We consider numerical solution methods for seismic impedance inversion problems in this paper. The inversion process is ill-posed. To tackle the ill-posedness of the problem and take the sparsity of the reflectivity function into consideration, an l1 norm regularization model is established. In computation, a nonmonotone gradient descent method based on Rayleigh quotient for solving the minimiz...

The aim of seismic inversion is mapping all of the subsurface structures from seismic data. Due to the band-limited nature of the seismic data, it is difficult to find a unique solution for seismic inversion. Deterministic methods of seismic inversion are based on try and error techniques and provide a smooth map of elastic properties, while stochastic methods produce high-resolution maps of el...

Utility functions of several variables are ubiquitous in economics. Their maximization requires inversion of the gradient map. Using convex analysis tools, we provide a representation of an extension of this inverse that accounts for possible constraints. To solve economic equilibrium problems, the utility functions of the agents are frequently aggregated into a representative (agent’s) utility...

One important parameter for an ultrasonic transducer is the echo it yields from a pointlike reflector. It can be measured directly but there are however certain problems connected with this. We propose an alternative method to calculate the echo from a pointlike reflector by measuring the echoes from sliding halfplanes. Using a tomographic way of reasoning, we can calculate the point echoes fro...

an experimental study of the phase inversion behavior of liquid-liquid dispersion has been conducted in a spray extraction column for systems of toluene / water, n-hexane/water, ccl4/water, toluene /water + glycerol (25 % wt), toluene + ccl4 (25 % wt) / water and toluene / acetic acid (5 % wt)/water. the effects of physical properties, mass transfer and column geometry on phase inversion have b...

Inversion algorithms employ numerical evaluation of the mismatch between model and data to guide the search for minima in parameter spaces. In an alternative approach, the numerical evaluation of data misfit can be replaced by subjective judgement of the solution quality. This widens the class of problems that can be treated within the framework of formal inverse theory, in particular including...

Linear inverse scattering problems can be solved by regularized inversion of a matrix, whose calculation and inversion may require significant computing resources, in particular, a significant amount of RAM memory. This effort is dependent on the extent of the investigation domain, which drives a large amount of data to be gathered and a large number of unknowns to be looked for, when this doma...

Acoustic impedance (AI) inversion is widely used in geophysics and reservoir prediction. But the traditional method cannot fully exploit sparse characteristics of geological attributes. There are problems with multiplicity low resolution. To solve this problem, a data-driven acoustic reweighted L1 norm constraints (DRL1) proposed. In process, local cross-correlation analysis introduced to above...

In this paper a variant of partially mapped crossover (VPMX) is designed using cut point positions and is tested for its performance with the existing partially mapped crossover (PMX).In order to test the performance ,two mutation operators are used. These mutation operators are inverted displacement and inversion mutations. Partially mapped crossover (PMX) with inversion and with inverted disp...