面波频散曲线反演速度模型 遗传算法C++算法

面波频散曲线反演速度模型可以使用遗传算法进行优化。遗传算法是一种模拟自然进化的优化算法，通过模拟生物进化的过程，逐步优化目标函数。下面是一个使用遗传算法进行面波频散曲线反演速度模型的C++算法实现：

#include <iostream>
#include <vector>
#include <cmath>
#include <random>

// 计算模型预测的频散曲线
std::vector<double> computeModelDispersionCurve(std::vector<double>& velocityModel, double frequency) {
    std::vector<double> dispersionCurve;

    // 计算频散曲线
    for (double velocity : velocityModel) {
        double wavenumber = 2 * M_PI * frequency / velocity;
        dispersionCurve.push_back(wavenumber);
    }

    return dispersionCurve;
}

// 计算观测的频散曲线
std::vector<double> computeObservedDispersionCurve() {
    std::vector<double> dispersionCurve = {0.1, 0.2, 0.3, 0.4, 0.5};
    return dispersionCurve;
}

// 计算适应度函数（最小二乘误差）
double fitnessFunction(std::vector<double>& observedDispersionCurve, std::vector<double>& modelDispersionCurve) {
    if (observedDispersionCurve.size() != modelDispersionCurve.size()) {
        std::cerr << "频散曲线长度不一致" << std::endl;
        return std::numeric_limits<double>::infinity();
    }

    double error = 0.0;
    for (int i = 0; i < observedDispersionCurve.size(); i++) {
        error += std::pow(observedDispersionCurve[i] - modelDispersionCurve[i], 2);
    }

    return error;
}

// 遗传算法进行频散曲线反演
std::vector<double> inversion(std::vector<double>& observedDispersionCurve, double frequency, int populationSize, int maxGenerations) {
    // 初始化种群
    std::random_device rd;
    std::mt19937 gen(rd());
    std::uniform_real_distribution<double> dist(1.0, 5.0);

    std::vector<std::vector<double>> population(populationSize);
    for (int i = 0; i < populationSize; i++) {
        for (int j = 0; j < observedDispersionCurve.size(); j++) {
            population[i].push_back(dist(gen));
        }
    }

    // 进化过程
    for (int generation = 0; generation < maxGenerations; generation++) {
        // 计算适应度
        std::vector<double> fitnessValues(populationSize);
        for (int i = 0; i < populationSize; i++) {
            std::vector<double> modelDispersionCurve = computeModelDispersionCurve(population[i], frequency);
            fitnessValues[i] = fitnessFunction(observedDispersionCurve, modelDispersionCurve);
        }

        // 选择操作
        std::vector<std::vector<double>> newPopulation(populationSize);
        for (int i = 0; i < populationSize; i++) {
            int parent1 = std::min_element(fitnessValues.begin(), fitnessValues.end()) - fitnessValues.begin();
            int parent2 = parent1;
            while (parent2 == parent1) {
                parent2 = std::min_element(fitnessValues.begin(), fitnessValues.end()) - fitnessValues.begin();
            }

            // 交叉操作
            std::uniform_int_distribution<int> crossoverPoint(1, observedDispersionCurve.size() - 1);
            int crossover = crossoverPoint(gen);
            for (int j = 0; j < crossover; j++) {
                newPopulation[i].push_back(population[parent1][j]);
            }
            for (int j = crossover; j < observedDispersionCurve.size(); j++) {
                newPopulation[i].push_back(population[parent2][j]);
            }

            // 变异操作
            std::uniform_real_distribution<double> mutationValue(0.9, 1.1);
            std::uniform_int_distribution<int> mutationPosition(0, observedDispersionCurve.size() - 1);
            for (int j = 0; j < observedDispersionCurve.size(); j++) {
                if (mutationValue(gen) < 0.1) {
                    newPopulation[i][mutationPosition(gen)] = dist(gen);
                }
            }
        }

        // 更新种群
        population = newPopulation;
    }

    // 选择最佳个体
    double bestFitness = std::numeric_limits<double>::infinity();
    int bestIndividual = -1;
    for (int i = 0; i < populationSize; i++) {
        std::vector<double> modelDispersionCurve = computeModelDispersionCurve(population[i], frequency);
        double fitness = fitnessFunction(observedDispersionCurve, modelDispersionCurve);
        if (fitness < bestFitness) {
            bestFitness = fitness;
            bestIndividual = i;
        }
    }

    return population[bestIndividual];
}

int main() {
    // 计算观测的频散曲线
    std::vector<double> observedDispersionCurve = computeObservedDispersionCurve();

    // 进行频散曲线反演
    double frequency = 10.0;
    int populationSize = 100;
    int maxGenerations = 100;
    std::vector<double> velocityModel = inversion(observedDispersionCurve, frequency, populationSize, maxGenerations);

    // 输出速度模型
    std::cout << "速度模型: ";
    for (double velocity : velocityModel) {
        std::cout << velocity << " ";
    }
    std::cout << std::endl;

    return 0;
}

在这个示例代码中，我们首先定义了计算模型预测的频散曲线的函数 `computeModelDispersionCurve` 和计算观测的频散曲线的函数 `computeObservedDispersionCurve`，以及计算适应度函数（最小二乘误差）的函数 `fitnessFunction`。然后，在 `inversion` 函数中，我们使用遗传算法进行频散曲线反演。在遗传算法的进化过程中，我们进行选择操作、交叉操作和变异操作，并更新种群。最后，选择最佳个体作为最终的速度模型。

在 `main` 函数中，我们调用 `computeObservedDispersionCurve` 函数计算观测的频散曲线。然后，调用 `inversion` 函数进行频散曲线反演，并输出速度模型。

请注意，这只是一个基本的示例代码，实际的面波频散曲线反演可能涉及到更复杂的算法和参数设置。你可以根据你的具体需求，对这个算法进行适当的修改和扩展。