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A Laplace transform system comprising a processor, a measured time domain wavefield, a velocity model, and Laplace damping constants, wherein the processor is programmed to calculate a substantially about zero frequency component of a Fourier transform of a time domain damped wavefield, wherein the

A Laplace transform system comprising a processor, a measured time domain wavefield, a velocity model, and Laplace damping constants, wherein the processor is programmed to calculate a substantially about zero frequency component of a Fourier transform of a time domain damped wavefield, wherein the time domain damped wavefield is damped by the Laplace damping constants to obtain long wavelength velocity information for deeper subsurface regions.

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What is claimed is: 1. A processor configured to execute a Laplace transform system comprising: a measured time domain wavefield; a velocity model; and Laplace damping constants, wherein the processor is programmed to calculate a substantially about zero frequency component of a Fourier transform o

What is claimed is: 1. A processor configured to execute a Laplace transform system comprising: a measured time domain wavefield; a velocity model; and Laplace damping constants, wherein the processor is programmed to calculate a substantially about zero frequency component of a Fourier transform of a time domain damped wavefield, wherein the time domain damped wavefield is damped by the Laplace damping constants to obtain long wavelength velocity information for deeper subsurface regions. 2. The processor of claim 1 wherein a Laplace transform of the measured time domain wavefield is equivalent to a Poisson's equation when the Laplace damping constant is equal to zero. 3. The processor of claim 1 wherein the measured time domain wavefield is measured using seismic sources and receivers on a surface of a geological site of interest. 4. The processor of claim 1 wherein the measured time domain wavefield is prestack reflection data from subsurface structure. 5. The processor of claim 1 wherein a Laplace transform of the measured time domain wavefield is numerically calculated by integrating the damped time domain wavefield in a limit of a maximum recording time. 6. The processor of claim 1 wherein optimum values from 0 to 100 are chosen for the Laplace damping constant of the measured time domain wavefield to minimize integration error. 7. The processor of claim 1 wherein a small Laplace damping constant is used in a Laplace transform of the measured time domain wavefield to obtain information of deep parts of the waveform velocity model. 8. The processor of claim 1 wherein a large Laplace damping constant is used in a Laplace transform of the measured time domain wavefield to resolve information of shallow parts of the waveform velocity model. 9. A processor configured to execute a Laplace domain inversion system comprising: a damped recorded wavefield in a Laplace domain; a wave equation; an objective function; and a velocity model, wherein the processor is programmed to solve the wave equation in the Laplace domain, minimize the objective function, and calculate the velocity model that corresponds to the damped recorded wavefield to analyze subsurface regions. 10. The processor of claim 9 further comprising a source wavelet, wherein the processor is programmed to calculate the source wavelet and the velocity model. 11. The processor of claim 9 wherein the objective function is one of a logarithmic, an integral, and a power function. 12. The processor of claim 9 wherein the damped recorded wavefield in a Laplace domain is converted from data in a time domain. 13. The processor of claim 9 wherein the wave equation in a time domain comprises a wavefield component, a second-order time derivative of the wavefield component, a mass matrix component, and a stiffness matrix component. 14. The processor of claim 9 wherein the wave equation with proper boundary conditions, and using one of a real Laplace damping constant, and a complex Laplace damping constant, is solved in the Laplace domain by a factorization of some components of the wave equation and using forward or backward mathematical substitutions to obtain a damped calculated wavefield. 15. The processor of claim 9 wherein the objective function is equal to a summed squares of all differences between one of logarithmic, integral or power values of the damped recorded wavefield and a calculated damped wavefield. 16. The processor of claim 9 wherein the objective function is smooth and comprises no local minima or a small number of local minima. 17. The processor of claim 9 wherein one of a steepest-descent method, and a Gauss-Newton method is used to minimize the objective function by solving for a velocity model value that reduces a derivative value of the logarithmic objective to zero. 18. The processor of claim 9 wherein the processor is programmed to iterate starting with an initially calculated damped wavefield. 19. The processor of claim 9 wherein the processor is programmed to converge to the velocity model that corresponds to the damped recorded wavefield even if a different damped wavefield is initially calculated. 20. A method, implemented by one or more processors, for analyzing subsurface regions, comprising: receiving, at the one or more processors, collected prestack reflection data in a time domain; transforming, by the one or more processors, the time domain prestack reflection data to Laplace domain reflection data; initializing, by the one or more processors, a preliminary velocity model that represents a subsurface structure; calculating, by the one or more processors, one of a logarithmic, an integral, and a power objective function; verifying, by the one or more processors, whether the objective function satisfies a convergence criterion; updating, by the one or more processors, the velocity model if the convergence criterion is not met; and generating, by the one or more processors, a subsurface image from the velocity model if the convergence criterion is met to analyze subsurface regions. 21. The method of claim 20 further comprising: using, by the one or more processors, both the transformed prestack reflection data in the Laplace domain and the updated velocity model to minimize one of the logarithmic, the integral, and the power objective function in an iterative manner until the convergence criterion is met. 22. The method of claim 21 further comprising: initializing, by the one or more processors, a preliminary source wavelet; and updating, by the one or more processors, the source wavelet. 23. The method of claim 20 further comprising: confirming, by the one or more processors, that the convergence criterion is met when the value of one of the logarithmic, the integral, and the power objective function at a final iteration is found below a certain minimum and with a negligible difference from the values of the preceding iterations. 24. The method of claim 20 further comprising: generating, by the one or more processors, a subsurface image from the final updated velocity model using prestack depth migration models.