transfer.ts

/*
 * Philip Crotwell
 * University of South Carolina, 2019
 * http://www.seis.sc.edu
 */
import {calcDFT, inverseDFT, FFTResult} from "./fft";
import {SeismogramSegment} from "./seismogramsegment";
import {Seismogram} from "./seismogram";
import {SacPoleZero} from "./sacpolezero";
import {Response, PolesZeros} from "./stationxml";
import {Complex} from "./oregondsputil";
// `allMeasures` includes all the measures packaged with this library
import configureMeasurements, { allMeasures,  AllMeasuresUnits } from 'convert-units';
const convert = configureMeasurements(allMeasures);


/**
 * Applies response, poles and zeros along with overall gain to the seismogram.
 * Should produce results similar to the sac command:
 * transfer from polezero to none
 *
 * @param   seis     seismogram to instrument correct
 * @param   response response to apply
 * @param   lowCut   low cut
 * @param   lowPass  low pass
 * @param   highPass high pass
 * @param   highCut  high cut
 * @returns           instrument corrected seismogram
 */
export function transfer(
  seis: Seismogram,
  response: Response,
  lowCut: number,
  lowPass: number,
  highPass: number,
  highCut: number,
): Seismogram {
  if (!response) {
    throw new Error("Response not exist???");
  }

  const sacPoleZero = convertToSacPoleZero(response);
  return transferSacPZ(seis, sacPoleZero, lowCut, lowPass, highPass, highCut);
}
export function transferSacPZ(
  seis: Seismogram,
  sacPoleZero: SacPoleZero,
  lowCut: number,
  lowPass: number,
  highPass: number,
  highCut: number,
): Seismogram {
  const outSeis = [];

  for (let i = 0; i < seis.segments.length; i++) {
    const result = transferSacPZSegment(
      seis.segments[i],
      sacPoleZero,
      lowCut,
      lowPass,
      highPass,
      highCut,
    );
    outSeis.push(result);
  }

  return new Seismogram(outSeis);
}
export function transferSacPZSegment(
  seis: SeismogramSegment,
  sacPoleZero: SacPoleZero,
  lowCut: number,
  lowPass: number,
  highPass: number,
  highCut: number,
): SeismogramSegment {
  const sampFreq = seis.sampleRate;
  const values = seis.y;
  let outData = Float32Array.from(values);

  /* sac premultiplies the data by the sample period before doing the fft. Later it
   * seems to be cancled out by premultiplying the pole zeros by a similar factor.
   * I don't understand why they do this, but am reproducing it in order to be
   * compatible.
   */
  outData.forEach((d, i) => (outData[i] = d / sampFreq));
  let freqValues = calcDFT(outData);
  freqValues = combine(
    freqValues,
    sampFreq,
    sacPoleZero,
    lowCut,
    lowPass,
    highPass,
    highCut,
  );
  outData = inverseDFT(freqValues, values.length);
  // a extra factor of nfft gets in somehow???
  outData.forEach((d, i) => (outData[i] = d * freqValues.length));
  const out = seis.cloneWithNewData(outData);
  out.yUnit = "m";
  return out;
}
export function calcResponse(
  response: Response,
  numPoints: number,
  sampleRate: number,
  unit: string,
): FFTResult {
  const sacPoleZero = convertToSacPoleZero(response);
  const unitQty = convert(1).getUnit(unit as AllMeasuresUnits);
  let gamma = 0;

  if (unitQty === null) {
    throw new Error("unknown response unit: " + unit);
  } else if (unitQty.measure == 'length') {
    gamma = 0;
  } else if (unitQty.measure == 'speed') {
    gamma = 1;
  } else if (unitQty.measure == 'acceleration') {
    gamma = 2;
  } else {
    throw new Error(
      "response unit is not displacement (m), velocity (m/s) or acceleration (m/s^2): " +
        unit,
    );
  }

  sacPoleZero.trimZeros(gamma);
  const out = calcResponseFromSacPoleZero(sacPoleZero, numPoints, sampleRate);
  return out;
}

/**
 * Caclulates the frequency response from the given poles and zeros.
 *
 * @param   sacPoleZero poles and zeros
 * @param   numPoints   number of points in the output fft
 * @param   sampleRate  sample rate to compute at
 * @returns             frequency response
 */
export function calcResponseFromSacPoleZero(
  sacPoleZero: SacPoleZero,
  numPoints: number,
  sampleRate: number,
): FFTResult {
  const deltaF = sampleRate / numPoints;
  // inst response as packed frequency array
  const freqValues = new Float32Array(numPoints);
  let respAtS;
  // zero freq
  respAtS = evalPoleZeroInverse(sacPoleZero, 0);
  respAtS = new Complex(1, 0).overComplex(respAtS);
  freqValues[0] = respAtS.real();
  // nyquist
  let freq = sampleRate / 2;
  respAtS = evalPoleZeroInverse(sacPoleZero, freq);
  respAtS = new Complex(1, 0).overComplex(respAtS);
  freqValues[freqValues.length / 2] = respAtS.real();

  for (let i = 1; i < freqValues.length / 2; i++) {
    freq = i * deltaF;
    respAtS = evalPoleZeroInverse(sacPoleZero, freq);
    //respAtS = respAtS.timesReal(deltaF*i);
    respAtS = new Complex(1, 0).overComplex(respAtS);

    if (respAtS.real() !== 0 || respAtS.imag() !== 0) {
      freqValues[i] = respAtS.real();
      freqValues[freqValues.length - i] = respAtS.imag();
    } else {
      freqValues[i] = 1e-10;
      freqValues[freqValues.length - i] = 0;
    }
  }

  const out = FFTResult.createFromPackedFreq(freqValues, numPoints, sampleRate);
  return out;
}

/**
 * Applies poles and zeros to the fft of a time series. Modifies the freqValues
 * in place.
 *
 * @param   freqValues  fft of a timeseries
 * @param   sampFreq    sampling frequency
 * @param   sacPoleZero poles and zeros
 * @param   lowCut      low cut
 * @param   lowPass     low pass
 * @param   highPass    high pass
 * @param   highCut     high cut
 * @returns             input freq values, with poles and zeros applied
 */
export function combine(
  freqValues: Float32Array,
  sampFreq: number,
  sacPoleZero: SacPoleZero,
  lowCut: number,
  lowPass: number,
  highPass: number,
  highCut: number,
): Float32Array {
  const deltaF = sampFreq / freqValues.length;
  // handle zero freq, no imag, set real to 0
  freqValues[0] = 0;
  // handle nyquist
  let freq = sampFreq / 2;
  let respAtS = evalPoleZeroInverse(sacPoleZero, freq);
  respAtS = respAtS.timesReal(
    deltaF * calcFreqTaper(freq, lowCut, lowPass, highPass, highCut),
  );
  freqValues[freqValues.length / 2] = respAtS
    .timesReal(freqValues[freqValues.length / 2])
    .real();

  for (let i = 1; i < freqValues.length / 2; i++) {
    freq = i * deltaF;
    respAtS = evalPoleZeroInverse(sacPoleZero, freq);
    respAtS = respAtS.timesReal(
      deltaF * calcFreqTaper(freq, lowCut, lowPass, highPass, highCut),
    );
    const freqComplex = new Complex(
      freqValues[i],
      freqValues[freqValues.length - i],
    ).timesComplex(respAtS);
    freqValues[i] = freqComplex.real();
    freqValues[freqValues.length - i] = freqComplex.imag();
  }

  return freqValues;
}

/**
 * Evaluates the poles and zeros at the given value. The return value is
 * 1/(pz(s) to avoid divide by zero issues. If there is a divide by zero
 * situation, then the response is set to be 0+0i.
 *
 * @param sacPoleZero SAC PoleZero response
 * @param freq frequency to evaluate
 * @returns complex frequency domain value for this frequency
 */
export function evalPoleZeroInverse(
  sacPoleZero: SacPoleZero,
  freq: number,
): InstanceType<typeof Complex> {
  return sacPoleZero.evalPoleZeroInverse(freq);
}

/**
 * Calculates the frequency taper for the given parameters.
 *
 * @param   freq     frequency
 * @param   lowCut   low cut
 * @param   lowPass  low pass
 * @param   highPass high pass
 * @param   highCut  high cut
 * @returns           taper value at the frequency
 */
export function calcFreqTaper(
  freq: number,
  lowCut: number,
  lowPass: number,
  highPass: number,
  highCut: number,
): number {
  if (lowCut > lowPass || lowPass > highPass || highPass > highCut) {
    throw new Error(
      "must be lowCut > lowPass > highPass > highCut: " +
        lowCut +
        " " +
        lowPass +
        " " +
        highPass +
        " " +
        highCut,
    );
  }

  if (freq <= lowCut || freq >= highCut) {
    return 0;
  }

  if (freq >= lowPass && freq <= highPass) {
    return 1;
  }

  if (freq > lowCut && freq < lowPass) {
    return (
      0.5 * (1.0 + Math.cos((Math.PI * (freq - lowPass)) / (lowCut - lowPass)))
    );
  }

  // freq > highPass && freq < highCut
  return (
    0.5 * (1.0 - Math.cos((Math.PI * (freq - highCut)) / (highPass - highCut)))
  );
}

/**
 * Applies the frequency taper to the fft of the time series.
 *
 * @param   fftResult  fft of time series
 * @param   sampleRate sample rate
 * @param   lowCut     low cut
 * @param   lowPass    low pass
 * @param   highPass   high pass
 * @param   highCut    high cut
 * @returns            fft with taper applied
 */
export function applyFreqTaper(
  fftResult: FFTResult,
  sampleRate: number,
  lowCut: number,
  lowPass: number,
  highPass: number,
  highCut: number,
): FFTResult {
  const deltaF = fftResult.fundamentalFrequency;
  return FFTResult.createFromAmpPhase(
    fftResult.amplitudes().map((v, i) =>
      i === 0
        ? 0
        : v * calcFreqTaper(i * deltaF, lowCut, lowPass, highPass, highCut),
    ),
    fftResult.phases(),
    fftResult.origLength,
    fftResult.sampleRate,
  );
}

/**
 * commonly used units
 */

export const METER = convert().getUnit("m");
export const METER_PER_SECOND = convert().getUnit("m/s");
export const METER_PER_SECOND_PER_SECOND = convert().getUnit("m/s2");

export function calcGamma(unit: string): number {
  let gamma;
  const unitQty = convert(1).getUnit(unit as AllMeasuresUnits);
  if (unitQty === null) {
    throw new Error("unknown response unit: " + unit);
  } else if (unitQty.measure == 'length') {
    gamma = 0;
  } else if (unitQty.measure == 'speed') {
    gamma = 1;
  } else if (unitQty.measure == 'acceleration') {
    gamma = 2;
  } else {
    throw new Error(
      "response unit is not displacement (m), velocity (m/s) or acceleration (m/s^2): " +
        unit,
    );
  }
  return gamma;
}
export function calcScaleUnit(unit: string): number {
  let scale;
  const unitQty = convert(1).getUnit(unit as AllMeasuresUnits);
  if (unitQty === null) {
    throw new Error("unknown response unit: " + unit);
  } else if (unitQty.measure == 'length') {
    scale = convert(1).from(unit as AllMeasuresUnits).to('m');
  } else if (unitQty.measure == 'speed') {
    scale = convert(1).from(unit as AllMeasuresUnits).to('m/s');
  } else if (unitQty.measure == 'acceleration') {
    scale = convert(1).from(unit as AllMeasuresUnits).to('m/s2');
  } else {
    throw new Error(
      "response unit is not displacement (m), velocity (m/s) or acceleration (m/s^2): " +
        unit,
    );
  }
  return scale;
}
/**
 * Converts a StationXML response to SAC PoleZero style. This
 * converts the analog to digital stage (usually 0) along
 * with the overall gain, but does not include later FIR stages.
 * To maintain compatibility with SAC, this includes extra zeros
 * if needed to convert to displacement. The number of extra zeros
 * added is kept as gamma in the result.
 *
 * @param response stationxml Response to convert
 * @returns SAC PoleZero style version of the response
 */
export function convertToSacPoleZero(response: Response): SacPoleZero {
  let polesZeros: PolesZeros;

  if (response.stages[0].filter instanceof PolesZeros) {
    polesZeros = response.stages[0].filter;
  } else {
    throw new Error("can't find PolesZeros");
  }
  if (response.instrumentSensitivity === null) {
    throw new Error("response.instrumentSensitivity missing");
  }

  let unit = response.instrumentSensitivity.inputUnits;

  if (unit === "M/S" || unit === "M/SEC") {
    unit = "m/s";
  }

  let gamma = calcGamma(unit);
  let scaleUnit = calcScaleUnit(unit);

  const scale_sensitivity =
    scaleUnit * response.instrumentSensitivity.sensitivity;
  return convertPoleZeroToSacStyle(
    polesZeros,
    scale_sensitivity,
    response.instrumentSensitivity.frequency,
    gamma,
  );
}
export function convertPoleZeroToSacStyle(
  polesZeros: PolesZeros,
  sensitivity: number,
  sensitivity_freq: number,
  gamma: number,
): SacPoleZero {
  let mulFactor = 1;

  if (polesZeros.pzTransferFunctionType === "LAPLACE (HERTZ)") {
    mulFactor = 2 * Math.PI;
  }

  const zeros = [];

  // extra gamma zeros are (0,0)
  for (let i = 0; i < polesZeros.zeros.length; i++) {
    zeros[i] = new Complex(
      polesZeros.zeros[i].real() * mulFactor,
      polesZeros.zeros[i].imag() * mulFactor,
    );
  }

  for (let i = 0; i < gamma; i++) {
    zeros.push(new Complex(0, 0));
  }

  const poles = [];

  for (let i = 0; i < polesZeros.poles.length; i++) {
    poles[i] = new Complex(
      polesZeros.poles[i].real() * mulFactor,
      polesZeros.poles[i].imag() * mulFactor,
    );
  }

  let constant = polesZeros.normalizationFactor;
  let sd = sensitivity;
  const fs = sensitivity_freq;
  sd *= Math.pow(2 * Math.PI * fs, gamma);
  let A0 = polesZeros.normalizationFactor;
  const fn = polesZeros.normalizationFrequency;
  A0 = A0 / Math.pow(2 * Math.PI * fn, gamma);

  if (polesZeros.pzTransferFunctionType === "LAPLACE (HERTZ)") {
    A0 *= Math.pow(
      2 * Math.PI,
      polesZeros.poles.length - polesZeros.zeros.length,
    );
  }

  if (poles.length === 0 && zeros.length === 0) {
    constant = sd * A0;
  } else {
    constant = sd * calc_A0(poles, zeros, fs);
  }

  const sacPZ = new SacPoleZero(poles, zeros, constant);
  sacPZ.gamma = gamma;
  sacPZ.mulFactor = mulFactor;
  sacPZ.sd = sd;
  sacPZ.A0 = A0;
  return sacPZ;
}
export function calc_A0(
  poles: Array<InstanceType<typeof Complex>>,
  zeros: Array<InstanceType<typeof Complex>>,
  ref_freq: number,
): number {
  let numer = new Complex(1, 0);
  let denom = new Complex(1, 0);
  let f0;
  let a0;
  f0 = new Complex(0, 2 * Math.PI * ref_freq);

  for (let i = 0; i < zeros.length; i++) {
    denom = denom.timesComplex(f0.minusComplex(zeros[i]));
  }

  for (let i = 0; i < poles.length; i++) {
    numer = numer.timesComplex(f0.minusComplex(poles[i]));
  }

  a0 = numer.overComplex(denom).abs();
  return a0;
}