying the gradient calculation process, with a modified version of the original random boundary to accommodate the low-frequency wave propagation in waveform inversion.

I demonstrate the effectiveness of the methodologies using synthetic and field data examples.